ABCF->ab-angle angle

Percentage Accurate: 53.7% → 80.5%

Time: 45.3s

Alternatives: 21

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: 53.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.6 \cdot 10^{+132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(\frac{C \cdot \left(-B\right)}{A} - B\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.6e+132)
   (* 180.0 (/ (atan (/ (* -0.5 (- (/ (* C (- B)) A) B)) A)) PI))
   (/ 180.0 (/ PI (atan (/ (- (- C A) (hypot B (- A C))) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.6e+132) {
		tmp = 180.0 * (atan(((-0.5 * (((C * -B) / A) - B)) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((C - A) - hypot(B, (A - C))) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.6e+132) {
		tmp = 180.0 * (Math.atan(((-0.5 * (((C * -B) / A) - B)) / A)) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.6e+132:
		tmp = 180.0 * (math.atan(((-0.5 * (((C * -B) / A) - B)) / A)) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((((C - A) - math.hypot(B, (A - C))) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.6e+132)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-0.5 * Float64(Float64(Float64(C * Float64(-B)) / A) - B)) / A)) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.6e+132)
		tmp = 180.0 * (atan(((-0.5 * (((C * -B) / A) - B)) / A)) / pi);
	else
		tmp = 180.0 / (pi / atan((((C - A) - hypot(B, (A - C))) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.6e+132], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 * N[(N[(N[(C * (-B)), $MachinePrecision] / A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -3.60000000000000016e132

   1. Initial program 9.7%

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

   3. Taylor expanded in A around -inf 93.5%

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

      1. associate-*r/ 93.5%

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

      2. mul-1-neg 93.5%

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

      3. distribute-lft-out 93.5%

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

      4. *-commutative 93.5%

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

   5. Simplified 93.5%

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

   if -3.60000000000000016e132 < A

   1. Initial program 59.1%

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

      1. *-commutative 59.1%

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

      2. associate--l- 58.0%

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

      3. +-commutative 58.0%

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

      4. unpow2 58.0%

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

      5. unpow2 58.0%

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

      6. hypot-undefine 77.9%

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

      7. div-inv 77.9%

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

      8. clear-num 77.9%

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

      9. un-div-inv 78.0%

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

   4. Applied egg-rr 79.1%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.6 \cdot 10^{+132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(\frac{C \cdot \left(-B\right)}{A} - B\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.85 \cdot 10^{+131}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(\frac{C \cdot \left(-B\right)}{A} - B\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-162}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.85e+131)
   (* 180.0 (/ (atan (/ (* -0.5 (- (/ (* C (- B)) A) B)) A)) PI))
   (if (<= A 6.5e-162)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (* (/ 180.0 PI) (atan (/ (+ A (hypot A B)) (- B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.85e+131) {
		tmp = 180.0 * (atan(((-0.5 * (((C * -B) / A) - B)) / A)) / ((double) M_PI));
	} else if (A <= 6.5e-162) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((A + hypot(A, B)) / -B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.85e+131) {
		tmp = 180.0 * (Math.atan(((-0.5 * (((C * -B) / A) - B)) / A)) / Math.PI);
	} else if (A <= 6.5e-162) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((A + Math.hypot(A, B)) / -B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.85e+131:
		tmp = 180.0 * (math.atan(((-0.5 * (((C * -B) / A) - B)) / A)) / math.pi)
	elif A <= 6.5e-162:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((A + math.hypot(A, B)) / -B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.85e+131)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-0.5 * Float64(Float64(Float64(C * Float64(-B)) / A) - B)) / A)) / pi));
	elseif (A <= 6.5e-162)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A + hypot(A, B)) / Float64(-B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.85e+131)
		tmp = 180.0 * (atan(((-0.5 * (((C * -B) / A) - B)) / A)) / pi);
	elseif (A <= 6.5e-162)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = (180.0 / pi) * atan(((A + hypot(A, B)) / -B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.85e+131], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 * N[(N[(N[(C * (-B)), $MachinePrecision] / A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6.5e-162], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.85e131

   1. Initial program 9.7%

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

   3. Taylor expanded in A around -inf 93.5%

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

      1. associate-*r/ 93.5%

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

      2. mul-1-neg 93.5%

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

      3. distribute-lft-out 93.5%

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

      4. *-commutative 93.5%

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

   5. Simplified 93.5%

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

   if -2.85e131 < A < 6.49999999999999989e-162

   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 A around 0 47.7%

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

      1. +-commutative 47.7%

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

      2. unpow2 47.7%

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

      3. unpow2 47.7%

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

      4. hypot-define 68.6%

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

   5. Simplified 68.6%

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

   if 6.49999999999999989e-162 < A

   1. Initial program 71.5%

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

      1. *-commutative 71.5%

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

      2. associate--l- 71.5%

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

      3. +-commutative 71.5%

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

      4. unpow2 71.5%

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

      5. unpow2 71.5%

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

      6. hypot-undefine 90.2%

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

      7. div-inv 90.2%

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

      8. clear-num 90.2%

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

      9. un-div-inv 90.2%

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

   4. Applied egg-rr 90.2%

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

   5. Taylor expanded in C around 0 71.5%

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

      1. associate-*r/ 71.6%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in C around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-neg-frac2 70.7%

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

      3. unpow2 70.7%

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

      4. unpow2 70.7%

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

      5. hypot-define 88.0%

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

   10. Simplified 88.0%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.85 \cdot 10^{+131}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(\frac{C \cdot \left(-B\right)}{A} - B\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-162}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.65 \cdot 10^{+132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(\frac{C \cdot \left(-B\right)}{A} - B\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{-162}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.65e+132)
   (* 180.0 (/ (atan (/ (* -0.5 (- (/ (* C (- B)) A) B)) A)) PI))
   (if (<= A 6.8e-162)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (* 180.0 (/ (atan (/ (+ A (hypot A B)) (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.65e+132) {
		tmp = 180.0 * (atan(((-0.5 * (((C * -B) / A) - B)) / A)) / ((double) M_PI));
	} else if (A <= 6.8e-162) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A + hypot(A, B)) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.65e+132) {
		tmp = 180.0 * (Math.atan(((-0.5 * (((C * -B) / A) - B)) / A)) / Math.PI);
	} else if (A <= 6.8e-162) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(A, B)) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.65e+132:
		tmp = 180.0 * (math.atan(((-0.5 * (((C * -B) / A) - B)) / A)) / math.pi)
	elif A <= 6.8e-162:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A + math.hypot(A, B)) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.65e+132)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-0.5 * Float64(Float64(Float64(C * Float64(-B)) / A) - B)) / A)) / pi));
	elseif (A <= 6.8e-162)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(A, B)) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.65e+132)
		tmp = 180.0 * (atan(((-0.5 * (((C * -B) / A) - B)) / A)) / pi);
	elseif (A <= 6.8e-162)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((A + hypot(A, B)) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.65e+132], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 * N[(N[(N[(C * (-B)), $MachinePrecision] / A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6.8e-162], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.65000000000000015e132

   1. Initial program 9.7%

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

   3. Taylor expanded in A around -inf 93.5%

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

      1. associate-*r/ 93.5%

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

      2. mul-1-neg 93.5%

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

      3. distribute-lft-out 93.5%

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

      4. *-commutative 93.5%

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

   5. Simplified 93.5%

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

   if -1.65000000000000015e132 < A < 6.8e-162

   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 A around 0 47.7%

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

      1. +-commutative 47.7%

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

      2. unpow2 47.7%

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

      3. unpow2 47.7%

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

      4. hypot-define 68.6%

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

   5. Simplified 68.6%

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

   if 6.8e-162 < A

   1. Initial program 71.5%

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

   3. Taylor expanded in C around 0 70.7%

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

      1. associate-*r/ 70.7%

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

      2. mul-1-neg 70.7%

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

      3. unpow2 70.7%

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

      4. unpow2 70.7%

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

      5. hypot-define 87.9%

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

   5. Simplified 87.9%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.65 \cdot 10^{+132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(\frac{C \cdot \left(-B\right)}{A} - B\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{-162}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -7.5 \cdot 10^{+139}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(\frac{C \cdot \left(-B\right)}{A} - B\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{+39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -7.5e+139)
   (* 180.0 (/ (atan (/ (* -0.5 (- (/ (* C (- B)) A) B)) A)) PI))
   (if (<= A 2.8e+39)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -7.5e+139) {
		tmp = 180.0 * (atan(((-0.5 * (((C * -B) / A) - B)) / A)) / ((double) M_PI));
	} else if (A <= 2.8e+39) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -7.5e+139) {
		tmp = 180.0 * (Math.atan(((-0.5 * (((C * -B) / A) - B)) / A)) / Math.PI);
	} else if (A <= 2.8e+39) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -7.5e+139:
		tmp = 180.0 * (math.atan(((-0.5 * (((C * -B) / A) - B)) / A)) / math.pi)
	elif A <= 2.8e+39:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -7.5e+139)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-0.5 * Float64(Float64(Float64(C * Float64(-B)) / A) - B)) / A)) / pi));
	elseif (A <= 2.8e+39)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -7.5e+139)
		tmp = 180.0 * (atan(((-0.5 * (((C * -B) / A) - B)) / A)) / pi);
	elseif (A <= 2.8e+39)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -7.5e+139], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 * N[(N[(N[(C * (-B)), $MachinePrecision] / A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.8e+39], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -7.49999999999999992e139

   1. Initial program 9.7%

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

   3. Taylor expanded in A around -inf 93.5%

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

      1. associate-*r/ 93.5%

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

      2. mul-1-neg 93.5%

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

      3. distribute-lft-out 93.5%

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

      4. *-commutative 93.5%

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

   5. Simplified 93.5%

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

   if -7.49999999999999992e139 < A < 2.80000000000000001e39

   1. Initial program 50.8%

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

   3. Taylor expanded in A around 0 44.6%

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

      1. +-commutative 44.6%

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

      2. unpow2 44.6%

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

      3. unpow2 44.6%

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

      4. hypot-define 67.9%

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

   5. Simplified 67.9%

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

   if 2.80000000000000001e39 < A

   1. Initial program 86.1%

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

   3. Taylor expanded in B around -inf 88.8%

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

      1. associate--l+ 88.8%

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

      2. div-sub 90.9%

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

   5. Simplified 90.9%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7.5 \cdot 10^{+139}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(\frac{C \cdot \left(-B\right)}{A} - B\right)}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{+39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+139}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(\frac{C \cdot \left(-B\right)}{A} - B\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.5e+139)
   (* 180.0 (/ (atan (/ (* -0.5 (- (/ (* C (- B)) A) B)) A)) PI))
   (* (atan (/ (- (- C A) (hypot B (- A C))) B)) (/ 180.0 PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.5e+139) {
		tmp = 180.0 * (atan(((-0.5 * (((C * -B) / A) - B)) / A)) / ((double) M_PI));
	} else {
		tmp = atan((((C - A) - hypot(B, (A - C))) / B)) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.5e+139) {
		tmp = 180.0 * (Math.atan(((-0.5 * (((C * -B) / A) - B)) / A)) / Math.PI);
	} else {
		tmp = Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.5e+139:
		tmp = 180.0 * (math.atan(((-0.5 * (((C * -B) / A) - B)) / A)) / math.pi)
	else:
		tmp = math.atan((((C - A) - math.hypot(B, (A - C))) / B)) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.5e+139)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-0.5 * Float64(Float64(Float64(C * Float64(-B)) / A) - B)) / A)) / pi));
	else
		tmp = Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.5e+139)
		tmp = 180.0 * (atan(((-0.5 * (((C * -B) / A) - B)) / A)) / pi);
	else
		tmp = atan((((C - A) - hypot(B, (A - C))) / B)) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.5e+139], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 * N[(N[(N[(C * (-B)), $MachinePrecision] / A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.5e139

   1. Initial program 9.7%

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

   3. Taylor expanded in A around -inf 93.5%

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

      1. associate-*r/ 93.5%

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

      2. mul-1-neg 93.5%

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

      3. distribute-lft-out 93.5%

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

      4. *-commutative 93.5%

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

   5. Simplified 93.5%

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

   if -1.5e139 < A

   1. Initial program 59.1%

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

      1. *-commutative 59.1%

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

      2. associate--l- 58.0%

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

      3. +-commutative 58.0%

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

      4. unpow2 58.0%

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

      5. unpow2 58.0%

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

      6. hypot-undefine 77.9%

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

      7. div-inv 77.9%

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

      8. clear-num 77.9%

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

      9. un-div-inv 78.0%

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

   4. Applied egg-rr 79.1%

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

   5. Taylor expanded in C around 0 58.0%

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

      1. associate-*r/ 58.0%

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

   7. Simplified 79.1%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+139}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(\frac{C \cdot \left(-B\right)}{A} - B\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.95 \cdot 10^{+135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(\frac{C \cdot \left(-B\right)}{A} - B\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.95e+135)
   (* 180.0 (/ (atan (/ (* -0.5 (- (/ (* C (- B)) A) 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 <= -1.95e+135) {
		tmp = 180.0 * (atan(((-0.5 * (((C * -B) / A) - 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 <= -1.95e+135) {
		tmp = 180.0 * (Math.atan(((-0.5 * (((C * -B) / A) - 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 <= -1.95e+135:
		tmp = 180.0 * (math.atan(((-0.5 * (((C * -B) / A) - 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 <= -1.95e+135)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-0.5 * Float64(Float64(Float64(C * Float64(-B)) / A) - B)) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.95e+135)
		tmp = 180.0 * (atan(((-0.5 * (((C * -B) / A) - 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, -1.95e+135], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 * N[(N[(N[(C * (-B)), $MachinePrecision] / A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.95000000000000016e135

   1. Initial program 9.7%

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

   3. Taylor expanded in A around -inf 93.5%

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

      1. associate-*r/ 93.5%

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

      2. mul-1-neg 93.5%

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

      3. distribute-lft-out 93.5%

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

      4. *-commutative 93.5%

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

   5. Simplified 93.5%

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

   if -1.95000000000000016e135 < A

   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

      1. associate-*l/ 59.1%

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

      2. *-lft-identity 59.1%

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

      3. +-commutative 59.1%

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

      4. unpow2 59.1%

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

      5. unpow2 59.1%

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

      6. hypot-define 79.1%

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

   3. Simplified 79.1%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.95 \cdot 10^{+135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(\frac{C \cdot \left(-B\right)}{A} - B\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8 \cdot 10^{+61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8e+61)
   (* 180.0 (/ (atan (/ (* B 0.5) 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 <= -8e+61) {
		tmp = 180.0 * (atan(((B * 0.5) / 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 <= -8e+61) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / 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 <= -8e+61:
		tmp = 180.0 * (math.atan(((B * 0.5) / 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 <= -8e+61)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / 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 <= -8e+61)
		tmp = 180.0 * (atan(((B * 0.5) / 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, -8e+61], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $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 < -7.9999999999999996e61

   1. Initial program 16.6%

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

   3. Taylor expanded in A around -inf 83.7%

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

      1. associate-*r/ 83.7%

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

   5. Simplified 83.7%

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

   if -7.9999999999999996e61 < A

   1. Initial program 61.1%

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

   3. Simplified 80.1%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8 \cdot 10^{+61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -0.0062:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.56 \cdot 10^{-195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 2.75 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3 \cdot 10^{-181}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -0.0062)
   (* 180.0 (/ (atan (/ C B)) PI))
   (if (<= C -1.56e-195)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= C 2.75e-281)
       (* 180.0 (/ (atan (/ A (- B))) PI))
       (if (<= C 3e-181)
         (* 180.0 (/ (atan -1.0) PI))
         (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -0.0062) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (C <= -1.56e-195) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (C <= 2.75e-281) {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	} else if (C <= 3e-181) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -0.0062) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (C <= -1.56e-195) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (C <= 2.75e-281) {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	} else if (C <= 3e-181) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -0.0062:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif C <= -1.56e-195:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif C <= 2.75e-281:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	elif C <= 3e-181:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -0.0062)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (C <= -1.56e-195)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (C <= 2.75e-281)
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	elseif (C <= 3e-181)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -0.0062)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (C <= -1.56e-195)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (C <= 2.75e-281)
		tmp = 180.0 * (atan((A / -B)) / pi);
	elseif (C <= 3e-181)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -0.0062], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -1.56e-195], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.75e-281], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3e-181], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -0.00619999999999999978

   1. Initial program 75.4%

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

   3. Taylor expanded in B around -inf 73.7%

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

      1. associate--l+ 73.7%

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

      2. div-sub 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in C around inf 69.9%

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

   if -0.00619999999999999978 < C < -1.56000000000000006e-195

   1. Initial program 55.5%

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

   3. Taylor expanded in B around -inf 36.7%

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

   if -1.56000000000000006e-195 < C < 2.7500000000000001e-281

   1. Initial program 44.9%

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

   3. Taylor expanded in B around -inf 41.9%

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

      1. associate--l+ 41.9%

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

      2. div-sub 41.9%

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

   5. Simplified 41.9%

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

   6. Taylor expanded in A around inf 33.7%

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

      1. associate-*r/ 33.7%

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

      2. mul-1-neg 33.7%

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

   8. Simplified 33.7%

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

   if 2.7500000000000001e-281 < C < 2.99999999999999974e-181

   1. Initial program 52.4%

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

   3. Taylor expanded in B around inf 49.1%

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

   if 2.99999999999999974e-181 < C

   1. Initial program 38.0%

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

   3. Taylor expanded in C around inf 56.7%

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

   4. Taylor expanded in A around inf 56.7%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -0.0062:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.56 \cdot 10^{-195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 2.75 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3 \cdot 10^{-181}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.1% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.3 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(\frac{C \cdot \left(-B\right)}{A} - B\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(\frac{C - A}{B} + 2\right) + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.3e-78)
   (* 180.0 (/ (atan (/ (* -0.5 (- (/ (* C (- B)) A) B)) A)) PI))
   (* 180.0 (/ (atan (+ (+ (/ (- C A) B) 2.0) -1.0)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.3e-78) {
		tmp = 180.0 * (atan(((-0.5 * (((C * -B) / A) - B)) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((((C - A) / B) + 2.0) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.3e-78) {
		tmp = 180.0 * (Math.atan(((-0.5 * (((C * -B) / A) - B)) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((((C - A) / B) + 2.0) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.3e-78:
		tmp = 180.0 * (math.atan(((-0.5 * (((C * -B) / A) - B)) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((((C - A) / B) + 2.0) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.3e-78)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-0.5 * Float64(Float64(Float64(C * Float64(-B)) / A) - B)) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(Float64(C - A) / B) + 2.0) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.3e-78)
		tmp = 180.0 * (atan(((-0.5 * (((C * -B) / A) - B)) / A)) / pi);
	else
		tmp = 180.0 * (atan(((((C - A) / B) + 2.0) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.3e-78], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 * N[(N[(N[(C * (-B)), $MachinePrecision] / A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 2.0), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -2.3000000000000002e-78

   1. Initial program 27.3%

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

   3. Taylor expanded in A around -inf 69.0%

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

      1. associate-*r/ 69.0%

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

      2. mul-1-neg 69.0%

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

      3. distribute-lft-out 69.0%

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

      4. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   if -2.3000000000000002e-78 < A

   1. Initial program 64.0%

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

   3. Taylor expanded in B around -inf 61.8%

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

      1. associate--l+ 61.8%

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

      2. div-sub 62.4%

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

   5. Simplified 62.4%

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

      1. expm1-log1p-u 47.5%

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

      2. expm1-undefine 47.5%

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

   7. Applied egg-rr 47.5%

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

      1. sub-neg 47.5%

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

      2. log1p-undefine 47.5%

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

      3. rem-exp-log 62.4%

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

      4. associate-+r+ 62.4%

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

      5. metadata-eval 62.4%

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

      6. metadata-eval 62.4%

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

   9. Simplified 62.4%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.3 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \left(\frac{C \cdot \left(-B\right)}{A} - B\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(\frac{C - A}{B} + 2\right) + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -290000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -5.9 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -290000000.0)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -5.9e-269)
     (* 180.0 (/ (atan (/ A (- B))) PI))
     (if (<= B 2.9e-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 <= -290000000.0) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -5.9e-269) {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	} else if (B <= 2.9e-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 <= -290000000.0) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -5.9e-269) {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	} else if (B <= 2.9e-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 <= -290000000.0:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -5.9e-269:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	elif B <= 2.9e-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 <= -290000000.0)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -5.9e-269)
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	elseif (B <= 2.9e-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 <= -290000000.0)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -5.9e-269)
		tmp = 180.0 * (atan((A / -B)) / pi);
	elseif (B <= 2.9e-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, -290000000.0], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -5.9e-269], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.9e-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 4 regimes

2. if B < -2.9e8

   1. Initial program 51.4%

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

   3. Taylor expanded in B around -inf 60.4%

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

   if -2.9e8 < B < -5.9e-269

   1. Initial program 60.8%

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

   3. Taylor expanded in B around -inf 54.3%

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

      1. associate--l+ 54.3%

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

      2. div-sub 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in A around inf 39.1%

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

      1. associate-*r/ 39.1%

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

      2. mul-1-neg 39.1%

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

   8. Simplified 39.1%

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

   if -5.9e-269 < B < 2.89999999999999992e-89

   1. Initial program 43.8%

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

   3. Taylor expanded in C around inf 40.8%

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

   4. Taylor expanded in B around 0 47.1%

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

      1. distribute-rgt1-in 47.1%

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

      2. metadata-eval 47.1%

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

      3. mul0-lft 47.1%

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

      4. div0 47.1%

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

      5. metadata-eval 47.1%

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

   6. Simplified 47.1%

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

   if 2.89999999999999992e-89 < B

   1. Initial program 46.0%

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

   3. Taylor expanded in B around inf 50.9%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -290000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -5.9 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.75 \cdot 10^{-81}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \left(B + C \cdot \frac{B}{A}\right)}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(\frac{C - A}{B} + 2\right) + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.75e-81)
   (/ 180.0 (/ PI (atan (/ (* 0.5 (+ B (* C (/ B A)))) A))))
   (* 180.0 (/ (atan (+ (+ (/ (- C A) B) 2.0) -1.0)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.75e-81) {
		tmp = 180.0 / (((double) M_PI) / atan(((0.5 * (B + (C * (B / A)))) / A)));
	} else {
		tmp = 180.0 * (atan(((((C - A) / B) + 2.0) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.75e-81) {
		tmp = 180.0 / (Math.PI / Math.atan(((0.5 * (B + (C * (B / A)))) / A)));
	} else {
		tmp = 180.0 * (Math.atan(((((C - A) / B) + 2.0) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.75e-81:
		tmp = 180.0 / (math.pi / math.atan(((0.5 * (B + (C * (B / A)))) / A)))
	else:
		tmp = 180.0 * (math.atan(((((C - A) / B) + 2.0) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.75e-81)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(0.5 * Float64(B + Float64(C * Float64(B / A)))) / A))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(Float64(C - A) / B) + 2.0) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.75e-81)
		tmp = 180.0 / (pi / atan(((0.5 * (B + (C * (B / A)))) / A)));
	else
		tmp = 180.0 * (atan(((((C - A) / B) + 2.0) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.75e-81], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(0.5 * N[(B + N[(C * N[(B / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 2.0), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.74999999999999993e-81

   1. Initial program 27.3%

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

      1. *-commutative 27.3%

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

      2. associate--l- 23.5%

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

      3. +-commutative 23.5%

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

      4. unpow2 23.5%

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

      5. unpow2 23.5%

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

      6. hypot-undefine 35.9%

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

      7. div-inv 35.9%

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

      8. clear-num 35.9%

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

      9. un-div-inv 35.9%

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

   4. Applied egg-rr 61.6%

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

   5. Taylor expanded in A around -inf 68.5%

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

      1. associate-*r/ 68.5%

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

      2. distribute-lft-out 68.5%

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

      3. associate-*r* 68.5%

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

      4. metadata-eval 68.5%

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

      5. *-commutative 68.5%

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

      6. associate-/l* 68.9%

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

   7. Simplified 68.9%

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

   if -1.74999999999999993e-81 < A

   1. Initial program 64.0%

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

   3. Taylor expanded in B around -inf 61.8%

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

      1. associate--l+ 61.8%

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

      2. div-sub 62.4%

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

   5. Simplified 62.4%

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

      1. expm1-log1p-u 47.5%

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

      2. expm1-undefine 47.5%

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

   7. Applied egg-rr 47.5%

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

      1. sub-neg 47.5%

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

      2. log1p-undefine 47.5%

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

      3. rem-exp-log 62.4%

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

      4. associate-+r+ 62.4%

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

      5. metadata-eval 62.4%

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

      6. metadata-eval 62.4%

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

   9. Simplified 62.4%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.75 \cdot 10^{-81}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \left(B + C \cdot \frac{B}{A}\right)}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(\frac{C - A}{B} + 2\right) + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.1 \cdot 10^{+61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.2 \cdot 10^{-174}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 - \frac{A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.1e+61)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 6.2e-174)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (/ 180.0 (/ PI (atan (- -1.0 (/ A B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.1e+61) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 6.2e-174) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((-1.0 - (A / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.1e+61) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 6.2e-174) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((-1.0 - (A / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.1e+61:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 6.2e-174:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((-1.0 - (A / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.1e+61)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 6.2e-174)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-1.0 - Float64(A / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.1e+61)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 6.2e-174)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 / (pi / atan((-1.0 - (A / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.1e+61], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6.2e-174], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.1000000000000001e61

   1. Initial program 16.6%

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

   3. Taylor expanded in A around -inf 83.7%

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

      1. associate-*r/ 83.7%

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

   5. Simplified 83.7%

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

   if -5.1000000000000001e61 < A < 6.1999999999999998e-174

   1. Initial program 51.6%

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

   3. Taylor expanded in B around -inf 45.6%

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

      1. associate--l+ 45.6%

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

      2. div-sub 46.6%

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

   5. Simplified 46.6%

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

   6. Taylor expanded in A around 0 46.5%

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

   if 6.1999999999999998e-174 < A

   1. Initial program 71.7%

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

      1. *-commutative 71.7%

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

      2. associate--l- 71.7%

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

      3. +-commutative 71.7%

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

      4. unpow2 71.7%

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

      5. unpow2 71.7%

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

      6. hypot-undefine 90.6%

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

      7. div-inv 90.6%

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

      8. clear-num 90.6%

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

      9. un-div-inv 90.7%

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

   4. Applied egg-rr 90.7%

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

   5. Taylor expanded in C around 0 70.9%

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

      1. mul-1-neg 71.0%

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

      2. distribute-neg-frac2 71.0%

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

      3. unpow2 71.0%

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

      4. unpow2 71.0%

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

      5. hypot-define 87.4%

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

   7. Simplified 87.4%

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

   8. Taylor expanded in A around 0 73.7%

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

      1. sub-neg 73.7%

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

      2. metadata-eval 73.7%

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

      3. +-commutative 73.7%

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

      4. neg-mul-1 73.7%

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

      5. unsub-neg 73.7%

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

   10. Simplified 73.7%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.1 \cdot 10^{+61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.2 \cdot 10^{-174}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 - \frac{A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{+62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-239}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.9e+62)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 3e-239)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e+62) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 3e-239) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e+62) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 3e-239) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.9e+62:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 3e-239:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.9e+62)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 3e-239)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.9e+62)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 3e-239)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.9e+62], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3e-239], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.89999999999999984e62

   1. Initial program 16.6%

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

   3. Taylor expanded in A around -inf 83.7%

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

      1. associate-*r/ 83.7%

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

   5. Simplified 83.7%

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

   if -2.89999999999999984e62 < A < 2.9999999999999998e-239

   1. Initial program 54.0%

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

   3. Taylor expanded in B around -inf 43.5%

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

      1. associate--l+ 43.5%

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

      2. div-sub 44.6%

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

   5. Simplified 44.6%

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

   6. Taylor expanded in A around 0 44.5%

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

   if 2.9999999999999998e-239 < A

   1. Initial program 66.8%

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

   3. Taylor expanded in B around -inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. div-sub 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in C around 0 69.6%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{+62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-239}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.55 \cdot 10^{+61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.1 \cdot 10^{-239}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.55e+61)
   (* 180.0 (/ (atan (* B (/ 0.5 A))) PI))
   (if (<= A 3.1e-239)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.55e+61) {
		tmp = 180.0 * (atan((B * (0.5 / A))) / ((double) M_PI));
	} else if (A <= 3.1e-239) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.55e+61) {
		tmp = 180.0 * (Math.atan((B * (0.5 / A))) / Math.PI);
	} else if (A <= 3.1e-239) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.55e+61:
		tmp = 180.0 * (math.atan((B * (0.5 / A))) / math.pi)
	elif A <= 3.1e-239:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.55e+61)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / A))) / pi));
	elseif (A <= 3.1e-239)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.55e+61)
		tmp = 180.0 * (atan((B * (0.5 / A))) / pi);
	elseif (A <= 3.1e-239)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.55e+61], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.1e-239], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.55e61

   1. Initial program 16.6%

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

   3. Taylor expanded in A around -inf 83.7%

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

      1. associate-*r/ 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in B around 0 83.7%

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

      1. associate-*r/ 83.7%

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

      2. *-commutative 83.7%

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

      3. associate-/l* 83.6%

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

   8. Simplified 83.6%

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

   if -1.55e61 < A < 3.09999999999999985e-239

   1. Initial program 54.0%

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

   3. Taylor expanded in B around -inf 43.5%

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

      1. associate--l+ 43.5%

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

      2. div-sub 44.6%

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

   5. Simplified 44.6%

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

   6. Taylor expanded in A around 0 44.5%

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

   if 3.09999999999999985e-239 < A

   1. Initial program 66.8%

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

   3. Taylor expanded in B around -inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. div-sub 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in C around 0 69.6%

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

Alternative 15: 54.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.6 \cdot 10^{+60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.6e+60)
   (* 180.0 (/ (atan (* B (/ 0.5 A))) PI))
   (if (<= A 4.5e-173)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (/ A (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.6e+60) {
		tmp = 180.0 * (atan((B * (0.5 / A))) / ((double) M_PI));
	} else if (A <= 4.5e-173) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.6e+60) {
		tmp = 180.0 * (Math.atan((B * (0.5 / A))) / Math.PI);
	} else if (A <= 4.5e-173) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.6e+60:
		tmp = 180.0 * (math.atan((B * (0.5 / A))) / math.pi)
	elif A <= 4.5e-173:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.6e+60)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / A))) / pi));
	elseif (A <= 4.5e-173)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.6e+60)
		tmp = 180.0 * (atan((B * (0.5 / A))) / pi);
	elseif (A <= 4.5e-173)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan((A / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.6e+60], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.5e-173], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.59999999999999942e60

   1. Initial program 16.6%

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

   3. Taylor expanded in A around -inf 83.7%

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

      1. associate-*r/ 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in B around 0 83.7%

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

      1. associate-*r/ 83.7%

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

      2. *-commutative 83.7%

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

      3. associate-/l* 83.6%

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

   8. Simplified 83.6%

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

   if -8.59999999999999942e60 < A < 4.50000000000000018e-173

   1. Initial program 51.6%

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

   3. Taylor expanded in B around -inf 45.6%

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

      1. associate--l+ 45.6%

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

      2. div-sub 46.6%

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

   5. Simplified 46.6%

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

   6. Taylor expanded in A around 0 46.5%

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

   if 4.50000000000000018e-173 < A

   1. Initial program 71.7%

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

   3. Taylor expanded in B around -inf 71.5%

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

      1. associate--l+ 71.5%

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

      2. div-sub 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in A around inf 60.1%

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

      1. associate-*r/ 60.1%

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

      2. mul-1-neg 60.1%

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

   8. Simplified 60.1%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.6 \cdot 10^{+60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 47.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{-124}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1e-80)
   (* 180.0 (/ (atan (* B (/ 0.5 A))) PI))
   (if (<= A 4.1e-124)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (* 180.0 (/ (atan (/ A (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1e-80) {
		tmp = 180.0 * (atan((B * (0.5 / A))) / ((double) M_PI));
	} else if (A <= 4.1e-124) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1e-80) {
		tmp = 180.0 * (Math.atan((B * (0.5 / A))) / Math.PI);
	} else if (A <= 4.1e-124) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1e-80:
		tmp = 180.0 * (math.atan((B * (0.5 / A))) / math.pi)
	elif A <= 4.1e-124:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1e-80)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / A))) / pi));
	elseif (A <= 4.1e-124)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1e-80)
		tmp = 180.0 * (atan((B * (0.5 / A))) / pi);
	elseif (A <= 4.1e-124)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = 180.0 * (atan((A / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1e-80], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.1e-124], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -9.99999999999999961e-81

   1. Initial program 27.3%

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

   3. Taylor expanded in A around -inf 67.6%

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

      1. associate-*r/ 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in B around 0 67.6%

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

      1. associate-*r/ 67.6%

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

      2. *-commutative 67.6%

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

      3. associate-/l* 67.6%

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

   8. Simplified 67.6%

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

   if -9.99999999999999961e-81 < A < 4.1000000000000004e-124

   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. Add Preprocessing

   3. Taylor expanded in C around inf 42.4%

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

   4. Taylor expanded in A around inf 42.4%

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

   if 4.1000000000000004e-124 < A

   1. Initial program 73.9%

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

   3. Taylor expanded in B around -inf 74.9%

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

      1. associate--l+ 74.9%

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

      2. div-sub 76.1%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in A around inf 62.4%

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

      1. associate-*r/ 62.4%

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

      2. mul-1-neg 62.4%

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

   8. Simplified 62.4%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{-124}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 60.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.7 \cdot 10^{+63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(\frac{C - A}{B} + 2\right) + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.7e+63)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (* 180.0 (/ (atan (+ (+ (/ (- C A) B) 2.0) -1.0)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.7e+63) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((((C - A) / B) + 2.0) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.7e+63) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((((C - A) / B) + 2.0) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.7e+63:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((((C - A) / B) + 2.0) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.7e+63)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(Float64(C - A) / B) + 2.0) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.7e+63)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	else
		tmp = 180.0 * (atan(((((C - A) / B) + 2.0) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.7e+63], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 2.0), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -2.70000000000000017e63

   1. Initial program 16.6%

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

   3. Taylor expanded in A around -inf 83.7%

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

      1. associate-*r/ 83.7%

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

   5. Simplified 83.7%

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

   if -2.70000000000000017e63 < A

   1. Initial program 61.1%

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

   3. Taylor expanded in B around -inf 57.8%

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

      1. associate--l+ 57.8%

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

      2. div-sub 58.8%

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

   5. Simplified 58.8%

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

      1. expm1-log1p-u 43.7%

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

      2. expm1-undefine 43.7%

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

   7. Applied egg-rr 43.7%

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

      1. sub-neg 43.7%

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

      2. log1p-undefine 43.7%

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

      3. rem-exp-log 58.8%

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

      4. associate-+r+ 58.8%

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

      5. metadata-eval 58.8%

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

      6. metadata-eval 58.8%

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

   9. Simplified 58.8%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.7 \cdot 10^{+63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(\frac{C - A}{B} + 2\right) + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 60.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{+61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.15e+61)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+61) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+61) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.15e+61:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.15e+61)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.15e+61)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.15e+61], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.15e61

   1. Initial program 16.6%

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

   3. Taylor expanded in A around -inf 83.7%

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

      1. associate-*r/ 83.7%

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

   5. Simplified 83.7%

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

   if -1.15e61 < A

   1. Initial program 61.1%

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

   3. Taylor expanded in B around -inf 57.8%

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

      1. associate--l+ 57.8%

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

      2. div-sub 58.8%

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

   5. Simplified 58.8%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{+61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 44.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.6 \cdot 10^{-65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8.6 \cdot 10^{-89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.6e-65)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 8.6e-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 <= -1.6e-65) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 8.6e-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 <= -1.6e-65) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 8.6e-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 <= -1.6e-65:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 8.6e-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 <= -1.6e-65)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 8.6e-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 <= -1.6e-65)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 8.6e-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, -1.6e-65], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.6e-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 3 regimes

2. if B < -1.6e-65

   1. Initial program 52.7%

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

   3. Taylor expanded in B around -inf 52.6%

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

   if -1.6e-65 < B < 8.59999999999999974e-89

   1. Initial program 52.0%

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

   3. Taylor expanded in C around inf 34.7%

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

   4. Taylor expanded in B around 0 37.6%

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

      1. distribute-rgt1-in 37.6%

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

      2. metadata-eval 37.6%

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

      3. mul0-lft 37.6%

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

      4. div0 37.6%

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

      5. metadata-eval 37.6%

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

   6. Simplified 37.6%

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

   if 8.59999999999999974e-89 < B

   1. Initial program 46.0%

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

   3. Taylor expanded in B around inf 50.9%

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

Alternative 20: 28.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 6.2 \cdot 10^{-90}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 6.2e-90) (* 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 <= 6.2e-90) {
		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 <= 6.2e-90) {
		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 <= 6.2e-90:
		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 <= 6.2e-90)
		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 <= 6.2e-90)
		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, 6.2e-90], 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 < 6.2000000000000003e-90

   1. Initial program 52.3%

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

   3. Taylor expanded in C around inf 32.6%

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

   4. Taylor expanded in B around 0 22.8%

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

      1. distribute-rgt1-in 22.8%

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

      2. metadata-eval 22.8%

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

      3. mul0-lft 22.8%

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

      4. div0 22.8%

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

      5. metadata-eval 22.8%

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

   6. Simplified 22.8%

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

   if 6.2000000000000003e-90 < B

   1. Initial program 46.0%

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

   3. Taylor expanded in B around inf 50.9%

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

Alternative 21: 20.7% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ 180 \cdot \frac{\tan^{-1} -1}{\pi} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 50.6%

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

3. Taylor expanded in B around inf 16.7%

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

Reproduce

herbie shell --seed 2024143 
(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)))