ABCF->ab-angle angle

Percentage Accurate: 54.2% → 81.9%

Time: 16.5s

Alternatives: 18

Speedup: 3.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.75 \cdot 10^{+151}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B + C \cdot \frac{B}{A}}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.75e+151)
   (* (atan (* 0.5 (/ (+ B (* C (/ B A))) A))) (/ 180.0 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 <= -1.75e+151) {
		tmp = atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / ((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 <= -1.75e+151) {
		tmp = Math.atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / 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 <= -1.75e+151:
		tmp = math.atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / 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 <= -1.75e+151)
		tmp = Float64(atan(Float64(0.5 * Float64(Float64(B + Float64(C * Float64(B / A))) / A))) * Float64(180.0 / 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 <= -1.75e+151)
		tmp = atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / 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, -1.75e+151], N[(N[ArcTan[N[(0.5 * N[(N[(B + N[(C * N[(B / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / 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 < -1.7500000000000001e151

   1. Initial program 4.4%

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

   3. Taylor expanded in A around -inf 87.7%

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

      1. associate-*r/ 87.7%

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

      2. mul-1-neg 87.7%

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

      3. distribute-lft-out 87.7%

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

      4. *-commutative 87.7%

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

   5. Simplified 87.7%

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

   6. Taylor expanded in B around 0 87.7%

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

      1. associate-*r/ 87.9%

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

      2. associate-*r/ 87.9%

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

      3. +-commutative 87.9%

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

      4. *-commutative 87.9%

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

      5. associate-*r/ 93.4%

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

      6. fma-undefine 93.4%

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

      7. *-commutative 93.4%

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

      8. associate-/l* 93.5%

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

      9. associate-/l* 93.5%

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

   8. Simplified 93.5%

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

      1. fma-undefine 93.5%

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

   10. Applied egg-rr 93.5%

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

   if -1.7500000000000001e151 < A

   1. Initial program 60.2%

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

      1. associate-*l/ 60.2%

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

      2. *-lft-identity 60.2%

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

      3. +-commutative 60.2%

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

      4. unpow2 60.2%

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

      5. unpow2 60.2%

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

      6. hypot-define 80.2%

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

   3. Simplified 80.2%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.75 \cdot 10^{+151}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B + C \cdot \frac{B}{A}}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.8 \cdot 10^{+141}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B + C \cdot \frac{B}{A}}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{-141}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right) \cdot \frac{-180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.8e+141)
   (* (atan (* 0.5 (/ (+ B (* C (/ B A))) A))) (/ 180.0 PI))
   (if (<= A 4.1e-141)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (* (atan (/ (+ A (hypot A B)) B)) (/ -180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.8e+141) {
		tmp = atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / ((double) M_PI));
	} else if (A <= 4.1e-141) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = atan(((A + hypot(A, B)) / B)) * (-180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.8e+141) {
		tmp = Math.atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / Math.PI);
	} else if (A <= 4.1e-141) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = Math.atan(((A + Math.hypot(A, B)) / B)) * (-180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.8e+141:
		tmp = math.atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / math.pi)
	elif A <= 4.1e-141:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = math.atan(((A + math.hypot(A, B)) / B)) * (-180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.8e+141)
		tmp = Float64(atan(Float64(0.5 * Float64(Float64(B + Float64(C * Float64(B / A))) / A))) * Float64(180.0 / pi));
	elseif (A <= 4.1e-141)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(atan(Float64(Float64(A + hypot(A, B)) / B)) * Float64(-180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.8e+141)
		tmp = atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / pi);
	elseif (A <= 4.1e-141)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = atan(((A + hypot(A, B)) / B)) * (-180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.8e+141], N[(N[ArcTan[N[(0.5 * N[(N[(B + N[(C * N[(B / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.1e-141], 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[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(-180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.80000000000000013e141

   1. Initial program 11.4%

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

   3. Taylor expanded in A around -inf 86.9%

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

      1. associate-*r/ 86.9%

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

      2. mul-1-neg 86.9%

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

      3. distribute-lft-out 86.9%

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

      4. *-commutative 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in B around 0 86.9%

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

      1. associate-*r/ 87.1%

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

      2. associate-*r/ 87.1%

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

      3. +-commutative 87.1%

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

      4. *-commutative 87.1%

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

      5. associate-*r/ 92.2%

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

      6. fma-undefine 92.2%

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

      7. *-commutative 92.2%

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

      8. associate-/l* 92.2%

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

      9. associate-/l* 92.2%

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

   8. Simplified 92.2%

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

      1. fma-undefine 92.2%

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

   10. Applied egg-rr 92.2%

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

   if -5.80000000000000013e141 < A < 4.10000000000000002e-141

   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 50.6%

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

      1. +-commutative 50.6%

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

      2. unpow2 50.6%

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

      3. unpow2 50.6%

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

      4. hypot-define 74.9%

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

   5. Simplified 74.9%

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

   if 4.10000000000000002e-141 < A

   1. Initial program 74.2%

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

   3. Taylor expanded in C around 0 69.5%

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

      1. associate-*r/ 69.5%

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

      2. mul-1-neg 69.5%

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

      3. unpow2 69.5%

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

      4. unpow2 69.5%

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

      5. hypot-define 80.0%

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

   5. Simplified 80.0%

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

      1. associate-*r/ 79.9%

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

      2. distribute-frac-neg 79.9%

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

      3. atan-neg 79.9%

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

   7. Applied egg-rr 79.9%

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

      1. distribute-rgt-neg-out 79.9%

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

      2. distribute-lft-neg-in 79.9%

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

      3. metadata-eval 79.9%

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

   9. Simplified 79.9%

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

   10. Taylor expanded in A around 0 69.5%

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

       1. unpow2 69.5%

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

       2. unpow2 69.5%

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

       3. hypot-undefine 80.0%

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

       4. associate-*r/ 79.9%

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

       5. associate-*l/ 80.0%

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

       6. *-commutative 80.0%

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

   12. Simplified 80.0%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.8 \cdot 10^{+141}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B + C \cdot \frac{B}{A}}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{-141}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right) \cdot \frac{-180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.1 \cdot 10^{+141}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B + C \cdot \frac{B}{A}}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 7 \cdot 10^{-157}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.1e+141)
   (* (atan (* 0.5 (/ (+ B (* C (/ B A))) A))) (/ 180.0 PI))
   (if (<= A 7e-157)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (/ 180.0 (/ PI (atan (+ 1.0 (/ (- C A) B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.1e+141) {
		tmp = atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / ((double) M_PI));
	} else if (A <= 7e-157) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((1.0 + ((C - A) / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.1e+141) {
		tmp = Math.atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / Math.PI);
	} else if (A <= 7e-157) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((1.0 + ((C - A) / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.1e+141:
		tmp = math.atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / math.pi)
	elif A <= 7e-157:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((1.0 + ((C - A) / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.1e+141)
		tmp = Float64(atan(Float64(0.5 * Float64(Float64(B + Float64(C * Float64(B / A))) / A))) * Float64(180.0 / pi));
	elseif (A <= 7e-157)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(1.0 + Float64(Float64(C - A) / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.1e+141)
		tmp = atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / pi);
	elseif (A <= 7e-157)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = 180.0 / (pi / atan((1.0 + ((C - A) / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.1e+141], N[(N[ArcTan[N[(0.5 * N[(N[(B + N[(C * N[(B / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 7e-157], 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[(Pi / N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -4.10000000000000022e141

   1. Initial program 11.4%

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

   3. Taylor expanded in A around -inf 86.9%

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

      1. associate-*r/ 86.9%

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

      2. mul-1-neg 86.9%

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

      3. distribute-lft-out 86.9%

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

      4. *-commutative 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in B around 0 86.9%

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

      1. associate-*r/ 87.1%

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

      2. associate-*r/ 87.1%

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

      3. +-commutative 87.1%

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

      4. *-commutative 87.1%

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

      5. associate-*r/ 92.2%

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

      6. fma-undefine 92.2%

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

      7. *-commutative 92.2%

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

      8. associate-/l* 92.2%

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

      9. associate-/l* 92.2%

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

   8. Simplified 92.2%

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

      1. fma-undefine 92.2%

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

   10. Applied egg-rr 92.2%

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

   if -4.10000000000000022e141 < A < 7.0000000000000004e-157

   1. Initial program 50.0%

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

   3. Taylor expanded in A around 0 50.2%

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

      1. +-commutative 50.2%

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

      2. unpow2 50.2%

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

      3. unpow2 50.2%

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

      4. hypot-define 74.7%

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

   5. Simplified 74.7%

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

   if 7.0000000000000004e-157 < A

   1. Initial program 74.5%

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

      1. *-commutative 74.5%

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

      2. associate--l- 74.5%

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

      3. +-commutative 74.5%

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

      4. unpow2 74.5%

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

      5. unpow2 74.5%

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

      6. hypot-undefine 87.8%

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

      7. div-inv 87.8%

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

      8. clear-num 87.8%

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

      9. un-div-inv 87.8%

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

   4. Applied egg-rr 87.8%

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

   5. Taylor expanded in B around -inf 76.1%

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

      1. associate--l+ 76.1%

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

      2. div-sub 78.5%

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

   7. Simplified 78.5%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.1 \cdot 10^{+141}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B + C \cdot \frac{B}{A}}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 7 \cdot 10^{-157}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.9 \cdot 10^{+74}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B + C \cdot \frac{B}{A}}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.9e+74)
   (* (atan (* 0.5 (/ (+ B (* C (/ B A))) A))) (/ 180.0 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 <= -8.9e+74) {
		tmp = atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / ((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 <= -8.9e+74) {
		tmp = Math.atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / 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 <= -8.9e+74:
		tmp = math.atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / 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 <= -8.9e+74)
		tmp = Float64(atan(Float64(0.5 * Float64(Float64(B + Float64(C * Float64(B / A))) / A))) * Float64(180.0 / 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 <= -8.9e+74)
		tmp = atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / 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, -8.9e+74], N[(N[ArcTan[N[(0.5 * N[(N[(B + N[(C * N[(B / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / 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 < -8.9000000000000002e74

   1. Initial program 17.2%

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

   3. Taylor expanded in A around -inf 79.2%

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

      1. associate-*r/ 79.2%

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

      2. mul-1-neg 79.2%

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

      3. distribute-lft-out 79.2%

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

      4. *-commutative 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in B around 0 79.2%

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

      1. associate-*r/ 79.3%

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

      2. associate-*r/ 79.3%

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

      3. +-commutative 79.3%

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

      4. *-commutative 79.3%

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

      5. associate-*r/ 83.1%

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

      6. fma-undefine 83.1%

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

      7. *-commutative 83.1%

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

      8. associate-/l* 83.3%

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

      9. associate-/l* 83.3%

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

   8. Simplified 83.3%

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

      1. fma-undefine 83.3%

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

   10. Applied egg-rr 83.3%

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

   if -8.9000000000000002e74 < A

   1. Initial program 62.5%

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

   3. Simplified 81.4%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.9 \cdot 10^{+74}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B + C \cdot \frac{B}{A}}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{-141}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B + C \cdot \frac{B}{A}}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.15e-141)
   (* (atan (* 0.5 (/ (+ B (* C (/ B A))) A))) (/ 180.0 PI))
   (/ 180.0 (/ PI (atan (+ 1.0 (/ (- C A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e-141) {
		tmp = atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((1.0 + ((C - A) / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e-141) {
		tmp = Math.atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((1.0 + ((C - A) / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.15e-141:
		tmp = math.atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((1.0 + ((C - A) / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.15e-141)
		tmp = Float64(atan(Float64(0.5 * Float64(Float64(B + Float64(C * Float64(B / A))) / A))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(1.0 + Float64(Float64(C - A) / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.15e-141)
		tmp = atan((0.5 * ((B + (C * (B / A))) / A))) * (180.0 / pi);
	else
		tmp = 180.0 / (pi / atan((1.0 + ((C - A) / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.15e-141], N[(N[ArcTan[N[(0.5 * N[(N[(B + N[(C * N[(B / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.14999999999999997e-141

   1. Initial program 26.7%

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

   3. Taylor expanded in A around -inf 65.3%

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

      1. associate-*r/ 65.3%

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

      2. mul-1-neg 65.3%

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

      3. distribute-lft-out 65.3%

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

      4. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in B around 0 65.3%

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

      1. associate-*r/ 65.4%

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

      2. associate-*r/ 65.4%

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

      3. +-commutative 65.4%

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

      4. *-commutative 65.4%

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

      5. associate-*r/ 68.1%

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

      6. fma-undefine 68.1%

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

      7. *-commutative 68.1%

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

      8. associate-/l* 68.1%

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

      9. associate-/l* 68.1%

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

   8. Simplified 68.1%

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

      1. fma-undefine 68.1%

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

   10. Applied egg-rr 68.1%

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

   if -1.14999999999999997e-141 < A

   1. Initial program 67.7%

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

      1. *-commutative 67.7%

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

      2. associate--l- 67.7%

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

      3. +-commutative 67.7%

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

      4. unpow2 67.7%

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

      5. unpow2 67.7%

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

      6. hypot-undefine 85.9%

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

      7. div-inv 85.9%

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

      8. clear-num 85.9%

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

      9. un-div-inv 85.9%

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

   4. Applied egg-rr 85.9%

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

   5. Taylor expanded in B around -inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. div-sub 67.2%

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

   7. Simplified 67.2%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{-141}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B + C \cdot \frac{B}{A}}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.1 \cdot 10^{-142}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B \cdot \left(1 + \frac{C}{A}\right)}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.1e-142)
   (* (/ 180.0 PI) (atan (* 0.5 (/ (* B (+ 1.0 (/ C A))) A))))
   (/ 180.0 (/ PI (atan (+ 1.0 (/ (- C A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.1e-142) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * ((B * (1.0 + (C / A))) / A)));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((1.0 + ((C - A) / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.1e-142) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * ((B * (1.0 + (C / A))) / A)));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((1.0 + ((C - A) / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.1e-142:
		tmp = (180.0 / math.pi) * math.atan((0.5 * ((B * (1.0 + (C / A))) / A)))
	else:
		tmp = 180.0 / (math.pi / math.atan((1.0 + ((C - A) / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.1e-142)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(Float64(B * Float64(1.0 + Float64(C / A))) / A))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(1.0 + Float64(Float64(C - A) / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.1e-142)
		tmp = (180.0 / pi) * atan((0.5 * ((B * (1.0 + (C / A))) / A)));
	else
		tmp = 180.0 / (pi / atan((1.0 + ((C - A) / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.1e-142], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(N[(B * N[(1.0 + N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -5.1000000000000001e-142

   1. Initial program 26.7%

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

   3. Taylor expanded in A around -inf 65.3%

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

      1. associate-*r/ 65.3%

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

      2. mul-1-neg 65.3%

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

      3. distribute-lft-out 65.3%

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

      4. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in B around 0 65.3%

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

      1. associate-*r/ 65.4%

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

      2. associate-*r/ 65.4%

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

      3. +-commutative 65.4%

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

      4. *-commutative 65.4%

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

      5. associate-*r/ 68.1%

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

      6. fma-undefine 68.1%

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

      7. *-commutative 68.1%

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

      8. associate-/l* 68.1%

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

      9. associate-/l* 68.1%

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

   8. Simplified 68.1%

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

   9. Taylor expanded in B around 0 67.3%

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

   if -5.1000000000000001e-142 < A

   1. Initial program 67.7%

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

      1. *-commutative 67.7%

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

      2. associate--l- 67.7%

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

      3. +-commutative 67.7%

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

      4. unpow2 67.7%

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

      5. unpow2 67.7%

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

      6. hypot-undefine 85.9%

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

      7. div-inv 85.9%

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

      8. clear-num 85.9%

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

      9. un-div-inv 85.9%

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

   4. Applied egg-rr 85.9%

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

   5. Taylor expanded in B around -inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. div-sub 67.2%

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

   7. Simplified 67.2%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.1 \cdot 10^{-142}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B \cdot \left(1 + \frac{C}{A}\right)}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.8% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.7 \cdot 10^{-141}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B + \frac{C \cdot B}{A}}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.7e-141)
   (* 180.0 (/ (atan (* 0.5 (/ (+ B (/ (* C B) A)) A))) PI))
   (/ 180.0 (/ PI (atan (+ 1.0 (/ (- C A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.7e-141) {
		tmp = 180.0 * (atan((0.5 * ((B + ((C * B) / A)) / A))) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((1.0 + ((C - A) / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.7e-141) {
		tmp = 180.0 * (Math.atan((0.5 * ((B + ((C * B) / A)) / A))) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((1.0 + ((C - A) / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.7e-141:
		tmp = 180.0 * (math.atan((0.5 * ((B + ((C * B) / A)) / A))) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((1.0 + ((C - A) / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.7e-141)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(Float64(B + Float64(Float64(C * B) / A)) / A))) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(1.0 + Float64(Float64(C - A) / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.7e-141)
		tmp = 180.0 * (atan((0.5 * ((B + ((C * B) / A)) / A))) / pi);
	else
		tmp = 180.0 / (pi / atan((1.0 + ((C - A) / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.7e-141], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(N[(B + N[(N[(C * B), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.6999999999999999e-141

   1. Initial program 26.7%

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

   3. Taylor expanded in A around -inf 65.3%

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

      1. associate-*r/ 65.3%

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

      2. mul-1-neg 65.3%

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

      3. distribute-lft-out 65.3%

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

      4. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in B around 0 65.3%

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

   if -1.6999999999999999e-141 < A

   1. Initial program 67.7%

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

      1. *-commutative 67.7%

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

      2. associate--l- 67.7%

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

      3. +-commutative 67.7%

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

      4. unpow2 67.7%

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

      5. unpow2 67.7%

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

      6. hypot-undefine 85.9%

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

      7. div-inv 85.9%

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

      8. clear-num 85.9%

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

      9. un-div-inv 85.9%

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

   4. Applied egg-rr 85.9%

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

   5. Taylor expanded in B around -inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. div-sub 67.2%

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

   7. Simplified 67.2%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.7 \cdot 10^{-141}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B + \frac{C \cdot B}{A}}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.2 \cdot 10^{-274}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{-51}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.2e-274)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (if (<= A 1.45e-51)
     (/ (* 180.0 (atan (* -0.5 (/ B C)))) PI)
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.2e-274) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (A <= 1.45e-51) {
		tmp = (180.0 * atan((-0.5 * (B / C)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.2e-274) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (A <= 1.45e-51) {
		tmp = (180.0 * Math.atan((-0.5 * (B / C)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.2e-274:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif A <= 1.45e-51:
		tmp = (180.0 * math.atan((-0.5 * (B / C)))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.2e-274)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (A <= 1.45e-51)
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / C)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.2e-274)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (A <= 1.45e-51)
		tmp = (180.0 * atan((-0.5 * (B / C)))) / pi;
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.2e-274], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.45e-51], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.19999999999999975e-274

   1. Initial program 35.6%

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

   3. Taylor expanded in A around -inf 62.0%

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

      1. associate-*r/ 62.0%

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

      2. mul-1-neg 62.0%

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

      3. distribute-lft-out 62.0%

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

      4. *-commutative 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in B around 0 62.0%

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

      1. associate-*r/ 62.1%

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

      2. associate-*r/ 62.1%

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

      3. +-commutative 62.1%

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

      4. *-commutative 62.1%

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

      5. associate-*r/ 64.0%

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

      6. fma-undefine 64.0%

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

      7. *-commutative 64.0%

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

      8. associate-/l* 64.0%

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

      9. associate-/l* 64.0%

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

   8. Simplified 64.0%

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

   9. Taylor expanded in C around 0 61.8%

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

   if -8.19999999999999975e-274 < A < 1.44999999999999986e-51

   1. Initial program 53.7%

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

   3. Taylor expanded in C around inf 42.1%

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

   4. Taylor expanded in B around 0 27.2%

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

      1. distribute-rgt1-in 27.2%

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

      2. metadata-eval 27.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right) + -0.5 \cdot \frac{{B}^{2}}{C}}{B}\right)}{\pi} \]

      3. mul0-lft 27.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0} + -0.5 \cdot \frac{{B}^{2}}{C}}{B}\right)}{\pi} \]

      4. metadata-eval 27.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0} + -0.5 \cdot \frac{{B}^{2}}{C}}{B}\right)}{\pi} \]

      5. +-lft-identity 27.2%

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

      6. *-commutative 27.2%

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

      7. associate-*l/ 27.2%

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

   6. Simplified 27.2%

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

   7. Taylor expanded in B around 0 42.1%

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

      1. associate-*r/ 42.3%

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

   9. Simplified 42.3%

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

   if 1.44999999999999986e-51 < A

   1. Initial program 80.0%

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

      1. associate-*l/ 80.0%

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

      2. *-lft-identity 80.0%

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

      3. +-commutative 80.0%

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

      4. unpow2 80.0%

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

      5. unpow2 80.0%

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

      6. hypot-define 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in A around inf 70.9%

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

      1. *-commutative 70.9%

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

   7. Simplified 70.9%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.2 \cdot 10^{-274}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{-51}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.25 \cdot 10^{-286}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{-51}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.25e-286)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (if (<= A 4.4e-51)
     (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.25e-286) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (A <= 4.4e-51) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.25e-286) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (A <= 4.4e-51) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.25e-286:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif A <= 4.4e-51:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.25e-286)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (A <= 4.4e-51)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.25e-286)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (A <= 4.4e-51)
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.25e-286], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.4e-51], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.25000000000000009e-286

   1. Initial program 35.6%

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

   3. Taylor expanded in A around -inf 62.0%

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

      1. associate-*r/ 62.0%

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

      2. mul-1-neg 62.0%

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

      3. distribute-lft-out 62.0%

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

      4. *-commutative 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in B around 0 62.0%

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

      1. associate-*r/ 62.1%

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

      2. associate-*r/ 62.1%

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

      3. +-commutative 62.1%

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

      4. *-commutative 62.1%

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

      5. associate-*r/ 64.0%

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

      6. fma-undefine 64.0%

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

      7. *-commutative 64.0%

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

      8. associate-/l* 64.0%

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

      9. associate-/l* 64.0%

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

   8. Simplified 64.0%

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

   9. Taylor expanded in C around 0 61.8%

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

   if -1.25000000000000009e-286 < A < 4.4e-51

   1. Initial program 53.7%

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

   3. Taylor expanded in C around inf 42.1%

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

   4. Taylor expanded in A around inf 42.1%

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

   6. Simplified 42.2%

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

   if 4.4e-51 < A

   1. Initial program 80.0%

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

      1. associate-*l/ 80.0%

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

      2. *-lft-identity 80.0%

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

      3. +-commutative 80.0%

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

      4. unpow2 80.0%

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

      5. unpow2 80.0%

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

      6. hypot-define 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in A around inf 70.9%

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

      1. *-commutative 70.9%

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

   7. Simplified 70.9%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.25 \cdot 10^{-286}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{-51}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.4 \cdot 10^{-285}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 1.32 \cdot 10^{-51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.4e-285)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (if (<= A 1.32e-51)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.4e-285) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (A <= 1.32e-51) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.4e-285) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (A <= 1.32e-51) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.4e-285:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif A <= 1.32e-51:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.4e-285)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (A <= 1.32e-51)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.4e-285)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (A <= 1.32e-51)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.4e-285], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.32e-51], 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[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.3999999999999997e-285

   1. Initial program 35.6%

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

   3. Taylor expanded in A around -inf 62.0%

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

      1. associate-*r/ 62.0%

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

      2. mul-1-neg 62.0%

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

      3. distribute-lft-out 62.0%

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

      4. *-commutative 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in B around 0 62.0%

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

      1. associate-*r/ 62.1%

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

      2. associate-*r/ 62.1%

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

      3. +-commutative 62.1%

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

      4. *-commutative 62.1%

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

      5. associate-*r/ 64.0%

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

      6. fma-undefine 64.0%

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

      7. *-commutative 64.0%

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

      8. associate-/l* 64.0%

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

      9. associate-/l* 64.0%

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

   8. Simplified 64.0%

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

   9. Taylor expanded in C around 0 61.8%

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

   if -5.3999999999999997e-285 < A < 1.31999999999999998e-51

   1. Initial program 53.7%

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

   3. Taylor expanded in C around inf 42.1%

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

   4. Taylor expanded in A around inf 42.1%

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

   if 1.31999999999999998e-51 < A

   1. Initial program 80.0%

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

      1. associate-*l/ 80.0%

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

      2. *-lft-identity 80.0%

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

      3. +-commutative 80.0%

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

      4. unpow2 80.0%

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

      5. unpow2 80.0%

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

      6. hypot-define 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in A around inf 70.9%

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

      1. *-commutative 70.9%

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

   7. Simplified 70.9%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.4 \cdot 10^{-285}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 1.32 \cdot 10^{-51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9.9 \cdot 10^{-287}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7 \cdot 10^{-52}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9.9e-287)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 7e-52)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.9e-287) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 7e-52) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.9e-287) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 7e-52) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -9.9e-287:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 7e-52:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -9.9e-287)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 7e-52)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -9.9e-287)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 7e-52)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -9.9e-287], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 7e-52], 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[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -9.89999999999999979e-287

   1. Initial program 35.6%

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

   3. Taylor expanded in A around -inf 61.7%

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

      1. associate-*r/ 61.7%

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

   5. Simplified 61.7%

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

   if -9.89999999999999979e-287 < A < 7.0000000000000001e-52

   1. Initial program 53.7%

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

   3. Taylor expanded in C around inf 42.1%

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

   4. Taylor expanded in A around inf 42.1%

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

   if 7.0000000000000001e-52 < A

   1. Initial program 80.0%

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

      1. associate-*l/ 80.0%

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

      2. *-lft-identity 80.0%

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

      3. +-commutative 80.0%

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

      4. unpow2 80.0%

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

      5. unpow2 80.0%

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

      6. hypot-define 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in A around inf 70.9%

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

      1. *-commutative 70.9%

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

   7. Simplified 70.9%

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

Alternative 12: 45.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{+71}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{+86}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e+71)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 5.8e+86)
     (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e+71) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 5.8e+86) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e+71) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 5.8e+86) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1e+71:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 5.8e+86:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1e+71)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 5.8e+86)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1e+71)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 5.8e+86)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1e+71], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.8e+86], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1e71

   1. Initial program 45.7%

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

   3. Taylor expanded in B around -inf 67.8%

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

   if -1e71 < B < 5.79999999999999981e86

   1. Initial program 56.0%

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

   3. Taylor expanded in A around -inf 40.1%

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

      1. associate-*r/ 40.1%

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

   5. Simplified 40.1%

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

   if 5.79999999999999981e86 < B

   1. Initial program 41.7%

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

   3. Taylor expanded in B around inf 66.8%

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

Alternative 13: 46.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.65 \cdot 10^{+69}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.65e+69)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.4e-55)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.65e+69) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.4e-55) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.65e+69) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.4e-55) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.65e+69:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.4e-55:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / 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 <= -1.65e+69)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.4e-55)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.65e+69)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.4e-55)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.65e+69], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.4e-55], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.6499999999999999e69

   1. Initial program 44.8%

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

   3. Taylor expanded in B around -inf 66.6%

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

   if -1.6499999999999999e69 < B < 4.3999999999999999e-55

   1. Initial program 53.4%

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

   3. Taylor expanded in C around inf 33.7%

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

   4. Taylor expanded in A around inf 33.7%

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

   if 4.3999999999999999e-55 < B

   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 B around inf 50.5%

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

Alternative 14: 60.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.5e-141)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (/ 180.0 (/ PI (atan (+ 1.0 (/ (- C A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.5e-141) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((1.0 + ((C - A) / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.5e-141) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((1.0 + ((C - A) / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.5e-141:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = 180.0 / (math.pi / math.atan((1.0 + ((C - A) / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.5e-141)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(1.0 + Float64(Float64(C - A) / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.5e-141)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 / (pi / atan((1.0 + ((C - A) / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.5e-141], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -2.5e-141

   1. Initial program 26.7%

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

   3. Taylor expanded in A around -inf 65.3%

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

      1. associate-*r/ 65.3%

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

      2. mul-1-neg 65.3%

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

      3. distribute-lft-out 65.3%

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

      4. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in B around 0 65.3%

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

      1. associate-*r/ 65.4%

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

      2. associate-*r/ 65.4%

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

      3. +-commutative 65.4%

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

      4. *-commutative 65.4%

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

      5. associate-*r/ 68.1%

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

      6. fma-undefine 68.1%

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

      7. *-commutative 68.1%

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

      8. associate-/l* 68.1%

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

      9. associate-/l* 68.1%

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

   8. Simplified 68.1%

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

   9. Taylor expanded in C around 0 64.9%

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

   if -2.5e-141 < A

   1. Initial program 67.7%

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

      1. *-commutative 67.7%

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

      2. associate--l- 67.7%

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

      3. +-commutative 67.7%

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

      4. unpow2 67.7%

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

      5. unpow2 67.7%

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

      6. hypot-undefine 85.9%

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

      7. div-inv 85.9%

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

      8. clear-num 85.9%

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

      9. un-div-inv 85.9%

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

   4. Applied egg-rr 85.9%

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

   5. Taylor expanded in B around -inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. div-sub 67.2%

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

   7. Simplified 67.2%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.5e-141)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.5e-141) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} 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 <= -2.5e-141) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} 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 <= -2.5e-141:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	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 <= -2.5e-141)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	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 <= -2.5e-141)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.5e-141], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $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 < -2.5e-141

   1. Initial program 26.7%

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

   3. Taylor expanded in A around -inf 65.3%

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

      1. associate-*r/ 65.3%

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

      2. mul-1-neg 65.3%

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

      3. distribute-lft-out 65.3%

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

      4. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in B around 0 65.3%

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

      1. associate-*r/ 65.4%

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

      2. associate-*r/ 65.4%

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

      3. +-commutative 65.4%

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

      4. *-commutative 65.4%

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

      5. associate-*r/ 68.1%

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

      6. fma-undefine 68.1%

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

      7. *-commutative 68.1%

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

      8. associate-/l* 68.1%

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

      9. associate-/l* 68.1%

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

   8. Simplified 68.1%

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

   9. Taylor expanded in C around 0 64.9%

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

   if -2.5e-141 < A

   1. Initial program 67.7%

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

   3. Taylor expanded in B around -inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. div-sub 67.2%

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

   5. Simplified 67.2%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 44.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.25 \cdot 10^{-105}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.25e-105)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4e-197)
     (* 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 <= -1.25e-105) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4e-197) {
		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 <= -1.25e-105) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4e-197) {
		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 <= -1.25e-105:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4e-197:
		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 <= -1.25e-105)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4e-197)
		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 <= -1.25e-105)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4e-197)
		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, -1.25e-105], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4e-197], 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 < -1.24999999999999991e-105

   1. Initial program 49.1%

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

   3. Taylor expanded in B around -inf 46.6%

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

   if -1.24999999999999991e-105 < B < 3.9999999999999999e-197

   1. Initial program 55.3%

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

   3. Taylor expanded in C around inf 36.4%

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

   4. Taylor expanded in B around 0 37.2%

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

      1. distribute-rgt1-in 37.2%

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

      2. metadata-eval 37.2%

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

      3. mul0-lft 37.2%

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

      4. div0 37.2%

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

      5. metadata-eval 37.2%

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

   6. Simplified 37.2%

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

   if 3.9999999999999999e-197 < B

   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 42.2%

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

Alternative 17: 28.9% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 4 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 4e-197) (* 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 <= 4e-197) {
		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 <= 4e-197) {
		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 <= 4e-197:
		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 <= 4e-197)
		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 <= 4e-197)
		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, 4e-197], 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 < 3.9999999999999999e-197

   1. Initial program 51.8%

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

   3. Taylor expanded in C around inf 29.1%

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

   4. Taylor expanded in B around 0 19.1%

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

      1. distribute-rgt1-in 19.1%

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

      2. metadata-eval 19.1%

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

      3. mul0-lft 19.1%

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

      4. div0 19.1%

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

      5. metadata-eval 19.1%

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

   6. Simplified 19.1%

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

   if 3.9999999999999999e-197 < B

   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 42.2%

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

Alternative 18: 21.2% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 51.7%

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

3. Taylor expanded in B around inf 18.3%

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

Reproduce

herbie shell --seed 2024129 
(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)))