ABCF->ab-angle angle

Percentage Accurate: 53.6% → 81.0%

Time: 20.0s

Alternatives: 18

Speedup: 3.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 7.6 \cdot 10^{+151}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 7.6e+151)
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))
   (/ (* 180.0 (atan (* -0.5 (/ B C)))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 7.6e+151) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((-0.5 * (B / C)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 7.6e+151) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((-0.5 * (B / C)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 7.6e+151:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan((-0.5 * (B / C)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 7.6e+151)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / C)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 7.6e+151)
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	else
		tmp = (180.0 * atan((-0.5 * (B / C)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 7.6e+151], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 7.6000000000000001e151

   1. Initial program 60.4%

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

      1. associate-*l/ 60.5%

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

      2. *-lft-identity 60.5%

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

      3. +-commutative 60.5%

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

      4. unpow2 60.5%

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

      5. unpow2 60.5%

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

      6. hypot-define 85.5%

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

   3. Simplified 85.5%

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

   if 7.6000000000000001e151 < C

   1. Initial program 7.3%

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

      1. associate-*r/ 7.3%

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

      2. associate-*l/ 7.3%

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

      3. *-un-lft-identity 7.3%

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

      4. unpow2 7.3%

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

      5. unpow2 7.3%

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

      6. hypot-define 51.5%

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

   4. Applied egg-rr 51.5%

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

   5. Taylor expanded in C around inf 92.7%

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

   6. Taylor expanded in A around inf 92.7%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 7.6 \cdot 10^{+151}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -4.6 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{+148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -4.6e-20)
   (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
   (if (<= C 4.6e+148)
     (* 180.0 (/ (atan (/ (+ A (hypot B A)) (- B))) PI))
     (/ (* 180.0 (atan (* -0.5 (/ B C)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.6e-20) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else if (C <= 4.6e+148) {
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((-0.5 * (B / C)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.6e-20) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else if (C <= 4.6e+148) {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(B, A)) / -B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((-0.5 * (B / C)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -4.6e-20:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	elif C <= 4.6e+148:
		tmp = 180.0 * (math.atan(((A + math.hypot(B, A)) / -B)) / math.pi)
	else:
		tmp = (180.0 * math.atan((-0.5 * (B / C)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -4.6e-20)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	elseif (C <= 4.6e+148)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / Float64(-B))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / C)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -4.6e-20)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	elseif (C <= 4.6e+148)
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / pi);
	else
		tmp = (180.0 * atan((-0.5 * (B / C)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -4.6e-20], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.6e+148], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -4.5999999999999998e-20

   1. Initial program 73.1%

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

   3. Taylor expanded in A around 0 71.7%

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

      1. unpow2 71.7%

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

      2. unpow2 71.7%

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

      3. hypot-define 88.8%

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

   5. Simplified 88.8%

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

   if -4.5999999999999998e-20 < C < 4.6000000000000001e148

   1. Initial program 54.8%

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

   3. Taylor expanded in C around 0 52.0%

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

      1. mul-1-neg 52.0%

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

      2. distribute-neg-frac2 52.0%

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

      3. +-commutative 52.0%

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

      4. unpow2 52.0%

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

      5. unpow2 52.0%

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

      6. hypot-define 77.9%

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

   5. Simplified 77.9%

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

   if 4.6000000000000001e148 < C

   1. Initial program 7.3%

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

      1. associate-*r/ 7.3%

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

      2. associate-*l/ 7.3%

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

      3. *-un-lft-identity 7.3%

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

      4. unpow2 7.3%

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

      5. unpow2 7.3%

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

      6. hypot-define 51.5%

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

   4. Applied egg-rr 51.5%

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

   5. Taylor expanded in C around inf 92.7%

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

   6. Taylor expanded in A around inf 92.7%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -4.6 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{+148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{+98}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 4.7 \cdot 10^{+76}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.9e+98)
   (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
   (if (<= A 4.7e+76)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e+98) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	} else if (A <= 4.7e+76) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e+98) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else if (A <= 4.7e+76) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.9e+98:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	elif A <= 4.7e+76:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.9e+98)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	elseif (A <= 4.7e+76)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.9e+98)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	elseif (A <= 4.7e+76)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.9e+98], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.7e+76], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.9000000000000001e98

   1. Initial program 29.0%

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

   3. Taylor expanded in A around -inf 72.5%

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

      1. associate-*r/ 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in B around 0 72.5%

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

      1. associate-*r/ 72.7%

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

      2. *-commutative 72.7%

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

      3. associate-/l* 72.8%

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

   8. Simplified 72.8%

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

   if -2.9000000000000001e98 < A < 4.7000000000000003e76

   1. Initial program 57.0%

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

   3. Taylor expanded in A around 0 51.1%

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

      1. unpow2 51.1%

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

      2. unpow2 51.1%

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

      3. hypot-define 76.9%

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

   5. Simplified 76.9%

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

   if 4.7000000000000003e76 < A

   1. Initial program 68.0%

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

   3. Taylor expanded in B around inf 78.4%

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

   4. Taylor expanded in C around 0 78.4%

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

      1. mul-1-neg 78.4%

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

      2. distribute-neg-frac2 78.4%

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

   6. Simplified 78.4%

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

   7. Taylor expanded in A around 0 78.4%

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

   9. Simplified 78.5%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{+98}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 4.7 \cdot 10^{+76}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.5 \cdot 10^{+98}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.5e+98)
   (* (atan (* 0.5 (/ B 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 <= -4.5e+98) {
		tmp = atan((0.5 * (B / 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 <= -4.5e+98) {
		tmp = Math.atan((0.5 * (B / 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 <= -4.5e+98:
		tmp = math.atan((0.5 * (B / 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 <= -4.5e+98)
		tmp = Float64(atan(Float64(0.5 * Float64(B / 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 <= -4.5e+98)
		tmp = atan((0.5 * (B / 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, -4.5e+98], N[(N[ArcTan[N[(0.5 * N[(B / 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 < -4.5000000000000002e98

   1. Initial program 29.0%

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

   3. Taylor expanded in A around -inf 72.5%

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

      1. associate-*r/ 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in B around 0 72.5%

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

      1. associate-*r/ 72.7%

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

      2. *-commutative 72.7%

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

      3. associate-/l* 72.8%

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

   8. Simplified 72.8%

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

   if -4.5000000000000002e98 < A

   1. Initial program 59.1%

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

   3. Simplified 84.4%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.5 \cdot 10^{+98}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.25 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-138}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq -1.98 \cdot 10^{-289}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;B \leq -5 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-247}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-111}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ C B)) PI)))
        (t_1 (* 180.0 (/ (atan (/ A (- B))) PI)))
        (t_2 (* 180.0 (/ (atan (/ 0.0 B)) PI))))
   (if (<= B -1.25e-67)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -3e-138)
       t_0
       (if (<= B -2.1e-184)
         (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
         (if (<= B -8.2e-195)
           t_1
           (if (<= B -1.98e-289)
             t_2
             (if (<= B -5e-296)
               t_1
               (if (<= B 1.7e-247)
                 t_0
                 (if (<= B 3.6e-111) t_2 (* 180.0 (/ (atan -1.0) PI))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan((A / -B)) / ((double) M_PI));
	double t_2 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double tmp;
	if (B <= -1.25e-67) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -3e-138) {
		tmp = t_0;
	} else if (B <= -2.1e-184) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= -8.2e-195) {
		tmp = t_1;
	} else if (B <= -1.98e-289) {
		tmp = t_2;
	} else if (B <= -5e-296) {
		tmp = t_1;
	} else if (B <= 1.7e-247) {
		tmp = t_0;
	} else if (B <= 3.6e-111) {
		tmp = t_2;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan((A / -B)) / Math.PI);
	double t_2 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double tmp;
	if (B <= -1.25e-67) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -3e-138) {
		tmp = t_0;
	} else if (B <= -2.1e-184) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= -8.2e-195) {
		tmp = t_1;
	} else if (B <= -1.98e-289) {
		tmp = t_2;
	} else if (B <= -5e-296) {
		tmp = t_1;
	} else if (B <= 1.7e-247) {
		tmp = t_0;
	} else if (B <= 3.6e-111) {
		tmp = t_2;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((C / B)) / math.pi)
	t_1 = 180.0 * (math.atan((A / -B)) / math.pi)
	t_2 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	tmp = 0
	if B <= -1.25e-67:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -3e-138:
		tmp = t_0
	elif B <= -2.1e-184:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= -8.2e-195:
		tmp = t_1
	elif B <= -1.98e-289:
		tmp = t_2
	elif B <= -5e-296:
		tmp = t_1
	elif B <= 1.7e-247:
		tmp = t_0
	elif B <= 3.6e-111:
		tmp = t_2
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi))
	t_2 = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi))
	tmp = 0.0
	if (B <= -1.25e-67)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -3e-138)
		tmp = t_0;
	elseif (B <= -2.1e-184)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= -8.2e-195)
		tmp = t_1;
	elseif (B <= -1.98e-289)
		tmp = t_2;
	elseif (B <= -5e-296)
		tmp = t_1;
	elseif (B <= 1.7e-247)
		tmp = t_0;
	elseif (B <= 3.6e-111)
		tmp = t_2;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((C / B)) / pi);
	t_1 = 180.0 * (atan((A / -B)) / pi);
	t_2 = 180.0 * (atan((0.0 / B)) / pi);
	tmp = 0.0;
	if (B <= -1.25e-67)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -3e-138)
		tmp = t_0;
	elseif (B <= -2.1e-184)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= -8.2e-195)
		tmp = t_1;
	elseif (B <= -1.98e-289)
		tmp = t_2;
	elseif (B <= -5e-296)
		tmp = t_1;
	elseif (B <= 1.7e-247)
		tmp = t_0;
	elseif (B <= 3.6e-111)
		tmp = t_2;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.25e-67], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3e-138], t$95$0, If[LessEqual[B, -2.1e-184], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.2e-195], t$95$1, If[LessEqual[B, -1.98e-289], t$95$2, If[LessEqual[B, -5e-296], t$95$1, If[LessEqual[B, 1.7e-247], t$95$0, If[LessEqual[B, 3.6e-111], t$95$2, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -1.25e-67

   1. Initial program 45.1%

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

   3. Taylor expanded in B around -inf 60.1%

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

   if -1.25e-67 < B < -3.0000000000000001e-138 or -5.0000000000000003e-296 < B < 1.7000000000000001e-247

   1. Initial program 82.2%

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

   3. Taylor expanded in B around inf 74.5%

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

   4. Taylor expanded in C around inf 65.4%

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

   if -3.0000000000000001e-138 < B < -2.0999999999999999e-184

   1. Initial program 42.2%

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

   3. Taylor expanded in C around inf 60.0%

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

   4. Taylor expanded in A around inf 60.0%

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

   if -2.0999999999999999e-184 < B < -8.20000000000000024e-195 or -1.98000000000000003e-289 < B < -5.0000000000000003e-296

   1. Initial program 85.8%

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

   3. Taylor expanded in B around inf 83.8%

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

   4. Taylor expanded in A around inf 83.8%

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

      1. associate-*r/ 83.8%

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

      2. mul-1-neg 83.8%

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

   6. Simplified 83.8%

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

   if -8.20000000000000024e-195 < B < -1.98000000000000003e-289 or 1.7000000000000001e-247 < B < 3.6000000000000001e-111

   1. Initial program 46.6%

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

   3. Taylor expanded in C around inf 58.9%

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

      1. associate-*r/ 58.9%

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

      2. distribute-rgt1-in 58.9%

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

      3. metadata-eval 58.9%

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

      4. mul0-lft 58.9%

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

      5. metadata-eval 58.9%

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

   5. Simplified 58.9%

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

   if 3.6000000000000001e-111 < B

   1. Initial program 51.2%

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

   3. Taylor expanded in B around inf 60.4%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.25 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-138}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.98 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5 \cdot 10^{-296}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-247}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-111}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 45.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.36 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-138}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.05 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-192}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -5.9 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-296}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 4.3 \cdot 10^{-248}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ A (- B))) PI)))
        (t_1 (* 180.0 (/ (atan (/ 0.0 B)) PI))))
   (if (<= B -2.36e-63)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -3.5e-138)
       (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
       (if (<= B -2.05e-184)
         (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
         (if (<= B -2.1e-192)
           t_0
           (if (<= B -5.9e-288)
             t_1
             (if (<= B -2e-296)
               t_0
               (if (<= B 4.3e-248)
                 (* 180.0 (/ (atan (/ C B)) PI))
                 (if (<= B 1.3e-111) t_1 (* 180.0 (/ (atan -1.0) PI))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((A / -B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double tmp;
	if (B <= -2.36e-63) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -3.5e-138) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	} else if (B <= -2.05e-184) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= -2.1e-192) {
		tmp = t_0;
	} else if (B <= -5.9e-288) {
		tmp = t_1;
	} else if (B <= -2e-296) {
		tmp = t_0;
	} else if (B <= 4.3e-248) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= 1.3e-111) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((A / -B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double tmp;
	if (B <= -2.36e-63) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -3.5e-138) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else if (B <= -2.05e-184) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= -2.1e-192) {
		tmp = t_0;
	} else if (B <= -5.9e-288) {
		tmp = t_1;
	} else if (B <= -2e-296) {
		tmp = t_0;
	} else if (B <= 4.3e-248) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= 1.3e-111) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((A / -B)) / math.pi)
	t_1 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	tmp = 0
	if B <= -2.36e-63:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -3.5e-138:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	elif B <= -2.05e-184:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= -2.1e-192:
		tmp = t_0
	elif B <= -5.9e-288:
		tmp = t_1
	elif B <= -2e-296:
		tmp = t_0
	elif B <= 4.3e-248:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= 1.3e-111:
		tmp = t_1
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi))
	tmp = 0.0
	if (B <= -2.36e-63)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -3.5e-138)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	elseif (B <= -2.05e-184)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= -2.1e-192)
		tmp = t_0;
	elseif (B <= -5.9e-288)
		tmp = t_1;
	elseif (B <= -2e-296)
		tmp = t_0;
	elseif (B <= 4.3e-248)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= 1.3e-111)
		tmp = t_1;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((A / -B)) / pi);
	t_1 = 180.0 * (atan((0.0 / B)) / pi);
	tmp = 0.0;
	if (B <= -2.36e-63)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -3.5e-138)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	elseif (B <= -2.05e-184)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= -2.1e-192)
		tmp = t_0;
	elseif (B <= -5.9e-288)
		tmp = t_1;
	elseif (B <= -2e-296)
		tmp = t_0;
	elseif (B <= 4.3e-248)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= 1.3e-111)
		tmp = t_1;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.36e-63], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.5e-138], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.05e-184], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.1e-192], t$95$0, If[LessEqual[B, -5.9e-288], t$95$1, If[LessEqual[B, -2e-296], t$95$0, If[LessEqual[B, 4.3e-248], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.3e-111], t$95$1, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if B < -2.35999999999999998e-63

   1. Initial program 45.1%

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

   3. Taylor expanded in B around -inf 60.1%

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

   if -2.35999999999999998e-63 < B < -3.4999999999999999e-138

   1. Initial program 79.1%

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

   3. Taylor expanded in C around -inf 62.1%

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

   if -3.4999999999999999e-138 < B < -2.05e-184

   1. Initial program 42.2%

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

   3. Taylor expanded in C around inf 60.0%

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

   4. Taylor expanded in A around inf 60.0%

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

   if -2.05e-184 < B < -2.09999999999999993e-192 or -5.90000000000000014e-288 < B < -2e-296

   1. Initial program 85.8%

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

   3. Taylor expanded in B around inf 83.8%

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

   4. Taylor expanded in A around inf 83.8%

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

      1. associate-*r/ 83.8%

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

      2. mul-1-neg 83.8%

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

   6. Simplified 83.8%

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

   if -2.09999999999999993e-192 < B < -5.90000000000000014e-288 or 4.3000000000000004e-248 < B < 1.29999999999999991e-111

   1. Initial program 46.6%

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

   3. Taylor expanded in C around inf 58.9%

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

      1. associate-*r/ 58.9%

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

      2. distribute-rgt1-in 58.9%

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

      3. metadata-eval 58.9%

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

      4. mul0-lft 58.9%

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

      5. metadata-eval 58.9%

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

   5. Simplified 58.9%

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

   if -2e-296 < B < 4.3000000000000004e-248

   1. Initial program 85.8%

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

   3. Taylor expanded in B around inf 74.5%

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

   4. Taylor expanded in C around inf 69.3%

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

   if 1.29999999999999991e-111 < B

   1. Initial program 51.2%

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

   3. Taylor expanded in B around inf 60.4%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.36 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-138}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.05 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-192}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5.9 \cdot 10^{-288}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-296}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.3 \cdot 10^{-248}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-111}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.1 \cdot 10^{-141}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.05 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-292}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-248}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-88}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ 0.0 B)) PI)))
        (t_1 (* 180.0 (/ (atan (/ A (- B))) PI))))
   (if (<= B -1.1e-141)
     (* 180.0 (/ (atan (+ (/ C B) 1.0)) PI))
     (if (<= B -2.05e-184)
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
       (if (<= B -4.5e-194)
         t_1
         (if (<= B -8.2e-292)
           t_0
           (if (<= B -7.5e-296)
             t_1
             (if (<= B 3.8e-248)
               (* 180.0 (/ (atan (/ C B)) PI))
               (if (<= B 2.4e-88) t_0 (* 180.0 (/ (atan -1.0) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan((A / -B)) / ((double) M_PI));
	double tmp;
	if (B <= -1.1e-141) {
		tmp = 180.0 * (atan(((C / B) + 1.0)) / ((double) M_PI));
	} else if (B <= -2.05e-184) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= -4.5e-194) {
		tmp = t_1;
	} else if (B <= -8.2e-292) {
		tmp = t_0;
	} else if (B <= -7.5e-296) {
		tmp = t_1;
	} else if (B <= 3.8e-248) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= 2.4e-88) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan((A / -B)) / Math.PI);
	double tmp;
	if (B <= -1.1e-141) {
		tmp = 180.0 * (Math.atan(((C / B) + 1.0)) / Math.PI);
	} else if (B <= -2.05e-184) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= -4.5e-194) {
		tmp = t_1;
	} else if (B <= -8.2e-292) {
		tmp = t_0;
	} else if (B <= -7.5e-296) {
		tmp = t_1;
	} else if (B <= 3.8e-248) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= 2.4e-88) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	t_1 = 180.0 * (math.atan((A / -B)) / math.pi)
	tmp = 0
	if B <= -1.1e-141:
		tmp = 180.0 * (math.atan(((C / B) + 1.0)) / math.pi)
	elif B <= -2.05e-184:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= -4.5e-194:
		tmp = t_1
	elif B <= -8.2e-292:
		tmp = t_0
	elif B <= -7.5e-296:
		tmp = t_1
	elif B <= 3.8e-248:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= 2.4e-88:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi))
	tmp = 0.0
	if (B <= -1.1e-141)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + 1.0)) / pi));
	elseif (B <= -2.05e-184)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= -4.5e-194)
		tmp = t_1;
	elseif (B <= -8.2e-292)
		tmp = t_0;
	elseif (B <= -7.5e-296)
		tmp = t_1;
	elseif (B <= 3.8e-248)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= 2.4e-88)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((0.0 / B)) / pi);
	t_1 = 180.0 * (atan((A / -B)) / pi);
	tmp = 0.0;
	if (B <= -1.1e-141)
		tmp = 180.0 * (atan(((C / B) + 1.0)) / pi);
	elseif (B <= -2.05e-184)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= -4.5e-194)
		tmp = t_1;
	elseif (B <= -8.2e-292)
		tmp = t_0;
	elseif (B <= -7.5e-296)
		tmp = t_1;
	elseif (B <= 3.8e-248)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= 2.4e-88)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.1e-141], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.05e-184], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4.5e-194], t$95$1, If[LessEqual[B, -8.2e-292], t$95$0, If[LessEqual[B, -7.5e-296], t$95$1, If[LessEqual[B, 3.8e-248], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.4e-88], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -1.10000000000000005e-141

   1. Initial program 52.3%

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

   3. Taylor expanded in A around 0 44.5%

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

      1. unpow2 44.5%

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

      2. unpow2 44.5%

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

      3. hypot-define 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in B around -inf 66.7%

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

   if -1.10000000000000005e-141 < B < -2.05e-184

   1. Initial program 42.2%

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

   3. Taylor expanded in C around inf 60.0%

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

   4. Taylor expanded in A around inf 60.0%

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

   if -2.05e-184 < B < -4.4999999999999999e-194 or -8.20000000000000087e-292 < B < -7.49999999999999991e-296

   1. Initial program 85.8%

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

   3. Taylor expanded in B around inf 83.8%

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

   4. Taylor expanded in A around inf 83.8%

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

      1. associate-*r/ 83.8%

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

      2. mul-1-neg 83.8%

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

   6. Simplified 83.8%

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

   if -4.4999999999999999e-194 < B < -8.20000000000000087e-292 or 3.7999999999999999e-248 < B < 2.4e-88

   1. Initial program 46.6%

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

   3. Taylor expanded in C around inf 58.9%

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

      1. associate-*r/ 58.9%

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

      2. distribute-rgt1-in 58.9%

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

      3. metadata-eval 58.9%

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

      4. mul0-lft 58.9%

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

      5. metadata-eval 58.9%

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

   5. Simplified 58.9%

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

   if -7.49999999999999991e-296 < B < 3.7999999999999999e-248

   1. Initial program 85.8%

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

   3. Taylor expanded in B around inf 74.5%

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

   4. Taylor expanded in C around inf 69.3%

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

   if 2.4e-88 < B

   1. Initial program 51.2%

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

   3. Taylor expanded in B around inf 60.4%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.1 \cdot 10^{-141}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.05 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-194}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-296}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-248}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -9.2 \cdot 10^{-71}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.6 \cdot 10^{-190}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-247}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ C B)) PI)))
        (t_1 (* 180.0 (/ (atan (/ 0.0 B)) PI))))
   (if (<= B -9.2e-71)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -2.6e-190)
       t_0
       (if (<= B -1.6e-262)
         t_1
         (if (<= B 5.5e-247)
           t_0
           (if (<= B 1.45e-103) t_1 (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double tmp;
	if (B <= -9.2e-71) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2.6e-190) {
		tmp = t_0;
	} else if (B <= -1.6e-262) {
		tmp = t_1;
	} else if (B <= 5.5e-247) {
		tmp = t_0;
	} else if (B <= 1.45e-103) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double tmp;
	if (B <= -9.2e-71) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2.6e-190) {
		tmp = t_0;
	} else if (B <= -1.6e-262) {
		tmp = t_1;
	} else if (B <= 5.5e-247) {
		tmp = t_0;
	} else if (B <= 1.45e-103) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((C / B)) / math.pi)
	t_1 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	tmp = 0
	if B <= -9.2e-71:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2.6e-190:
		tmp = t_0
	elif B <= -1.6e-262:
		tmp = t_1
	elif B <= 5.5e-247:
		tmp = t_0
	elif B <= 1.45e-103:
		tmp = t_1
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi))
	tmp = 0.0
	if (B <= -9.2e-71)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2.6e-190)
		tmp = t_0;
	elseif (B <= -1.6e-262)
		tmp = t_1;
	elseif (B <= 5.5e-247)
		tmp = t_0;
	elseif (B <= 1.45e-103)
		tmp = t_1;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((C / B)) / pi);
	t_1 = 180.0 * (atan((0.0 / B)) / pi);
	tmp = 0.0;
	if (B <= -9.2e-71)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2.6e-190)
		tmp = t_0;
	elseif (B <= -1.6e-262)
		tmp = t_1;
	elseif (B <= 5.5e-247)
		tmp = t_0;
	elseif (B <= 1.45e-103)
		tmp = t_1;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -9.2e-71], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.6e-190], t$95$0, If[LessEqual[B, -1.6e-262], t$95$1, If[LessEqual[B, 5.5e-247], t$95$0, If[LessEqual[B, 1.45e-103], t$95$1, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -9.1999999999999994e-71

   1. Initial program 45.1%

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

   3. Taylor expanded in B around -inf 60.1%

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

   if -9.1999999999999994e-71 < B < -2.5999999999999998e-190 or -1.6e-262 < B < 5.49999999999999995e-247

   1. Initial program 76.5%

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

   3. Taylor expanded in B around inf 69.2%

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

   4. Taylor expanded in C around inf 54.7%

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

   if -2.5999999999999998e-190 < B < -1.6e-262 or 5.49999999999999995e-247 < B < 1.4499999999999999e-103

   1. Initial program 43.6%

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

   3. Taylor expanded in C around inf 59.3%

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

      1. associate-*r/ 59.3%

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

      2. distribute-rgt1-in 59.3%

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

      3. metadata-eval 59.3%

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

      4. mul0-lft 59.3%

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

      5. metadata-eval 59.3%

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

   5. Simplified 59.3%

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

   if 1.4499999999999999e-103 < B

   1. Initial program 51.2%

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

   3. Taylor expanded in B around inf 60.4%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9.2 \cdot 10^{-71}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.6 \cdot 10^{-190}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-262}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-247}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-103}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -5 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.75 \cdot 10^{-188}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq -2.3 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 4.8 \cdot 10^{-90}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))
   (if (<= C -5e-54)
     (* 180.0 (/ (atan (+ (/ C B) 1.0)) PI))
     (if (<= C -1.75e-188)
       t_0
       (if (<= C -2.3e-203)
         (* 180.0 (/ (atan -1.0) PI))
         (if (<= C 4.8e-90) t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	double tmp;
	if (C <= -5e-54) {
		tmp = 180.0 * (atan(((C / B) + 1.0)) / ((double) M_PI));
	} else if (C <= -1.75e-188) {
		tmp = t_0;
	} else if (C <= -2.3e-203) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (C <= 4.8e-90) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	double tmp;
	if (C <= -5e-54) {
		tmp = 180.0 * (Math.atan(((C / B) + 1.0)) / Math.PI);
	} else if (C <= -1.75e-188) {
		tmp = t_0;
	} else if (C <= -2.3e-203) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (C <= 4.8e-90) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	tmp = 0
	if C <= -5e-54:
		tmp = 180.0 * (math.atan(((C / B) + 1.0)) / math.pi)
	elif C <= -1.75e-188:
		tmp = t_0
	elif C <= -2.3e-203:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif C <= 4.8e-90:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi))
	tmp = 0.0
	if (C <= -5e-54)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + 1.0)) / pi));
	elseif (C <= -1.75e-188)
		tmp = t_0;
	elseif (C <= -2.3e-203)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (C <= 4.8e-90)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 - (A / B))) / pi);
	tmp = 0.0;
	if (C <= -5e-54)
		tmp = 180.0 * (atan(((C / B) + 1.0)) / pi);
	elseif (C <= -1.75e-188)
		tmp = t_0;
	elseif (C <= -2.3e-203)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (C <= 4.8e-90)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -5e-54], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -1.75e-188], t$95$0, If[LessEqual[C, -2.3e-203], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.8e-90], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -5.00000000000000015e-54

   1. Initial program 73.6%

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

   3. Taylor expanded in A around 0 70.1%

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

      1. unpow2 70.1%

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

      2. unpow2 70.1%

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

      3. hypot-define 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in B around -inf 71.6%

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

   if -5.00000000000000015e-54 < C < -1.75e-188 or -2.29999999999999991e-203 < C < 4.8000000000000003e-90

   1. Initial program 61.1%

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

   3. Taylor expanded in C around 0 61.1%

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

      1. mul-1-neg 61.1%

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

      2. distribute-neg-frac2 61.1%

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

      3. +-commutative 61.1%

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

      4. unpow2 61.1%

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

      5. unpow2 61.1%

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

      6. hypot-define 91.0%

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

   5. Simplified 91.0%

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

   6. Taylor expanded in B around -inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. unsub-neg 62.2%

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

   8. Simplified 62.2%

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

   if -1.75e-188 < C < -2.29999999999999991e-203

   1. Initial program 43.2%

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

   3. Taylor expanded in B around inf 70.1%

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

   if 4.8000000000000003e-90 < C

   1. Initial program 27.3%

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

   3. Taylor expanded in C around inf 61.5%

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

   4. Taylor expanded in A around inf 61.5%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -5 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.75 \cdot 10^{-188}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.3 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 4.8 \cdot 10^{-90}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.55 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.75 \cdot 10^{-188}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq -2.3 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 6 \cdot 10^{-89}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))
   (if (<= C -1.55e-54)
     (* 180.0 (/ (atan (+ (/ C B) 1.0)) PI))
     (if (<= C -1.75e-188)
       t_0
       (if (<= C -2.3e-203)
         (* 180.0 (/ (atan -1.0) PI))
         (if (<= C 6e-89) t_0 (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	double tmp;
	if (C <= -1.55e-54) {
		tmp = 180.0 * (atan(((C / B) + 1.0)) / ((double) M_PI));
	} else if (C <= -1.75e-188) {
		tmp = t_0;
	} else if (C <= -2.3e-203) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (C <= 6e-89) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	double tmp;
	if (C <= -1.55e-54) {
		tmp = 180.0 * (Math.atan(((C / B) + 1.0)) / Math.PI);
	} else if (C <= -1.75e-188) {
		tmp = t_0;
	} else if (C <= -2.3e-203) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (C <= 6e-89) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	tmp = 0
	if C <= -1.55e-54:
		tmp = 180.0 * (math.atan(((C / B) + 1.0)) / math.pi)
	elif C <= -1.75e-188:
		tmp = t_0
	elif C <= -2.3e-203:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif C <= 6e-89:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi))
	tmp = 0.0
	if (C <= -1.55e-54)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + 1.0)) / pi));
	elseif (C <= -1.75e-188)
		tmp = t_0;
	elseif (C <= -2.3e-203)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (C <= 6e-89)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 - (A / B))) / pi);
	tmp = 0.0;
	if (C <= -1.55e-54)
		tmp = 180.0 * (atan(((C / B) + 1.0)) / pi);
	elseif (C <= -1.75e-188)
		tmp = t_0;
	elseif (C <= -2.3e-203)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (C <= 6e-89)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.55e-54], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -1.75e-188], t$95$0, If[LessEqual[C, -2.3e-203], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6e-89], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.55000000000000002e-54

   1. Initial program 73.6%

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

   3. Taylor expanded in A around 0 70.1%

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

      1. unpow2 70.1%

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

      2. unpow2 70.1%

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

      3. hypot-define 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in B around -inf 71.6%

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

   if -1.55000000000000002e-54 < C < -1.75e-188 or -2.29999999999999991e-203 < C < 5.9999999999999999e-89

   1. Initial program 61.1%

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

   3. Taylor expanded in C around 0 61.1%

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

      1. mul-1-neg 61.1%

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

      2. distribute-neg-frac2 61.1%

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

      3. +-commutative 61.1%

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

      4. unpow2 61.1%

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

      5. unpow2 61.1%

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

      6. hypot-define 91.0%

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

   5. Simplified 91.0%

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

   6. Taylor expanded in B around -inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. unsub-neg 62.2%

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

   8. Simplified 62.2%

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

   if -1.75e-188 < C < -2.29999999999999991e-203

   1. Initial program 43.2%

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

   3. Taylor expanded in B around inf 70.1%

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

   if 5.9999999999999999e-89 < C

   1. Initial program 27.3%

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

   3. Taylor expanded in C around inf 61.5%

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

   4. Taylor expanded in A around inf 61.5%

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

   6. Simplified 61.6%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.55 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.75 \cdot 10^{-188}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.3 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 6 \cdot 10^{-89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.8 \cdot 10^{-53}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.7 \cdot 10^{-284}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 1.55 \cdot 10^{-244}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.8 \cdot 10^{-89}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))
   (if (<= C -1.8e-53)
     (* 180.0 (/ (atan (+ (/ C B) 1.0)) PI))
     (if (<= C 1.7e-284)
       t_0
       (if (<= C 1.55e-244)
         (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI)
         (if (<= C 5.8e-89) t_0 (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	double tmp;
	if (C <= -1.8e-53) {
		tmp = 180.0 * (atan(((C / B) + 1.0)) / ((double) M_PI));
	} else if (C <= 1.7e-284) {
		tmp = t_0;
	} else if (C <= 1.55e-244) {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	} else if (C <= 5.8e-89) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	double tmp;
	if (C <= -1.8e-53) {
		tmp = 180.0 * (Math.atan(((C / B) + 1.0)) / Math.PI);
	} else if (C <= 1.7e-284) {
		tmp = t_0;
	} else if (C <= 1.55e-244) {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	} else if (C <= 5.8e-89) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	tmp = 0
	if C <= -1.8e-53:
		tmp = 180.0 * (math.atan(((C / B) + 1.0)) / math.pi)
	elif C <= 1.7e-284:
		tmp = t_0
	elif C <= 1.55e-244:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	elif C <= 5.8e-89:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi))
	tmp = 0.0
	if (C <= -1.8e-53)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + 1.0)) / pi));
	elseif (C <= 1.7e-284)
		tmp = t_0;
	elseif (C <= 1.55e-244)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	elseif (C <= 5.8e-89)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 - (A / B))) / pi);
	tmp = 0.0;
	if (C <= -1.8e-53)
		tmp = 180.0 * (atan(((C / B) + 1.0)) / pi);
	elseif (C <= 1.7e-284)
		tmp = t_0;
	elseif (C <= 1.55e-244)
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	elseif (C <= 5.8e-89)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.8e-53], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.7e-284], t$95$0, If[LessEqual[C, 1.55e-244], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 5.8e-89], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.7999999999999999e-53

   1. Initial program 73.6%

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

   3. Taylor expanded in A around 0 70.1%

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

      1. unpow2 70.1%

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

      2. unpow2 70.1%

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

      3. hypot-define 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in B around -inf 71.6%

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

   if -1.7999999999999999e-53 < C < 1.69999999999999996e-284 or 1.55e-244 < C < 5.79999999999999984e-89

   1. Initial program 58.4%

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

   3. Taylor expanded in C around 0 57.4%

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

      1. mul-1-neg 57.4%

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

      2. distribute-neg-frac2 57.4%

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

      3. +-commutative 57.4%

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

      4. unpow2 57.4%

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

      5. unpow2 57.4%

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

      6. hypot-define 89.6%

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

   5. Simplified 89.6%

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

   6. Taylor expanded in B around -inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. unsub-neg 61.6%

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

   8. Simplified 61.6%

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

   if 1.69999999999999996e-284 < C < 1.55e-244

   1. Initial program 74.1%

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

   3. Taylor expanded in B around inf 90.3%

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

   4. Taylor expanded in C around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. distribute-neg-frac2 90.3%

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

   6. Simplified 90.3%

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

   7. Taylor expanded in A around 0 90.3%

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

   9. Simplified 90.3%

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

   if 5.79999999999999984e-89 < C

   1. Initial program 27.3%

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

   3. Taylor expanded in C around inf 61.5%

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

   4. Taylor expanded in A around inf 61.5%

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

   6. Simplified 61.6%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.8 \cdot 10^{-53}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.7 \cdot 10^{-284}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.55 \cdot 10^{-244}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.8 \cdot 10^{-89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.7% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{if}\;B \leq -8 \cdot 10^{-195}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-262}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-24}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ (/ (- C A) B) 1.0)) PI))))
   (if (<= B -8e-195)
     t_0
     (if (<= B -6.2e-262)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 2.5e-24) t_0 (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((((C - A) / B) + 1.0)) / ((double) M_PI));
	double tmp;
	if (B <= -8e-195) {
		tmp = t_0;
	} else if (B <= -6.2e-262) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 2.5e-24) {
		tmp = t_0;
	} else {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((((C - A) / B) + 1.0)) / Math.PI);
	double tmp;
	if (B <= -8e-195) {
		tmp = t_0;
	} else if (B <= -6.2e-262) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 2.5e-24) {
		tmp = t_0;
	} else {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((((C - A) / B) + 1.0)) / math.pi)
	tmp = 0
	if B <= -8e-195:
		tmp = t_0
	elif B <= -6.2e-262:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 2.5e-24:
		tmp = t_0
	else:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + 1.0)) / pi))
	tmp = 0.0
	if (B <= -8e-195)
		tmp = t_0;
	elseif (B <= -6.2e-262)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 2.5e-24)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((((C - A) / B) + 1.0)) / pi);
	tmp = 0.0;
	if (B <= -8e-195)
		tmp = t_0;
	elseif (B <= -6.2e-262)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 2.5e-24)
		tmp = t_0;
	else
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -8e-195], t$95$0, If[LessEqual[B, -6.2e-262], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.5e-24], t$95$0, N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -8.0000000000000007e-195 or -6.1999999999999997e-262 < B < 2.4999999999999999e-24

   1. Initial program 57.0%

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

   3. Taylor expanded in B around -inf 65.1%

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

      1. associate--l+ 65.1%

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

      2. div-sub 66.8%

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

   5. Simplified 66.8%

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

   if -8.0000000000000007e-195 < B < -6.1999999999999997e-262

   1. Initial program 38.5%

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

   3. Taylor expanded in C around inf 73.7%

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

      1. associate-*r/ 73.7%

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

      2. distribute-rgt1-in 73.7%

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

      3. metadata-eval 73.7%

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

      4. mul0-lft 73.7%

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

      5. metadata-eval 73.7%

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

   5. Simplified 73.7%

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

   if 2.4999999999999999e-24 < B

   1. Initial program 48.0%

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

   3. Taylor expanded in B around inf 78.4%

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

   4. Taylor expanded in C around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. distribute-neg-frac2 75.1%

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

   6. Simplified 75.1%

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

   7. Taylor expanded in A around 0 75.1%

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

   9. Simplified 75.1%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8 \cdot 10^{-195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-262}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.7% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{C - A}{B} + 1\right)\\ \mathbf{if}\;B \leq -8 \cdot 10^{-195}:\\ \;\;\;\;\frac{180 \cdot t\_0}{\pi}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-262}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-26}:\\ \;\;\;\;180 \cdot \frac{t\_0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (+ (/ (- C A) B) 1.0))))
   (if (<= B -8e-195)
     (/ (* 180.0 t_0) PI)
     (if (<= B -4.5e-262)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 1.95e-26)
         (* 180.0 (/ t_0 PI))
         (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = atan((((C - A) / B) + 1.0));
	double tmp;
	if (B <= -8e-195) {
		tmp = (180.0 * t_0) / ((double) M_PI);
	} else if (B <= -4.5e-262) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 1.95e-26) {
		tmp = 180.0 * (t_0 / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan((((C - A) / B) + 1.0));
	double tmp;
	if (B <= -8e-195) {
		tmp = (180.0 * t_0) / Math.PI;
	} else if (B <= -4.5e-262) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 1.95e-26) {
		tmp = 180.0 * (t_0 / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan((((C - A) / B) + 1.0))
	tmp = 0
	if B <= -8e-195:
		tmp = (180.0 * t_0) / math.pi
	elif B <= -4.5e-262:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 1.95e-26:
		tmp = 180.0 * (t_0 / math.pi)
	else:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(Float64(Float64(C - A) / B) + 1.0))
	tmp = 0.0
	if (B <= -8e-195)
		tmp = Float64(Float64(180.0 * t_0) / pi);
	elseif (B <= -4.5e-262)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 1.95e-26)
		tmp = Float64(180.0 * Float64(t_0 / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan((((C - A) / B) + 1.0));
	tmp = 0.0;
	if (B <= -8e-195)
		tmp = (180.0 * t_0) / pi;
	elseif (B <= -4.5e-262)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 1.95e-26)
		tmp = 180.0 * (t_0 / pi);
	else
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[B, -8e-195], N[(N[(180.0 * t$95$0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, -4.5e-262], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.95e-26], N[(180.0 * N[(t$95$0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -8.0000000000000007e-195

   1. Initial program 52.7%

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

      1. associate-*r/ 52.6%

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

      2. associate-*l/ 52.7%

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

      3. *-un-lft-identity 52.7%

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

      4. unpow2 52.7%

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

      5. unpow2 52.7%

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

      6. hypot-define 78.7%

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

   4. Applied egg-rr 78.7%

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

   5. Taylor expanded in B around -inf 72.5%

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

      1. associate--l+ 72.5%

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

      2. div-sub 72.5%

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

   7. Simplified 72.5%

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

   if -8.0000000000000007e-195 < B < -4.49999999999999998e-262

   1. Initial program 38.5%

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

   3. Taylor expanded in C around inf 73.7%

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

      1. associate-*r/ 73.7%

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

      2. distribute-rgt1-in 73.7%

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

      3. metadata-eval 73.7%

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

      4. mul0-lft 73.7%

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

      5. metadata-eval 73.7%

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

   5. Simplified 73.7%

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

   if -4.49999999999999998e-262 < B < 1.94999999999999993e-26

   1. Initial program 65.7%

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

   3. Taylor expanded in B around -inf 50.3%

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

      1. associate--l+ 50.3%

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

      2. div-sub 55.4%

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

   5. Simplified 55.4%

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

   if 1.94999999999999993e-26 < B

   1. Initial program 48.0%

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

   3. Taylor expanded in B around inf 78.4%

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

   4. Taylor expanded in C around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. distribute-neg-frac2 75.1%

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

   6. Simplified 75.1%

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

   7. Taylor expanded in A around 0 75.1%

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

   9. Simplified 75.1%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8 \cdot 10^{-195}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-262}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-26}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8 \cdot 10^{-195}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq -6 \cdot 10^{-262}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8e-195)
   (/ (* 180.0 (atan (+ (/ (- C A) B) 1.0))) PI)
   (if (<= B -6e-262)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (/ (* 180.0 (atan (/ (- C (+ A B)) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -8e-195) {
		tmp = (180.0 * atan((((C - A) / B) + 1.0))) / ((double) M_PI);
	} else if (B <= -6e-262) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((C - (A + B)) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -8e-195) {
		tmp = (180.0 * Math.atan((((C - A) / B) + 1.0))) / Math.PI;
	} else if (B <= -6e-262) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((C - (A + B)) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -8e-195:
		tmp = (180.0 * math.atan((((C - A) / B) + 1.0))) / math.pi
	elif B <= -6e-262:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan(((C - (A + B)) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -8e-195)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) / B) + 1.0))) / pi);
	elseif (B <= -6e-262)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - Float64(A + B)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -8e-195)
		tmp = (180.0 * atan((((C - A) / B) + 1.0))) / pi;
	elseif (B <= -6e-262)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = (180.0 * atan(((C - (A + B)) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -8e-195], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, -6e-262], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -8.0000000000000007e-195

   1. Initial program 52.7%

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

      1. associate-*r/ 52.6%

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

      2. associate-*l/ 52.7%

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

      3. *-un-lft-identity 52.7%

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

      4. unpow2 52.7%

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

      5. unpow2 52.7%

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

      6. hypot-define 78.7%

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

   4. Applied egg-rr 78.7%

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

   5. Taylor expanded in B around -inf 72.5%

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

      1. associate--l+ 72.5%

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

      2. div-sub 72.5%

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

   7. Simplified 72.5%

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

   if -8.0000000000000007e-195 < B < -6.00000000000000036e-262

   1. Initial program 38.5%

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

   3. Taylor expanded in C around inf 73.7%

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

      1. associate-*r/ 73.7%

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

      2. distribute-rgt1-in 73.7%

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

      3. metadata-eval 73.7%

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

      4. mul0-lft 73.7%

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

      5. metadata-eval 73.7%

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

   5. Simplified 73.7%

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

   if -6.00000000000000036e-262 < B

   1. Initial program 56.7%

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

   3. Taylor expanded in B around inf 68.7%

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

      1. associate-*r/ 68.7%

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

      2. associate-*l/ 68.7%

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

      3. *-un-lft-identity 68.7%

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

      4. associate--l- 68.7%

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

   5. Applied egg-rr 68.7%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8 \cdot 10^{-195}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq -6 \cdot 10^{-262}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8 \cdot 10^{-195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) + B\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-262}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8e-195)
   (* 180.0 (/ (atan (* (/ 1.0 B) (+ (- C A) B))) PI))
   (if (<= B -1.45e-262)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (/ (* 180.0 (atan (/ (- C (+ A B)) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -8e-195) {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) + B))) / ((double) M_PI));
	} else if (B <= -1.45e-262) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((C - (A + B)) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -8e-195) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C - A) + B))) / Math.PI);
	} else if (B <= -1.45e-262) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((C - (A + B)) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -8e-195:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C - A) + B))) / math.pi)
	elif B <= -1.45e-262:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan(((C - (A + B)) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -8e-195)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) + B))) / pi));
	elseif (B <= -1.45e-262)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - Float64(A + B)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -8e-195)
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) + B))) / pi);
	elseif (B <= -1.45e-262)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = (180.0 * atan(((C - (A + B)) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -8e-195], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] + B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.45e-262], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -8.0000000000000007e-195

   1. Initial program 52.7%

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

   3. Taylor expanded in B around -inf 72.5%

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

      1. neg-mul-1 72.5%

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

   5. Simplified 72.5%

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

   if -8.0000000000000007e-195 < B < -1.44999999999999998e-262

   1. Initial program 38.5%

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

   3. Taylor expanded in C around inf 73.7%

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

      1. associate-*r/ 73.7%

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

      2. distribute-rgt1-in 73.7%

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

      3. metadata-eval 73.7%

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

      4. mul0-lft 73.7%

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

      5. metadata-eval 73.7%

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

   5. Simplified 73.7%

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

   if -1.44999999999999998e-262 < B

   1. Initial program 56.7%

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

   3. Taylor expanded in B around inf 68.7%

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

      1. associate-*r/ 68.7%

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

      2. associate-*l/ 68.7%

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

      3. *-un-lft-identity 68.7%

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

      4. associate--l- 68.7%

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

   5. Applied egg-rr 68.7%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8 \cdot 10^{-195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) + B\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-262}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.8 \cdot 10^{-128}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-114}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.8e-128)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 9.5e-114)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.8e-128) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 9.5e-114) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.8e-128) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 9.5e-114) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.8e-128:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 9.5e-114:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.8e-128)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 9.5e-114)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.8e-128)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 9.5e-114)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.8e-128], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.5e-114], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.80000000000000012e-128

   1. Initial program 50.4%

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

   3. Taylor expanded in B around -inf 53.5%

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

   if -1.80000000000000012e-128 < B < 9.49999999999999958e-114

   1. Initial program 61.3%

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

   3. Taylor expanded in C around inf 38.9%

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

      1. associate-*r/ 38.9%

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

      2. distribute-rgt1-in 38.9%

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

      3. metadata-eval 38.9%

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

      4. mul0-lft 38.9%

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

      5. metadata-eval 38.9%

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

   5. Simplified 38.9%

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

   if 9.49999999999999958e-114 < B

   1. Initial program 51.2%

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

   3. Taylor expanded in B around inf 60.4%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.8 \cdot 10^{-128}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-114}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 40.1% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if B < -4.999999999999985e-310

   1. Initial program 54.0%

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

   3. Taylor expanded in B around -inf 41.9%

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

   if -4.999999999999985e-310 < B

   1. Initial program 54.1%

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

   3. Taylor expanded in B around inf 43.2%

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

4. Final simplification 42.5%

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

Alternative 18: 20.9% 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 54.0%

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

3. Taylor expanded in B around inf 20.4%

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

4. Final simplification 20.4%

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

Reproduce

herbie shell --seed 2024073 
(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)))