ABCF->ab-angle angle

Percentage Accurate: 54.0% → 84.1%

Time: 33.2s

Alternatives: 22

Speedup: 2.4×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.0% 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: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -0.5:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -0.5)
     (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))
     (if (<= t_0 0.0)
       (* (/ 180.0 PI) (atan (/ -0.5 (/ (- C A) B))))
       (/ (* 180.0 (atan (/ (- C (+ A (hypot (- A C) B))) B))) PI)))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	} else if (t_0 <= 0.0) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 / ((C - A) / B)));
	} else {
		tmp = (180.0 * atan(((C - (A + hypot((A - C), B))) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	} else if (t_0 <= 0.0) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 / ((C - A) / B)));
	} else {
		tmp = (180.0 * Math.atan(((C - (A + Math.hypot((A - C), B))) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_0 <= -0.5:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	elif t_0 <= 0.0:
		tmp = (180.0 / math.pi) * math.atan((-0.5 / ((C - A) / B)))
	else:
		tmp = (180.0 * math.atan(((C - (A + math.hypot((A - C), B))) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 / Float64(Float64(C - A) / B))));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - Float64(A + hypot(Float64(A - C), B))) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	elseif (t_0 <= 0.0)
		tmp = (180.0 / pi) * atan((-0.5 / ((C - A) / B)));
	else
		tmp = (180.0 * atan(((C - (A + hypot((A - C), B))) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, If[LessEqual[t$95$0, -0.5], 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], If[LessEqual[t$95$0, 0.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 / N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.5

   1. Initial program 56.3%

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

   3. Simplified 81.2%

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

   if -0.5 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 0.0

   1. Initial program 29.6%

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

   3. Simplified 15.1%

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

   4. Taylor expanded in B around 0 98.9%

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

      1. associate-*r/ 98.9%

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

   6. Simplified 98.9%

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

      1. *-un-lft-identity 98.9%

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

      2. associate-/l* 99.1%

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

   8. Applied egg-rr 99.1%

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

   if 0.0 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 64.4%

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

      1. associate-*r/ 64.5%

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

      2. associate-*l/ 64.5%

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

      3. *-un-lft-identity 64.5%

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

      4. associate--l- 64.5%

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

      5. unpow2 64.5%

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

      6. pow2 64.5%

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

      7. hypot-def 86.3%

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

   3. Applied egg-rr 86.3%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.5:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 2: 81.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.45 \cdot 10^{+18}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.45e+18)
   (/ (* 180.0 (atan (/ (* B -0.5) (- C A)))) PI)
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.45e+18) {
		tmp = (180.0 * atan(((B * -0.5) / (C - A)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.45e+18) {
		tmp = (180.0 * Math.atan(((B * -0.5) / (C - A)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.45e+18:
		tmp = (180.0 * math.atan(((B * -0.5) / (C - A)))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.45e+18)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / Float64(C - A)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.45e+18)
		tmp = (180.0 * atan(((B * -0.5) / (C - A)))) / pi;
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.45e+18], N[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.45e18

   1. Initial program 28.7%

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

   3. Simplified 29.1%

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

   4. Taylor expanded in B around 0 78.8%

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

      1. associate-*r/ 78.8%

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

   6. Simplified 78.8%

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

   7. Taylor expanded in B around 0 78.7%

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

      1. associate-*r/ 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*l/ 78.9%

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

   9. Simplified 78.9%

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

   if -1.45e18 < A

   1. Initial program 63.4%

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

   3. Simplified 86.0%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.45 \cdot 10^{+18}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3: 81.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.5e+18)
   (/ (* 180.0 (atan (/ (* B -0.5) (- C A)))) PI)
   (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B (- C A)))) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.5e+18) {
		tmp = (180.0 * atan(((B * -0.5) / (C - A)))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(B, (C - A)))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.5e+18) {
		tmp = (180.0 * Math.atan(((B * -0.5) / (C - A)))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, (C - A)))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.5e+18:
		tmp = (180.0 * math.atan(((B * -0.5) / (C - A)))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(B, (C - A)))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.5e+18)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / Float64(C - A)))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(B, Float64(C - A)))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.5e+18)
		tmp = (180.0 * atan(((B * -0.5) / (C - A)))) / pi;
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(B, (C - A)))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.5e+18], N[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.5e18

   1. Initial program 28.7%

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

   3. Simplified 29.1%

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

   4. Taylor expanded in B around 0 78.8%

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

      1. associate-*r/ 78.8%

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

   6. Simplified 78.8%

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

   7. Taylor expanded in B around 0 78.7%

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

      1. associate-*r/ 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*l/ 78.9%

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

   9. Simplified 78.9%

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

   if -1.5e18 < A

   1. Initial program 63.4%

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

   3. Simplified 86.0%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \]

Alternative 4: 76.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{+17}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.35e+17)
   (/ (* 180.0 (atan (/ (* B -0.5) (- C A)))) PI)
   (if (<= A 6.8e+72)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (/ (* 180.0 (atan (/ (- B A) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e+17) {
		tmp = (180.0 * atan(((B * -0.5) / (C - A)))) / ((double) M_PI);
	} else if (A <= 6.8e+72) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((B - A) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e+17) {
		tmp = (180.0 * Math.atan(((B * -0.5) / (C - A)))) / Math.PI;
	} else if (A <= 6.8e+72) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((B - A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.35e+17:
		tmp = (180.0 * math.atan(((B * -0.5) / (C - A)))) / math.pi
	elif A <= 6.8e+72:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan(((B - A) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.35e+17)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / Float64(C - A)))) / pi);
	elseif (A <= 6.8e+72)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B - A) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.35e+17)
		tmp = (180.0 * atan(((B * -0.5) / (C - A)))) / pi;
	elseif (A <= 6.8e+72)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = (180.0 * atan(((B - A) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.35e+17], N[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 6.8e+72], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.35e17

   1. Initial program 28.7%

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

   3. Simplified 29.1%

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

   4. Taylor expanded in B around 0 78.8%

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

      1. associate-*r/ 78.8%

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

   6. Simplified 78.8%

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

   7. Taylor expanded in B around 0 78.7%

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

      1. associate-*r/ 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*l/ 78.9%

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

   9. Simplified 78.9%

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

   if -1.35e17 < A < 6.7999999999999997e72

   1. Initial program 59.8%

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

   3. Simplified 59.8%

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

   4. Taylor expanded in A around 0 58.0%

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

      1. unpow2 58.0%

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

      2. unpow2 58.0%

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

      3. hypot-def 81.8%

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

   6. Simplified 81.8%

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

   if 6.7999999999999997e72 < A

   1. Initial program 74.6%

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

      1. associate-*r/ 74.6%

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

      2. associate-*l/ 74.6%

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

      3. *-un-lft-identity 74.6%

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

      4. associate--l- 74.6%

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

      5. unpow2 74.6%

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

      6. pow2 74.6%

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

      7. hypot-def 94.0%

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

   3. Applied egg-rr 94.0%

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

   4. Taylor expanded in B around -inf 81.7%

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

   5. Taylor expanded in C around 0 81.7%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{+17}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 76.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8 \cdot 10^{+18}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.7 \cdot 10^{+71}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8e+18)
   (/ (* 180.0 (atan (/ (* B -0.5) (- C A)))) PI)
   (if (<= A 2.7e+71)
     (/ (* 180.0 (atan (/ (- C (hypot B C)) B))) PI)
     (/ (* 180.0 (atan (/ (- B A) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8e+18) {
		tmp = (180.0 * atan(((B * -0.5) / (C - A)))) / ((double) M_PI);
	} else if (A <= 2.7e+71) {
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(((B - A) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8e+18) {
		tmp = (180.0 * Math.atan(((B * -0.5) / (C - A)))) / Math.PI;
	} else if (A <= 2.7e+71) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(B, C)) / B))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan(((B - A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8e+18:
		tmp = (180.0 * math.atan(((B * -0.5) / (C - A)))) / math.pi
	elif A <= 2.7e+71:
		tmp = (180.0 * math.atan(((C - math.hypot(B, C)) / B))) / math.pi
	else:
		tmp = (180.0 * math.atan(((B - A) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8e+18)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / Float64(C - A)))) / pi);
	elseif (A <= 2.7e+71)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(B, C)) / B))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B - A) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8e+18)
		tmp = (180.0 * atan(((B * -0.5) / (C - A)))) / pi;
	elseif (A <= 2.7e+71)
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / pi;
	else
		tmp = (180.0 * atan(((B - A) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8e+18], N[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 2.7e+71], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8e18

   1. Initial program 28.7%

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

   3. Simplified 29.1%

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

   4. Taylor expanded in B around 0 78.8%

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

      1. associate-*r/ 78.8%

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

   6. Simplified 78.8%

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

   7. Taylor expanded in B around 0 78.7%

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

      1. associate-*r/ 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*l/ 78.9%

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

   9. Simplified 78.9%

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

   if -8e18 < A < 2.69999999999999997e71

   1. Initial program 59.8%

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

      1. associate-*r/ 59.8%

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

      2. associate-*l/ 59.8%

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

      3. *-un-lft-identity 59.8%

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

      4. associate--l- 59.8%

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

      5. unpow2 59.8%

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

      6. pow2 59.8%

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

      7. hypot-def 83.5%

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

   3. Applied egg-rr 83.5%

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

   4. Taylor expanded in A around 0 58.0%

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

      1. unpow2 58.0%

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

      2. unpow2 58.0%

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

      3. hypot-def 81.9%

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

   6. Simplified 81.9%

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

   if 2.69999999999999997e71 < A

   1. Initial program 74.6%

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

      1. associate-*r/ 74.6%

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

      2. associate-*l/ 74.6%

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

      3. *-un-lft-identity 74.6%

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

      4. associate--l- 74.6%

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

      5. unpow2 74.6%

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

      6. pow2 74.6%

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

      7. hypot-def 94.0%

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

   3. Applied egg-rr 94.0%

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

   4. Taylor expanded in B around -inf 81.7%

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

   5. Taylor expanded in C around 0 81.7%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8 \cdot 10^{+18}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.7 \cdot 10^{+71}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 6: 45.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ t_1 := \frac{180 \cdot \tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -4.3 \cdot 10^{-7}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-92}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -2.8 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-180}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7.1 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (* B 0.5) A)) PI)))
        (t_1 (/ (* 180.0 (atan (- (/ A B)))) PI))
        (t_2 (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))))
   (if (<= B -4.3e-7)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -7.5e-92)
       t_0
       (if (<= B -9.5e-120)
         t_2
         (if (<= B -2.8e-205)
           t_1
           (if (<= B 1.2e-180)
             t_0
             (if (<= B 7.1e-130)
               t_1
               (if (<= B 1.15e-17) t_2 (* 180.0 (/ (atan -1.0) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	double t_1 = (180.0 * atan(-(A / B))) / ((double) M_PI);
	double t_2 = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	double tmp;
	if (B <= -4.3e-7) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -7.5e-92) {
		tmp = t_0;
	} else if (B <= -9.5e-120) {
		tmp = t_2;
	} else if (B <= -2.8e-205) {
		tmp = t_1;
	} else if (B <= 1.2e-180) {
		tmp = t_0;
	} else if (B <= 7.1e-130) {
		tmp = t_1;
	} else if (B <= 1.15e-17) {
		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(((B * 0.5) / A)) / Math.PI);
	double t_1 = (180.0 * Math.atan(-(A / B))) / Math.PI;
	double t_2 = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	double tmp;
	if (B <= -4.3e-7) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -7.5e-92) {
		tmp = t_0;
	} else if (B <= -9.5e-120) {
		tmp = t_2;
	} else if (B <= -2.8e-205) {
		tmp = t_1;
	} else if (B <= 1.2e-180) {
		tmp = t_0;
	} else if (B <= 7.1e-130) {
		tmp = t_1;
	} else if (B <= 1.15e-17) {
		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(((B * 0.5) / A)) / math.pi)
	t_1 = (180.0 * math.atan(-(A / B))) / math.pi
	t_2 = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	tmp = 0
	if B <= -4.3e-7:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -7.5e-92:
		tmp = t_0
	elif B <= -9.5e-120:
		tmp = t_2
	elif B <= -2.8e-205:
		tmp = t_1
	elif B <= 1.2e-180:
		tmp = t_0
	elif B <= 7.1e-130:
		tmp = t_1
	elif B <= 1.15e-17:
		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(Float64(B * 0.5) / A)) / pi))
	t_1 = Float64(Float64(180.0 * atan(Float64(-Float64(A / B)))) / pi)
	t_2 = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi))
	tmp = 0.0
	if (B <= -4.3e-7)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -7.5e-92)
		tmp = t_0;
	elseif (B <= -9.5e-120)
		tmp = t_2;
	elseif (B <= -2.8e-205)
		tmp = t_1;
	elseif (B <= 1.2e-180)
		tmp = t_0;
	elseif (B <= 7.1e-130)
		tmp = t_1;
	elseif (B <= 1.15e-17)
		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(((B * 0.5) / A)) / pi);
	t_1 = (180.0 * atan(-(A / B))) / pi;
	t_2 = 180.0 * (atan(((B * -0.5) / C)) / pi);
	tmp = 0.0;
	if (B <= -4.3e-7)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -7.5e-92)
		tmp = t_0;
	elseif (B <= -9.5e-120)
		tmp = t_2;
	elseif (B <= -2.8e-205)
		tmp = t_1;
	elseif (B <= 1.2e-180)
		tmp = t_0;
	elseif (B <= 7.1e-130)
		tmp = t_1;
	elseif (B <= 1.15e-17)
		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[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 * N[ArcTan[(-N[(A / B), $MachinePrecision])], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -4.3e-7], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7.5e-92], t$95$0, If[LessEqual[B, -9.5e-120], t$95$2, If[LessEqual[B, -2.8e-205], t$95$1, If[LessEqual[B, 1.2e-180], t$95$0, If[LessEqual[B, 7.1e-130], t$95$1, If[LessEqual[B, 1.15e-17], t$95$2, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -4.3000000000000001e-7

   1. Initial program 59.6%

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

   3. Simplified 59.6%

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

   4. Taylor expanded in B around -inf 72.0%

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

   if -4.3000000000000001e-7 < B < -7.5000000000000005e-92 or -2.79999999999999991e-205 < B < 1.1999999999999999e-180

   1. Initial program 54.0%

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

   3. Simplified 45.3%

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

   4. Taylor expanded in A around -inf 51.2%

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

      1. associate-*r/ 51.2%

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

   6. Simplified 51.2%

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

   if -7.5000000000000005e-92 < B < -9.49999999999999937e-120 or 7.1000000000000001e-130 < B < 1.15000000000000004e-17

   1. Initial program 42.3%

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

   3. Simplified 42.5%

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

   4. Taylor expanded in A around 0 28.3%

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

      1. unpow2 28.3%

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

      2. unpow2 28.3%

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

      3. hypot-def 38.7%

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

   6. Simplified 38.7%

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

   7. Taylor expanded in C around inf 45.9%

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

      1. associate-*r/ 45.9%

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

   9. Simplified 45.9%

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

   if -9.49999999999999937e-120 < B < -2.79999999999999991e-205 or 1.1999999999999999e-180 < B < 7.1000000000000001e-130

   1. Initial program 69.2%

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

      1. associate-*r/ 69.2%

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

      2. associate-*l/ 69.2%

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

      3. *-un-lft-identity 69.2%

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

      4. associate--l- 69.4%

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

      5. unpow2 69.4%

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

      6. pow2 69.4%

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

      7. hypot-def 78.7%

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

   3. Applied egg-rr 78.7%

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

   4. Taylor expanded in B around -inf 71.8%

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

   5. Taylor expanded in A around inf 53.7%

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

      1. mul-1-neg 53.7%

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

   7. Simplified 53.7%

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

   if 1.15000000000000004e-17 < B

   1. Initial program 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in B around inf 74.8%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.3 \cdot 10^{-7}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-92}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.8 \cdot 10^{-205}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-180}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.1 \cdot 10^{-130}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 7: 45.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -3 \cdot 10^{-13}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-92}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3.3 \cdot 10^{-121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -4.2 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-180}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.65 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (* B 0.5) A)) PI)))
        (t_1 (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))
        (t_2 (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))))
   (if (<= B -3e-13)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -2e-92)
       t_0
       (if (<= B -3.3e-121)
         t_2
         (if (<= B -4.2e-204)
           t_1
           (if (<= B 1.8e-180)
             t_0
             (if (<= B 2.65e-129)
               t_1
               (if (<= B 1.1e-17) t_2 (* 180.0 (/ (atan -1.0) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	double t_1 = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	double t_2 = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	double tmp;
	if (B <= -3e-13) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2e-92) {
		tmp = t_0;
	} else if (B <= -3.3e-121) {
		tmp = t_2;
	} else if (B <= -4.2e-204) {
		tmp = t_1;
	} else if (B <= 1.8e-180) {
		tmp = t_0;
	} else if (B <= 2.65e-129) {
		tmp = t_1;
	} else if (B <= 1.1e-17) {
		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(((B * 0.5) / A)) / Math.PI);
	double t_1 = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	double t_2 = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	double tmp;
	if (B <= -3e-13) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2e-92) {
		tmp = t_0;
	} else if (B <= -3.3e-121) {
		tmp = t_2;
	} else if (B <= -4.2e-204) {
		tmp = t_1;
	} else if (B <= 1.8e-180) {
		tmp = t_0;
	} else if (B <= 2.65e-129) {
		tmp = t_1;
	} else if (B <= 1.1e-17) {
		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(((B * 0.5) / A)) / math.pi)
	t_1 = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	t_2 = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	tmp = 0
	if B <= -3e-13:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2e-92:
		tmp = t_0
	elif B <= -3.3e-121:
		tmp = t_2
	elif B <= -4.2e-204:
		tmp = t_1
	elif B <= 1.8e-180:
		tmp = t_0
	elif B <= 2.65e-129:
		tmp = t_1
	elif B <= 1.1e-17:
		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(Float64(B * 0.5) / A)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi))
	t_2 = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi))
	tmp = 0.0
	if (B <= -3e-13)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2e-92)
		tmp = t_0;
	elseif (B <= -3.3e-121)
		tmp = t_2;
	elseif (B <= -4.2e-204)
		tmp = t_1;
	elseif (B <= 1.8e-180)
		tmp = t_0;
	elseif (B <= 2.65e-129)
		tmp = t_1;
	elseif (B <= 1.1e-17)
		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(((B * 0.5) / A)) / pi);
	t_1 = 180.0 * (atan(((A * -2.0) / B)) / pi);
	t_2 = 180.0 * (atan(((B * -0.5) / C)) / pi);
	tmp = 0.0;
	if (B <= -3e-13)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2e-92)
		tmp = t_0;
	elseif (B <= -3.3e-121)
		tmp = t_2;
	elseif (B <= -4.2e-204)
		tmp = t_1;
	elseif (B <= 1.8e-180)
		tmp = t_0;
	elseif (B <= 2.65e-129)
		tmp = t_1;
	elseif (B <= 1.1e-17)
		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[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3e-13], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2e-92], t$95$0, If[LessEqual[B, -3.3e-121], t$95$2, If[LessEqual[B, -4.2e-204], t$95$1, If[LessEqual[B, 1.8e-180], t$95$0, If[LessEqual[B, 2.65e-129], t$95$1, If[LessEqual[B, 1.1e-17], t$95$2, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.99999999999999984e-13

   1. Initial program 59.6%

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

   3. Simplified 59.6%

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

   4. Taylor expanded in B around -inf 72.0%

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

   if -2.99999999999999984e-13 < B < -1.99999999999999998e-92 or -4.20000000000000018e-204 < B < 1.8e-180

   1. Initial program 54.0%

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

   3. Simplified 45.3%

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

   4. Taylor expanded in A around -inf 51.2%

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

      1. associate-*r/ 51.2%

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

   6. Simplified 51.2%

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

   if -1.99999999999999998e-92 < B < -3.3000000000000001e-121 or 2.64999999999999987e-129 < B < 1.1e-17

   1. Initial program 42.3%

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

   3. Simplified 42.5%

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

   4. Taylor expanded in A around 0 28.3%

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

      1. unpow2 28.3%

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

      2. unpow2 28.3%

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

      3. hypot-def 38.7%

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

   6. Simplified 38.7%

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

   7. Taylor expanded in C around inf 45.9%

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

      1. associate-*r/ 45.9%

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

   9. Simplified 45.9%

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

   if -3.3000000000000001e-121 < B < -4.20000000000000018e-204 or 1.8e-180 < B < 2.64999999999999987e-129

   1. Initial program 69.2%

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

   3. Simplified 69.4%

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

   4. Taylor expanded in A around inf 53.7%

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

      1. associate-*r/ 53.7%

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

      2. *-commutative 53.7%

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

   6. Simplified 53.7%

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

   if 1.1e-17 < B

   1. Initial program 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in B around inf 74.8%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3 \cdot 10^{-13}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-92}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.3 \cdot 10^{-121}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.2 \cdot 10^{-204}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-180}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.65 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 8: 59.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -9 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-147}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-230}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A)))))
        (t_1 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B -9e-49)
     t_1
     (if (<= B -4.8e-147)
       t_0
       (if (<= B -6.5e-195)
         t_1
         (if (<= B 6e-230)
           t_0
           (if (<= B 6.5e-136)
             t_1
             (if (<= B 1.22e-17) t_0 (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	double t_1 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (B <= -9e-49) {
		tmp = t_1;
	} else if (B <= -4.8e-147) {
		tmp = t_0;
	} else if (B <= -6.5e-195) {
		tmp = t_1;
	} else if (B <= 6e-230) {
		tmp = t_0;
	} else if (B <= 6.5e-136) {
		tmp = t_1;
	} else if (B <= 1.22e-17) {
		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.PI) * Math.atan(((B * -0.5) / (C - A)));
	double t_1 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= -9e-49) {
		tmp = t_1;
	} else if (B <= -4.8e-147) {
		tmp = t_0;
	} else if (B <= -6.5e-195) {
		tmp = t_1;
	} else if (B <= 6e-230) {
		tmp = t_0;
	} else if (B <= 6.5e-136) {
		tmp = t_1;
	} else if (B <= 1.22e-17) {
		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.pi) * math.atan(((B * -0.5) / (C - A)))
	t_1 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= -9e-49:
		tmp = t_1
	elif B <= -4.8e-147:
		tmp = t_0
	elif B <= -6.5e-195:
		tmp = t_1
	elif B <= 6e-230:
		tmp = t_0
	elif B <= 6.5e-136:
		tmp = t_1
	elif B <= 1.22e-17:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))))
	t_1 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= -9e-49)
		tmp = t_1;
	elseif (B <= -4.8e-147)
		tmp = t_0;
	elseif (B <= -6.5e-195)
		tmp = t_1;
	elseif (B <= 6e-230)
		tmp = t_0;
	elseif (B <= 6.5e-136)
		tmp = t_1;
	elseif (B <= 1.22e-17)
		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 / pi) * atan(((B * -0.5) / (C - A)));
	t_1 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= -9e-49)
		tmp = t_1;
	elseif (B <= -4.8e-147)
		tmp = t_0;
	elseif (B <= -6.5e-195)
		tmp = t_1;
	elseif (B <= 6e-230)
		tmp = t_0;
	elseif (B <= 6.5e-136)
		tmp = t_1;
	elseif (B <= 1.22e-17)
		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[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -9e-49], t$95$1, If[LessEqual[B, -4.8e-147], t$95$0, If[LessEqual[B, -6.5e-195], t$95$1, If[LessEqual[B, 6e-230], t$95$0, If[LessEqual[B, 6.5e-136], t$95$1, If[LessEqual[B, 1.22e-17], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -9.0000000000000004e-49 or -4.79999999999999997e-147 < B < -6.50000000000000004e-195 or 6e-230 < B < 6.50000000000000011e-136

   1. Initial program 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in B around -inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. div-sub 79.2%

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

   6. Simplified 79.2%

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

   if -9.0000000000000004e-49 < B < -4.79999999999999997e-147 or -6.50000000000000004e-195 < B < 6e-230 or 6.50000000000000011e-136 < B < 1.22e-17

   1. Initial program 49.2%

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

   3. Simplified 50.6%

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

   4. Taylor expanded in B around 0 65.8%

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

      1. associate-*r/ 65.8%

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

   6. Simplified 65.8%

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

   if 1.22e-17 < B

   1. Initial program 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in B around inf 74.8%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9 \cdot 10^{-49}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-147}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-230}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-136}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{-17}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 9: 59.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ t_1 := \frac{C - A}{B}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(1 + t_1\right)}{\pi}\\ \mathbf{if}\;B \leq -1.12 \cdot 10^{-48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{-141}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.14 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-230}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5}{t_1}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.6 \cdot 10^{-133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A)))))
        (t_1 (/ (- C A) B))
        (t_2 (* 180.0 (/ (atan (+ 1.0 t_1)) PI))))
   (if (<= B -1.12e-48)
     t_2
     (if (<= B -1.15e-141)
       t_0
       (if (<= B -1.14e-197)
         t_2
         (if (<= B 1.1e-230)
           (/ (* 180.0 (atan (/ -0.5 t_1))) PI)
           (if (<= B 8.6e-133)
             t_2
             (if (<= B 1.22e-17) t_0 (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	double t_1 = (C - A) / B;
	double t_2 = 180.0 * (atan((1.0 + t_1)) / ((double) M_PI));
	double tmp;
	if (B <= -1.12e-48) {
		tmp = t_2;
	} else if (B <= -1.15e-141) {
		tmp = t_0;
	} else if (B <= -1.14e-197) {
		tmp = t_2;
	} else if (B <= 1.1e-230) {
		tmp = (180.0 * atan((-0.5 / t_1))) / ((double) M_PI);
	} else if (B <= 8.6e-133) {
		tmp = t_2;
	} else if (B <= 1.22e-17) {
		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.PI) * Math.atan(((B * -0.5) / (C - A)));
	double t_1 = (C - A) / B;
	double t_2 = 180.0 * (Math.atan((1.0 + t_1)) / Math.PI);
	double tmp;
	if (B <= -1.12e-48) {
		tmp = t_2;
	} else if (B <= -1.15e-141) {
		tmp = t_0;
	} else if (B <= -1.14e-197) {
		tmp = t_2;
	} else if (B <= 1.1e-230) {
		tmp = (180.0 * Math.atan((-0.5 / t_1))) / Math.PI;
	} else if (B <= 8.6e-133) {
		tmp = t_2;
	} else if (B <= 1.22e-17) {
		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.pi) * math.atan(((B * -0.5) / (C - A)))
	t_1 = (C - A) / B
	t_2 = 180.0 * (math.atan((1.0 + t_1)) / math.pi)
	tmp = 0
	if B <= -1.12e-48:
		tmp = t_2
	elif B <= -1.15e-141:
		tmp = t_0
	elif B <= -1.14e-197:
		tmp = t_2
	elif B <= 1.1e-230:
		tmp = (180.0 * math.atan((-0.5 / t_1))) / math.pi
	elif B <= 8.6e-133:
		tmp = t_2
	elif B <= 1.22e-17:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))))
	t_1 = Float64(Float64(C - A) / B)
	t_2 = Float64(180.0 * Float64(atan(Float64(1.0 + t_1)) / pi))
	tmp = 0.0
	if (B <= -1.12e-48)
		tmp = t_2;
	elseif (B <= -1.15e-141)
		tmp = t_0;
	elseif (B <= -1.14e-197)
		tmp = t_2;
	elseif (B <= 1.1e-230)
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 / t_1))) / pi);
	elseif (B <= 8.6e-133)
		tmp = t_2;
	elseif (B <= 1.22e-17)
		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 / pi) * atan(((B * -0.5) / (C - A)));
	t_1 = (C - A) / B;
	t_2 = 180.0 * (atan((1.0 + t_1)) / pi);
	tmp = 0.0;
	if (B <= -1.12e-48)
		tmp = t_2;
	elseif (B <= -1.15e-141)
		tmp = t_0;
	elseif (B <= -1.14e-197)
		tmp = t_2;
	elseif (B <= 1.1e-230)
		tmp = (180.0 * atan((-0.5 / t_1))) / pi;
	elseif (B <= 8.6e-133)
		tmp = t_2;
	elseif (B <= 1.22e-17)
		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[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$1), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.12e-48], t$95$2, If[LessEqual[B, -1.15e-141], t$95$0, If[LessEqual[B, -1.14e-197], t$95$2, If[LessEqual[B, 1.1e-230], N[(N[(180.0 * N[ArcTan[N[(-0.5 / t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 8.6e-133], t$95$2, If[LessEqual[B, 1.22e-17], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.11999999999999999e-48 or -1.14999999999999997e-141 < B < -1.14000000000000006e-197 or 1.0999999999999999e-230 < B < 8.60000000000000032e-133

   1. Initial program 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in B around -inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. div-sub 79.2%

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

   6. Simplified 79.2%

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

   if -1.11999999999999999e-48 < B < -1.14999999999999997e-141 or 8.60000000000000032e-133 < B < 1.22e-17

   1. Initial program 40.2%

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

   3. Simplified 47.4%

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

   4. Taylor expanded in B around 0 64.1%

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

      1. associate-*r/ 64.1%

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

   6. Simplified 64.1%

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

   if -1.14000000000000006e-197 < B < 1.0999999999999999e-230

   1. Initial program 58.8%

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

   3. Simplified 54.1%

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

   4. Taylor expanded in B around 0 67.6%

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

      1. associate-*r/ 67.6%

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

   6. Simplified 67.6%

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

      1. associate-*l/ 67.6%

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

      2. associate-/l* 67.6%

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

   8. Applied egg-rr 67.6%

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

   if 1.22e-17 < B

   1. Initial program 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in B around inf 74.8%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.12 \cdot 10^{-48}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.15 \cdot 10^{-141}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;B \leq -1.14 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-230}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.6 \cdot 10^{-133}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{-17}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 10: 59.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ t_1 := \frac{C - A}{B}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(1 + t_1\right)}{\pi}\\ \mathbf{if}\;B \leq -9.4 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -1.02 \cdot 10^{-143}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.36 \cdot 10^{-193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 2.45 \cdot 10^{-228}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5}{t_1}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ (* B -0.5) (- C A)))) PI))
        (t_1 (/ (- C A) B))
        (t_2 (* 180.0 (/ (atan (+ 1.0 t_1)) PI))))
   (if (<= B -9.4e-49)
     t_2
     (if (<= B -1.02e-143)
       t_0
       (if (<= B -1.36e-193)
         t_2
         (if (<= B 2.45e-228)
           (/ (* 180.0 (atan (/ -0.5 t_1))) PI)
           (if (<= B 1.5e-133)
             t_2
             (if (<= B 1.22e-17) t_0 (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan(((B * -0.5) / (C - A)))) / ((double) M_PI);
	double t_1 = (C - A) / B;
	double t_2 = 180.0 * (atan((1.0 + t_1)) / ((double) M_PI));
	double tmp;
	if (B <= -9.4e-49) {
		tmp = t_2;
	} else if (B <= -1.02e-143) {
		tmp = t_0;
	} else if (B <= -1.36e-193) {
		tmp = t_2;
	} else if (B <= 2.45e-228) {
		tmp = (180.0 * atan((-0.5 / t_1))) / ((double) M_PI);
	} else if (B <= 1.5e-133) {
		tmp = t_2;
	} else if (B <= 1.22e-17) {
		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(((B * -0.5) / (C - A)))) / Math.PI;
	double t_1 = (C - A) / B;
	double t_2 = 180.0 * (Math.atan((1.0 + t_1)) / Math.PI);
	double tmp;
	if (B <= -9.4e-49) {
		tmp = t_2;
	} else if (B <= -1.02e-143) {
		tmp = t_0;
	} else if (B <= -1.36e-193) {
		tmp = t_2;
	} else if (B <= 2.45e-228) {
		tmp = (180.0 * Math.atan((-0.5 / t_1))) / Math.PI;
	} else if (B <= 1.5e-133) {
		tmp = t_2;
	} else if (B <= 1.22e-17) {
		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(((B * -0.5) / (C - A)))) / math.pi
	t_1 = (C - A) / B
	t_2 = 180.0 * (math.atan((1.0 + t_1)) / math.pi)
	tmp = 0
	if B <= -9.4e-49:
		tmp = t_2
	elif B <= -1.02e-143:
		tmp = t_0
	elif B <= -1.36e-193:
		tmp = t_2
	elif B <= 2.45e-228:
		tmp = (180.0 * math.atan((-0.5 / t_1))) / math.pi
	elif B <= 1.5e-133:
		tmp = t_2
	elif B <= 1.22e-17:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / Float64(C - A)))) / pi)
	t_1 = Float64(Float64(C - A) / B)
	t_2 = Float64(180.0 * Float64(atan(Float64(1.0 + t_1)) / pi))
	tmp = 0.0
	if (B <= -9.4e-49)
		tmp = t_2;
	elseif (B <= -1.02e-143)
		tmp = t_0;
	elseif (B <= -1.36e-193)
		tmp = t_2;
	elseif (B <= 2.45e-228)
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 / t_1))) / pi);
	elseif (B <= 1.5e-133)
		tmp = t_2;
	elseif (B <= 1.22e-17)
		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(((B * -0.5) / (C - A)))) / pi;
	t_1 = (C - A) / B;
	t_2 = 180.0 * (atan((1.0 + t_1)) / pi);
	tmp = 0.0;
	if (B <= -9.4e-49)
		tmp = t_2;
	elseif (B <= -1.02e-143)
		tmp = t_0;
	elseif (B <= -1.36e-193)
		tmp = t_2;
	elseif (B <= 2.45e-228)
		tmp = (180.0 * atan((-0.5 / t_1))) / pi;
	elseif (B <= 1.5e-133)
		tmp = t_2;
	elseif (B <= 1.22e-17)
		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[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$1), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -9.4e-49], t$95$2, If[LessEqual[B, -1.02e-143], t$95$0, If[LessEqual[B, -1.36e-193], t$95$2, If[LessEqual[B, 2.45e-228], N[(N[(180.0 * N[ArcTan[N[(-0.5 / t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.5e-133], t$95$2, If[LessEqual[B, 1.22e-17], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -9.40000000000000043e-49 or -1.02e-143 < B < -1.36000000000000004e-193 or 2.44999999999999994e-228 < B < 1.5000000000000001e-133

   1. Initial program 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in B around -inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. div-sub 79.2%

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

   6. Simplified 79.2%

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

   if -9.40000000000000043e-49 < B < -1.02e-143 or 1.5000000000000001e-133 < B < 1.22e-17

   1. Initial program 40.2%

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

   3. Simplified 47.4%

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

   4. Taylor expanded in B around 0 64.1%

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

      1. associate-*r/ 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in B around 0 64.0%

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

      1. associate-*r/ 64.2%

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

      2. *-commutative 64.2%

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

      3. associate-*l/ 64.2%

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

   9. Simplified 64.2%

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

   if -1.36000000000000004e-193 < B < 2.44999999999999994e-228

   1. Initial program 58.8%

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

   3. Simplified 54.1%

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

   4. Taylor expanded in B around 0 67.6%

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

      1. associate-*r/ 67.6%

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

   6. Simplified 67.6%

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

      1. associate-*l/ 67.6%

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

      2. associate-/l* 67.6%

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

   8. Applied egg-rr 67.6%

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

   if 1.22e-17 < B

   1. Initial program 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in B around inf 74.8%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9.4 \cdot 10^{-49}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.02 \cdot 10^{-143}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.36 \cdot 10^{-193}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.45 \cdot 10^{-228}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-133}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{-17}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11: 59.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ t_1 := \frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{if}\;B \leq -9.2 \cdot 10^{-49}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.5 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-228}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5}{t_0}\right)}{\pi}\\ \mathbf{elif}\;B \leq 10^{-131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B))
        (t_1 (/ (* 180.0 (atan (/ (* B -0.5) (- C A)))) PI))
        (t_2 (* 180.0 (/ (atan (+ 1.0 t_0)) PI))))
   (if (<= B -9.2e-49)
     (/ (* 180.0 (atan (/ (- (+ B C) A) B))) PI)
     (if (<= B -2.5e-140)
       t_1
       (if (<= B -3.5e-194)
         t_2
         (if (<= B 1.5e-228)
           (/ (* 180.0 (atan (/ -0.5 t_0))) PI)
           (if (<= B 1e-131)
             t_2
             (if (<= B 1.22e-17) t_1 (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double t_1 = (180.0 * atan(((B * -0.5) / (C - A)))) / ((double) M_PI);
	double t_2 = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	double tmp;
	if (B <= -9.2e-49) {
		tmp = (180.0 * atan((((B + C) - A) / B))) / ((double) M_PI);
	} else if (B <= -2.5e-140) {
		tmp = t_1;
	} else if (B <= -3.5e-194) {
		tmp = t_2;
	} else if (B <= 1.5e-228) {
		tmp = (180.0 * atan((-0.5 / t_0))) / ((double) M_PI);
	} else if (B <= 1e-131) {
		tmp = t_2;
	} else if (B <= 1.22e-17) {
		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 = (C - A) / B;
	double t_1 = (180.0 * Math.atan(((B * -0.5) / (C - A)))) / Math.PI;
	double t_2 = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	double tmp;
	if (B <= -9.2e-49) {
		tmp = (180.0 * Math.atan((((B + C) - A) / B))) / Math.PI;
	} else if (B <= -2.5e-140) {
		tmp = t_1;
	} else if (B <= -3.5e-194) {
		tmp = t_2;
	} else if (B <= 1.5e-228) {
		tmp = (180.0 * Math.atan((-0.5 / t_0))) / Math.PI;
	} else if (B <= 1e-131) {
		tmp = t_2;
	} else if (B <= 1.22e-17) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	t_1 = (180.0 * math.atan(((B * -0.5) / (C - A)))) / math.pi
	t_2 = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	tmp = 0
	if B <= -9.2e-49:
		tmp = (180.0 * math.atan((((B + C) - A) / B))) / math.pi
	elif B <= -2.5e-140:
		tmp = t_1
	elif B <= -3.5e-194:
		tmp = t_2
	elif B <= 1.5e-228:
		tmp = (180.0 * math.atan((-0.5 / t_0))) / math.pi
	elif B <= 1e-131:
		tmp = t_2
	elif B <= 1.22e-17:
		tmp = t_1
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	t_1 = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / Float64(C - A)))) / pi)
	t_2 = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi))
	tmp = 0.0
	if (B <= -9.2e-49)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(B + C) - A) / B))) / pi);
	elseif (B <= -2.5e-140)
		tmp = t_1;
	elseif (B <= -3.5e-194)
		tmp = t_2;
	elseif (B <= 1.5e-228)
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 / t_0))) / pi);
	elseif (B <= 1e-131)
		tmp = t_2;
	elseif (B <= 1.22e-17)
		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 = (C - A) / B;
	t_1 = (180.0 * atan(((B * -0.5) / (C - A)))) / pi;
	t_2 = 180.0 * (atan((1.0 + t_0)) / pi);
	tmp = 0.0;
	if (B <= -9.2e-49)
		tmp = (180.0 * atan((((B + C) - A) / B))) / pi;
	elseif (B <= -2.5e-140)
		tmp = t_1;
	elseif (B <= -3.5e-194)
		tmp = t_2;
	elseif (B <= 1.5e-228)
		tmp = (180.0 * atan((-0.5 / t_0))) / pi;
	elseif (B <= 1e-131)
		tmp = t_2;
	elseif (B <= 1.22e-17)
		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[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -9.2e-49], N[(N[(180.0 * N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, -2.5e-140], t$95$1, If[LessEqual[B, -3.5e-194], t$95$2, If[LessEqual[B, 1.5e-228], N[(N[(180.0 * N[ArcTan[N[(-0.5 / t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1e-131], t$95$2, If[LessEqual[B, 1.22e-17], t$95$1, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -9.1999999999999996e-49

   1. Initial program 59.2%

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

      1. associate-*r/ 59.2%

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

      2. associate-*l/ 59.2%

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

      3. *-un-lft-identity 59.2%

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

      4. associate--l- 59.3%

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

      5. unpow2 59.3%

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

      6. pow2 59.3%

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

      7. hypot-def 84.7%

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

   3. Applied egg-rr 84.7%

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

   4. Taylor expanded in B around -inf 83.2%

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

   if -9.1999999999999996e-49 < B < -2.50000000000000007e-140 or 9.9999999999999999e-132 < B < 1.22e-17

   1. Initial program 40.2%

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

   3. Simplified 47.4%

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

   4. Taylor expanded in B around 0 64.1%

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

      1. associate-*r/ 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in B around 0 64.0%

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

      1. associate-*r/ 64.2%

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

      2. *-commutative 64.2%

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

      3. associate-*l/ 64.2%

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

   9. Simplified 64.2%

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

   if -2.50000000000000007e-140 < B < -3.5000000000000003e-194 or 1.5e-228 < B < 9.9999999999999999e-132

   1. Initial program 68.9%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in B around -inf 68.2%

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

      1. associate--l+ 68.2%

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

      2. div-sub 71.1%

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

   6. Simplified 71.1%

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

   if -3.5000000000000003e-194 < B < 1.5e-228

   1. Initial program 58.8%

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

   3. Simplified 54.1%

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

   4. Taylor expanded in B around 0 67.6%

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

      1. associate-*r/ 67.6%

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

   6. Simplified 67.6%

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

      1. associate-*l/ 67.6%

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

      2. associate-/l* 67.6%

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

   8. Applied egg-rr 67.6%

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

   if 1.22e-17 < B

   1. Initial program 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in B around inf 74.8%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9.2 \cdot 10^{-49}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.5 \cdot 10^{-140}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-194}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-228}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi}\\ \mathbf{elif}\;B \leq 10^{-131}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{-17}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12: 57.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.45 \cdot 10^{-205}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-232}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-130}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-75}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{+28}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B -1.45e-205)
     t_0
     (if (<= B 5e-232)
       (/ (* 180.0 (atan 0.0)) PI)
       (if (<= B 6.8e-130)
         t_0
         (if (<= B 9.5e-75)
           (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))
           (if (<= B 1.45e+28) t_0 (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (B <= -1.45e-205) {
		tmp = t_0;
	} else if (B <= 5e-232) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (B <= 6.8e-130) {
		tmp = t_0;
	} else if (B <= 9.5e-75) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	} else if (B <= 1.45e+28) {
		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((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= -1.45e-205) {
		tmp = t_0;
	} else if (B <= 5e-232) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (B <= 6.8e-130) {
		tmp = t_0;
	} else if (B <= 9.5e-75) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	} else if (B <= 1.45e+28) {
		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((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= -1.45e-205:
		tmp = t_0
	elif B <= 5e-232:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif B <= 6.8e-130:
		tmp = t_0
	elif B <= 9.5e-75:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	elif B <= 1.45e+28:
		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(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= -1.45e-205)
		tmp = t_0;
	elseif (B <= 5e-232)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (B <= 6.8e-130)
		tmp = t_0;
	elseif (B <= 9.5e-75)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	elseif (B <= 1.45e+28)
		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((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= -1.45e-205)
		tmp = t_0;
	elseif (B <= 5e-232)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (B <= 6.8e-130)
		tmp = t_0;
	elseif (B <= 9.5e-75)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	elseif (B <= 1.45e+28)
		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[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.45e-205], t$95$0, If[LessEqual[B, 5e-232], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 6.8e-130], t$95$0, If[LessEqual[B, 9.5e-75], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.45e+28], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.45000000000000009e-205 or 4.9999999999999999e-232 < B < 6.8000000000000001e-130 or 9.4999999999999991e-75 < B < 1.4500000000000001e28

   1. Initial program 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in B around -inf 68.4%

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

      1. associate--l+ 68.4%

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

      2. div-sub 69.1%

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

   6. Simplified 69.1%

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

   if -1.45000000000000009e-205 < B < 4.9999999999999999e-232

   1. Initial program 59.1%

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

      1. associate-*r/ 59.1%

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

      2. associate-*l/ 59.1%

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

      3. *-un-lft-identity 59.1%

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

      4. associate--l- 44.5%

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

      5. unpow2 44.5%

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

      6. pow2 44.5%

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

      7. hypot-def 54.2%

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

   3. Applied egg-rr 54.2%

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

      1. div-sub 34.2%

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

      2. div-inv 34.2%

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

      3. fma-neg 34.7%

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

   5. Applied egg-rr 34.7%

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

      1. fma-udef 34.2%

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

      2. unsub-neg 34.2%

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

   7. Simplified 34.2%

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

   8. Taylor expanded in C around inf 16.2%

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

      1. distribute-lft1-in 16.2%

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

      2. metadata-eval 16.2%

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

      3. mul0-lft 56.7%

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

      4. metadata-eval 56.7%

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

   10. Simplified 56.7%

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

   if 6.8000000000000001e-130 < B < 9.4999999999999991e-75

   1. Initial program 27.7%

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

   3. Simplified 28.0%

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

   4. Taylor expanded in A around 0 14.3%

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

      1. unpow2 14.3%

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

      2. unpow2 14.3%

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

      3. hypot-def 31.3%

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

   6. Simplified 31.3%

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

   7. Taylor expanded in C around inf 61.0%

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

      1. associate-*r/ 61.0%

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

   9. Simplified 61.0%

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

   if 1.4500000000000001e28 < B

   1. Initial program 45.5%

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

   3. Simplified 45.5%

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

   4. Taylor expanded in B around inf 79.1%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.45 \cdot 10^{-205}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-232}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-130}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-75}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{+28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 13: 46.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -7 \cdot 10^{-31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.2 \cdot 10^{-204}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-230}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 7.6 \cdot 10^{-130}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{-73}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (- (/ A B)))) PI)))
   (if (<= B -7e-31)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -2.2e-204)
       t_0
       (if (<= B 2.2e-230)
         (/ (* 180.0 (atan 0.0)) PI)
         (if (<= B 7.6e-130)
           t_0
           (if (<= B 5.6e-73)
             (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))
             (if (<= B 3.3e-26)
               (/ (* 180.0 (atan (/ C B))) PI)
               (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan(-(A / B))) / ((double) M_PI);
	double tmp;
	if (B <= -7e-31) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2.2e-204) {
		tmp = t_0;
	} else if (B <= 2.2e-230) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (B <= 7.6e-130) {
		tmp = t_0;
	} else if (B <= 5.6e-73) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	} else if (B <= 3.3e-26) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan(-(A / B))) / Math.PI;
	double tmp;
	if (B <= -7e-31) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2.2e-204) {
		tmp = t_0;
	} else if (B <= 2.2e-230) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (B <= 7.6e-130) {
		tmp = t_0;
	} else if (B <= 5.6e-73) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	} else if (B <= 3.3e-26) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan(-(A / B))) / math.pi
	tmp = 0
	if B <= -7e-31:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2.2e-204:
		tmp = t_0
	elif B <= 2.2e-230:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif B <= 7.6e-130:
		tmp = t_0
	elif B <= 5.6e-73:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	elif B <= 3.3e-26:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(-Float64(A / B)))) / pi)
	tmp = 0.0
	if (B <= -7e-31)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2.2e-204)
		tmp = t_0;
	elseif (B <= 2.2e-230)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (B <= 7.6e-130)
		tmp = t_0;
	elseif (B <= 5.6e-73)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	elseif (B <= 3.3e-26)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan(-(A / B))) / pi;
	tmp = 0.0;
	if (B <= -7e-31)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2.2e-204)
		tmp = t_0;
	elseif (B <= 2.2e-230)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (B <= 7.6e-130)
		tmp = t_0;
	elseif (B <= 5.6e-73)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	elseif (B <= 3.3e-26)
		tmp = (180.0 * atan((C / B))) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[(-N[(A / B), $MachinePrecision])], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[B, -7e-31], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.2e-204], t$95$0, If[LessEqual[B, 2.2e-230], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 7.6e-130], t$95$0, If[LessEqual[B, 5.6e-73], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.3e-26], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -6.99999999999999971e-31

   1. Initial program 58.8%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in B around -inf 71.1%

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

   if -6.99999999999999971e-31 < B < -2.1999999999999998e-204 or 2.1999999999999998e-230 < B < 7.5999999999999997e-130

   1. Initial program 58.3%

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

      1. associate-*r/ 58.3%

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

      2. associate-*l/ 58.3%

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

      3. *-un-lft-identity 58.3%

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

      4. associate--l- 58.3%

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

      5. unpow2 58.3%

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

      6. pow2 58.3%

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

      7. hypot-def 64.7%

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

   3. Applied egg-rr 64.7%

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

   4. Taylor expanded in B around -inf 59.2%

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

   5. Taylor expanded in A around inf 41.9%

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

      1. mul-1-neg 41.9%

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

   7. Simplified 41.9%

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

   if -2.1999999999999998e-204 < B < 2.1999999999999998e-230

   1. Initial program 59.1%

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

      1. associate-*r/ 59.1%

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

      2. associate-*l/ 59.1%

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

      3. *-un-lft-identity 59.1%

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

      4. associate--l- 44.5%

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

      5. unpow2 44.5%

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

      6. pow2 44.5%

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

      7. hypot-def 54.2%

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

   3. Applied egg-rr 54.2%

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

      1. div-sub 34.2%

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

      2. div-inv 34.2%

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

      3. fma-neg 34.7%

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

   5. Applied egg-rr 34.7%

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

      1. fma-udef 34.2%

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

      2. unsub-neg 34.2%

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

   7. Simplified 34.2%

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

   8. Taylor expanded in C around inf 16.2%

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

      1. distribute-lft1-in 16.2%

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

      2. metadata-eval 16.2%

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

      3. mul0-lft 56.7%

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

      4. metadata-eval 56.7%

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

   10. Simplified 56.7%

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

   if 7.5999999999999997e-130 < B < 5.60000000000000023e-73

   1. Initial program 27.7%

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

   3. Simplified 28.0%

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

   4. Taylor expanded in A around 0 14.3%

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

      1. unpow2 14.3%

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

      2. unpow2 14.3%

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

      3. hypot-def 31.3%

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

   6. Simplified 31.3%

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

   7. Taylor expanded in C around inf 61.0%

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

      1. associate-*r/ 61.0%

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

   9. Simplified 61.0%

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

   if 5.60000000000000023e-73 < B < 3.2999999999999998e-26

   1. Initial program 61.5%

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

      1. associate-*r/ 61.5%

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

      2. associate-*l/ 61.5%

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

      3. *-un-lft-identity 61.5%

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

      4. associate--l- 61.5%

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

      5. unpow2 61.5%

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

      6. pow2 61.5%

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

      7. hypot-def 62.6%

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

   3. Applied egg-rr 62.6%

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

   4. Taylor expanded in B around -inf 51.2%

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

   5. Taylor expanded in C around inf 43.5%

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

   if 3.2999999999999998e-26 < B

   1. Initial program 50.6%

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

   3. Simplified 50.6%

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

   4. Taylor expanded in B around inf 71.5%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7 \cdot 10^{-31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.2 \cdot 10^{-204}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-230}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 7.6 \cdot 10^{-130}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{-73}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 14: 55.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -2.45 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{-223}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -6.2 \cdot 10^{-291}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{+75}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (+ B C) B)) PI))))
   (if (<= A -2.45e+72)
     (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
     (if (<= A -7.5e-223)
       t_0
       (if (<= A -6.2e-291)
         (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))
         (if (<= A 4.1e+75) t_0 (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	double tmp;
	if (A <= -2.45e+72) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= -7.5e-223) {
		tmp = t_0;
	} else if (A <= -6.2e-291) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	} else if (A <= 4.1e+75) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	double tmp;
	if (A <= -2.45e+72) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= -7.5e-223) {
		tmp = t_0;
	} else if (A <= -6.2e-291) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	} else if (A <= 4.1e+75) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	tmp = 0
	if A <= -2.45e+72:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= -7.5e-223:
		tmp = t_0
	elif A <= -6.2e-291:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	elif A <= 4.1e+75:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi))
	tmp = 0.0
	if (A <= -2.45e+72)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= -7.5e-223)
		tmp = t_0;
	elseif (A <= -6.2e-291)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	elseif (A <= 4.1e+75)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((B + C) / B)) / pi);
	tmp = 0.0;
	if (A <= -2.45e+72)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= -7.5e-223)
		tmp = t_0;
	elseif (A <= -6.2e-291)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	elseif (A <= 4.1e+75)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -2.45e+72], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -7.5e-223], t$95$0, If[LessEqual[A, -6.2e-291], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.1e+75], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -2.45000000000000003e72

   1. Initial program 26.5%

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

   3. Simplified 15.3%

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

   4. Taylor expanded in A around -inf 81.0%

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

      1. associate-*r/ 81.0%

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

   6. Simplified 81.0%

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

   if -2.45000000000000003e72 < A < -7.50000000000000074e-223 or -6.20000000000000023e-291 < A < 4.0999999999999998e75

   1. Initial program 60.4%

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

   3. Simplified 60.4%

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

   4. Taylor expanded in A around 0 58.5%

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

      1. unpow2 58.5%

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

      2. unpow2 58.5%

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

      3. hypot-def 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in B around -inf 54.0%

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

   if -7.50000000000000074e-223 < A < -6.20000000000000023e-291

   1. Initial program 44.9%

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

   3. Simplified 44.9%

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

   4. Taylor expanded in A around 0 44.9%

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

      1. unpow2 44.9%

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

      2. unpow2 44.9%

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

      3. hypot-def 56.1%

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

   6. Simplified 56.1%

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

   7. Taylor expanded in C around inf 49.3%

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

      1. associate-*r/ 49.3%

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

   9. Simplified 49.3%

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

   if 4.0999999999999998e75 < A

   1. Initial program 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in A around inf 73.9%

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

      1. associate-*r/ 73.9%

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

      2. *-commutative 73.9%

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

   6. Simplified 73.9%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.45 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -6.2 \cdot 10^{-291}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{+75}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 15: 55.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -5 \cdot 10^{+69}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{-223}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -8.6 \cdot 10^{-291}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.3 \cdot 10^{+74}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (+ B C) B)) PI))))
   (if (<= A -5e+69)
     (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
     (if (<= A -7.5e-223)
       t_0
       (if (<= A -8.6e-291)
         (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))
         (if (<= A 2.3e+74) t_0 (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	double tmp;
	if (A <= -5e+69) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= -7.5e-223) {
		tmp = t_0;
	} else if (A <= -8.6e-291) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	} else if (A <= 2.3e+74) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	double tmp;
	if (A <= -5e+69) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= -7.5e-223) {
		tmp = t_0;
	} else if (A <= -8.6e-291) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	} else if (A <= 2.3e+74) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	tmp = 0
	if A <= -5e+69:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= -7.5e-223:
		tmp = t_0
	elif A <= -8.6e-291:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	elif A <= 2.3e+74:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi))
	tmp = 0.0
	if (A <= -5e+69)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= -7.5e-223)
		tmp = t_0;
	elseif (A <= -8.6e-291)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	elseif (A <= 2.3e+74)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((B + C) / B)) / pi);
	tmp = 0.0;
	if (A <= -5e+69)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= -7.5e-223)
		tmp = t_0;
	elseif (A <= -8.6e-291)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	elseif (A <= 2.3e+74)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -5e+69], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -7.5e-223], t$95$0, If[LessEqual[A, -8.6e-291], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.3e+74], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -5.00000000000000036e69

   1. Initial program 26.5%

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

      1. associate-*r/ 26.5%

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

      2. associate-*l/ 26.5%

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

      3. *-un-lft-identity 26.5%

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

      4. associate--l- 15.3%

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

      5. unpow2 15.3%

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

      6. pow2 15.3%

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

      7. hypot-def 26.8%

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

   3. Applied egg-rr 26.8%

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

   4. Taylor expanded in A around -inf 81.2%

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

   if -5.00000000000000036e69 < A < -7.50000000000000074e-223 or -8.60000000000000071e-291 < A < 2.2999999999999999e74

   1. Initial program 60.4%

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

   3. Simplified 60.4%

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

   4. Taylor expanded in A around 0 58.5%

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

      1. unpow2 58.5%

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

      2. unpow2 58.5%

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

      3. hypot-def 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in B around -inf 54.0%

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

   if -7.50000000000000074e-223 < A < -8.60000000000000071e-291

   1. Initial program 44.9%

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

   3. Simplified 44.9%

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

   4. Taylor expanded in A around 0 44.9%

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

      1. unpow2 44.9%

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

      2. unpow2 44.9%

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

      3. hypot-def 56.1%

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

   6. Simplified 56.1%

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

   7. Taylor expanded in C around inf 49.3%

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

      1. associate-*r/ 49.3%

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

   9. Simplified 49.3%

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

   if 2.2999999999999999e74 < A

   1. Initial program 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in A around inf 73.9%

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

      1. associate-*r/ 73.9%

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

      2. *-commutative 73.9%

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

   6. Simplified 73.9%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{+69}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.6 \cdot 10^{-291}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.3 \cdot 10^{+74}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 16: 55.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{if}\;A \leq -2.2 \cdot 10^{+72}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1 \cdot 10^{-221}:\\ \;\;\;\;180 \cdot \frac{t_0}{\pi}\\ \mathbf{elif}\;A \leq -7.4 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{+74}:\\ \;\;\;\;\frac{180 \cdot t_0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (/ (+ B C) B))))
   (if (<= A -2.2e+72)
     (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
     (if (<= A -1e-221)
       (* 180.0 (/ t_0 PI))
       (if (<= A -7.4e-292)
         (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))
         (if (<= A 3.8e+74)
           (/ (* 180.0 t_0) PI)
           (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((B + C) / B));
	double tmp;
	if (A <= -2.2e+72) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= -1e-221) {
		tmp = 180.0 * (t_0 / ((double) M_PI));
	} else if (A <= -7.4e-292) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	} else if (A <= 3.8e+74) {
		tmp = (180.0 * t_0) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((B + C) / B));
	double tmp;
	if (A <= -2.2e+72) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= -1e-221) {
		tmp = 180.0 * (t_0 / Math.PI);
	} else if (A <= -7.4e-292) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	} else if (A <= 3.8e+74) {
		tmp = (180.0 * t_0) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((B + C) / B))
	tmp = 0
	if A <= -2.2e+72:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= -1e-221:
		tmp = 180.0 * (t_0 / math.pi)
	elif A <= -7.4e-292:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	elif A <= 3.8e+74:
		tmp = (180.0 * t_0) / math.pi
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(Float64(B + C) / B))
	tmp = 0.0
	if (A <= -2.2e+72)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= -1e-221)
		tmp = Float64(180.0 * Float64(t_0 / pi));
	elseif (A <= -7.4e-292)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	elseif (A <= 3.8e+74)
		tmp = Float64(Float64(180.0 * t_0) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((B + C) / B));
	tmp = 0.0;
	if (A <= -2.2e+72)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= -1e-221)
		tmp = 180.0 * (t_0 / pi);
	elseif (A <= -7.4e-292)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	elseif (A <= 3.8e+74)
		tmp = (180.0 * t_0) / pi;
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -2.2e+72], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -1e-221], N[(180.0 * N[(t$95$0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -7.4e-292], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.8e+74], N[(N[(180.0 * t$95$0), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -2.2e72

   1. Initial program 26.5%

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

      1. associate-*r/ 26.5%

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

      2. associate-*l/ 26.5%

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

      3. *-un-lft-identity 26.5%

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

      4. associate--l- 15.3%

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

      5. unpow2 15.3%

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

      6. pow2 15.3%

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

      7. hypot-def 26.8%

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

   3. Applied egg-rr 26.8%

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

   4. Taylor expanded in A around -inf 81.2%

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

   if -2.2e72 < A < -1.00000000000000002e-221

   1. Initial program 57.6%

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

   3. Simplified 57.6%

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

   4. Taylor expanded in A around 0 57.5%

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

      1. unpow2 57.5%

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

      2. unpow2 57.5%

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

      3. hypot-def 78.0%

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

   6. Simplified 78.0%

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

   7. Taylor expanded in B around -inf 48.8%

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

   if -1.00000000000000002e-221 < A < -7.39999999999999993e-292

   1. Initial program 44.9%

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

   3. Simplified 44.9%

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

   4. Taylor expanded in A around 0 44.9%

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

      1. unpow2 44.9%

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

      2. unpow2 44.9%

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

      3. hypot-def 56.1%

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

   6. Simplified 56.1%

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

   7. Taylor expanded in C around inf 49.3%

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

      1. associate-*r/ 49.3%

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

   9. Simplified 49.3%

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

   if -7.39999999999999993e-292 < A < 3.7999999999999998e74

   1. Initial program 62.8%

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

      1. associate-*r/ 62.8%

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

      2. associate-*l/ 62.8%

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

      3. *-un-lft-identity 62.8%

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

      4. associate--l- 62.8%

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

      5. unpow2 62.8%

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

      6. pow2 62.8%

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

      7. hypot-def 90.2%

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

   3. Applied egg-rr 90.2%

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

   4. Taylor expanded in B around -inf 61.8%

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

   5. Taylor expanded in A around 0 58.4%

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

      1. +-commutative 58.4%

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

   7. Simplified 58.4%

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

   if 3.7999999999999998e74 < A

   1. Initial program 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in A around inf 73.9%

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

      1. associate-*r/ 73.9%

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

      2. *-commutative 73.9%

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

   6. Simplified 73.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{A \cdot -2}{B}\right)}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.2 \cdot 10^{+72}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1 \cdot 10^{-221}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7.4 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{+74}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 17: 57.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{if}\;A \leq -3.45 \cdot 10^{+75}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.7 \cdot 10^{-222}:\\ \;\;\;\;180 \cdot \frac{t_0}{\pi}\\ \mathbf{elif}\;A \leq -8.6 \cdot 10^{-291}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 0.012:\\ \;\;\;\;\frac{180 \cdot t_0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (/ (+ B C) B))))
   (if (<= A -3.45e+75)
     (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
     (if (<= A -2.7e-222)
       (* 180.0 (/ t_0 PI))
       (if (<= A -8.6e-291)
         (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))
         (if (<= A 0.012)
           (/ (* 180.0 t_0) PI)
           (/ (* 180.0 (atan (/ (- B A) B))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((B + C) / B));
	double tmp;
	if (A <= -3.45e+75) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= -2.7e-222) {
		tmp = 180.0 * (t_0 / ((double) M_PI));
	} else if (A <= -8.6e-291) {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	} else if (A <= 0.012) {
		tmp = (180.0 * t_0) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(((B - A) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((B + C) / B));
	double tmp;
	if (A <= -3.45e+75) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= -2.7e-222) {
		tmp = 180.0 * (t_0 / Math.PI);
	} else if (A <= -8.6e-291) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	} else if (A <= 0.012) {
		tmp = (180.0 * t_0) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan(((B - A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((B + C) / B))
	tmp = 0
	if A <= -3.45e+75:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= -2.7e-222:
		tmp = 180.0 * (t_0 / math.pi)
	elif A <= -8.6e-291:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	elif A <= 0.012:
		tmp = (180.0 * t_0) / math.pi
	else:
		tmp = (180.0 * math.atan(((B - A) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(Float64(B + C) / B))
	tmp = 0.0
	if (A <= -3.45e+75)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= -2.7e-222)
		tmp = Float64(180.0 * Float64(t_0 / pi));
	elseif (A <= -8.6e-291)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	elseif (A <= 0.012)
		tmp = Float64(Float64(180.0 * t_0) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B - A) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((B + C) / B));
	tmp = 0.0;
	if (A <= -3.45e+75)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= -2.7e-222)
		tmp = 180.0 * (t_0 / pi);
	elseif (A <= -8.6e-291)
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	elseif (A <= 0.012)
		tmp = (180.0 * t_0) / pi;
	else
		tmp = (180.0 * atan(((B - A) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -3.45e+75], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -2.7e-222], N[(180.0 * N[(t$95$0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -8.6e-291], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 0.012], N[(N[(180.0 * t$95$0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -3.4500000000000002e75

   1. Initial program 26.5%

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

      1. associate-*r/ 26.5%

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

      2. associate-*l/ 26.5%

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

      3. *-un-lft-identity 26.5%

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

      4. associate--l- 15.3%

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

      5. unpow2 15.3%

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

      6. pow2 15.3%

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

      7. hypot-def 26.8%

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

   3. Applied egg-rr 26.8%

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

   4. Taylor expanded in A around -inf 81.2%

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

   if -3.4500000000000002e75 < A < -2.7e-222

   1. Initial program 57.6%

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

   3. Simplified 57.6%

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

   4. Taylor expanded in A around 0 57.5%

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

      1. unpow2 57.5%

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

      2. unpow2 57.5%

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

      3. hypot-def 78.0%

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

   6. Simplified 78.0%

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

   7. Taylor expanded in B around -inf 48.8%

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

   if -2.7e-222 < A < -8.60000000000000071e-291

   1. Initial program 44.9%

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

   3. Simplified 44.9%

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

   4. Taylor expanded in A around 0 44.9%

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

      1. unpow2 44.9%

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

      2. unpow2 44.9%

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

      3. hypot-def 56.1%

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

   6. Simplified 56.1%

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

   7. Taylor expanded in C around inf 49.3%

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

      1. associate-*r/ 49.3%

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

   9. Simplified 49.3%

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

   if -8.60000000000000071e-291 < A < 0.012

   1. Initial program 61.2%

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

      1. associate-*r/ 61.2%

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

      2. associate-*l/ 61.2%

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

      3. *-un-lft-identity 61.2%

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

      4. associate--l- 61.2%

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

      5. unpow2 61.2%

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

      6. pow2 61.2%

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

      7. hypot-def 89.6%

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

   3. Applied egg-rr 89.6%

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

   4. Taylor expanded in B around -inf 62.7%

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

   5. Taylor expanded in A around 0 61.1%

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

      1. +-commutative 61.1%

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

   7. Simplified 61.1%

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

   if 0.012 < A

   1. Initial program 74.5%

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

      1. associate-*r/ 74.5%

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

      2. associate-*l/ 74.5%

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

      3. *-un-lft-identity 74.5%

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

      4. associate--l- 74.5%

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

      5. unpow2 74.5%

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

      6. pow2 74.5%

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

      7. hypot-def 93.7%

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

   3. Applied egg-rr 93.7%

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

   4. Taylor expanded in B around -inf 75.9%

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

   5. Taylor expanded in C around 0 74.7%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.45 \cdot 10^{+75}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.7 \cdot 10^{-222}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.6 \cdot 10^{-291}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;A \leq 0.012:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 18: 46.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -5 \cdot 10^{-30}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -4.4 \cdot 10^{-205}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-232}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-21}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (- (/ A B)))) PI)))
   (if (<= B -5e-30)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -4.4e-205)
       t_0
       (if (<= B 1.55e-232)
         (/ (* 180.0 (atan 0.0)) PI)
         (if (<= B 2.5e-21) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan(-(A / B))) / ((double) M_PI);
	double tmp;
	if (B <= -5e-30) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -4.4e-205) {
		tmp = t_0;
	} else if (B <= 1.55e-232) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (B <= 2.5e-21) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan(-(A / B))) / Math.PI;
	double tmp;
	if (B <= -5e-30) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -4.4e-205) {
		tmp = t_0;
	} else if (B <= 1.55e-232) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (B <= 2.5e-21) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan(-(A / B))) / math.pi
	tmp = 0
	if B <= -5e-30:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -4.4e-205:
		tmp = t_0
	elif B <= 1.55e-232:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif B <= 2.5e-21:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(-Float64(A / B)))) / pi)
	tmp = 0.0
	if (B <= -5e-30)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -4.4e-205)
		tmp = t_0;
	elseif (B <= 1.55e-232)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (B <= 2.5e-21)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan(-(A / B))) / pi;
	tmp = 0.0;
	if (B <= -5e-30)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -4.4e-205)
		tmp = t_0;
	elseif (B <= 1.55e-232)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (B <= 2.5e-21)
		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[(N[(180.0 * N[ArcTan[(-N[(A / B), $MachinePrecision])], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[B, -5e-30], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4.4e-205], t$95$0, If[LessEqual[B, 1.55e-232], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 2.5e-21], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -4.99999999999999972e-30

   1. Initial program 58.8%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in B around -inf 71.1%

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

   if -4.99999999999999972e-30 < B < -4.40000000000000018e-205 or 1.5499999999999999e-232 < B < 2.49999999999999986e-21

   1. Initial program 54.3%

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

      1. associate-*r/ 54.3%

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

      2. associate-*l/ 54.3%

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

      3. *-un-lft-identity 54.3%

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

      4. associate--l- 54.3%

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

      5. unpow2 54.3%

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

      6. pow2 54.3%

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

      7. hypot-def 61.4%

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

   3. Applied egg-rr 61.4%

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

   4. Taylor expanded in B around -inf 52.5%

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

   5. Taylor expanded in A around inf 37.9%

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

      1. mul-1-neg 37.9%

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

   7. Simplified 37.9%

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

   if -4.40000000000000018e-205 < B < 1.5499999999999999e-232

   1. Initial program 59.1%

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

      1. associate-*r/ 59.1%

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

      2. associate-*l/ 59.1%

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

      3. *-un-lft-identity 59.1%

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

      4. associate--l- 44.5%

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

      5. unpow2 44.5%

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

      6. pow2 44.5%

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

      7. hypot-def 54.2%

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

   3. Applied egg-rr 54.2%

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

      1. div-sub 34.2%

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

      2. div-inv 34.2%

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

      3. fma-neg 34.7%

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

   5. Applied egg-rr 34.7%

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

      1. fma-udef 34.2%

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

      2. unsub-neg 34.2%

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

   7. Simplified 34.2%

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

   8. Taylor expanded in C around inf 16.2%

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

      1. distribute-lft1-in 16.2%

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

      2. metadata-eval 16.2%

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

      3. mul0-lft 56.7%

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

      4. metadata-eval 56.7%

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

   10. Simplified 56.7%

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

   if 2.49999999999999986e-21 < B

   1. Initial program 50.5%

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

   3. Simplified 50.5%

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

   4. Taylor expanded in B around inf 73.6%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-30}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -4.4 \cdot 10^{-205}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-232}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-21}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 19: 45.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.25 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-235}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-26}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.25e-203)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.8e-235)
     (/ (* 180.0 (atan 0.0)) PI)
     (if (<= B 1.05e-26)
       (/ (* 180.0 (atan (/ C B))) PI)
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.25e-203) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.8e-235) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (B <= 1.05e-26) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.25e-203) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.8e-235) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (B <= 1.05e-26) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.25e-203:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.8e-235:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif B <= 1.05e-26:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.25e-203)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.8e-235)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (B <= 1.05e-26)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.25e-203)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.8e-235)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (B <= 1.05e-26)
		tmp = (180.0 * atan((C / B))) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.25e-203], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.8e-235], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.05e-26], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.25e-203

   1. Initial program 57.1%

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

   3. Simplified 57.1%

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

   4. Taylor expanded in B around -inf 54.6%

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

   if -1.25e-203 < B < 4.80000000000000022e-235

   1. Initial program 59.1%

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

      1. associate-*r/ 59.1%

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

      2. associate-*l/ 59.1%

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

      3. *-un-lft-identity 59.1%

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

      4. associate--l- 44.5%

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

      5. unpow2 44.5%

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

      6. pow2 44.5%

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

      7. hypot-def 54.2%

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

   3. Applied egg-rr 54.2%

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

      1. div-sub 34.2%

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

      2. div-inv 34.2%

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

      3. fma-neg 34.7%

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

   5. Applied egg-rr 34.7%

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

      1. fma-udef 34.2%

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

      2. unsub-neg 34.2%

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

   7. Simplified 34.2%

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

   8. Taylor expanded in C around inf 16.2%

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

      1. distribute-lft1-in 16.2%

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

      2. metadata-eval 16.2%

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

      3. mul0-lft 56.7%

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

      4. metadata-eval 56.7%

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

   10. Simplified 56.7%

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

   if 4.80000000000000022e-235 < B < 1.05000000000000004e-26

   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. Step-by-step derivation

      1. associate-*r/ 54.8%

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

      2. associate-*l/ 54.8%

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

      3. *-un-lft-identity 54.8%

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

      4. associate--l- 54.9%

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

      5. unpow2 54.9%

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

      6. pow2 54.9%

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

      7. hypot-def 61.3%

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

   3. Applied egg-rr 61.3%

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

   4. Taylor expanded in B around -inf 50.3%

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

   5. Taylor expanded in C around inf 35.2%

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

   if 1.05000000000000004e-26 < B

   1. Initial program 50.6%

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

   3. Simplified 50.6%

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

   4. Taylor expanded in B around inf 71.5%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.25 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-235}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-26}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 20: 44.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.2 \cdot 10^{-204}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.2e-204)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 6.5e-87)
     (/ (* 180.0 (atan 0.0)) PI)
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.2e-204) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 6.5e-87) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.2e-204) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 6.5e-87) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4.2e-204:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 6.5e-87:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -4.2e-204)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 6.5e-87)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -4.2e-204)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 6.5e-87)
		tmp = (180.0 * atan(0.0)) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.2e-204], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.5e-87], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -4.20000000000000018e-204

   1. Initial program 57.1%

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

   3. Simplified 57.1%

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

   4. Taylor expanded in B around -inf 54.6%

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

   if -4.20000000000000018e-204 < B < 6.5000000000000003e-87

   1. Initial program 57.1%

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

      1. associate-*r/ 57.1%

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

      2. associate-*l/ 57.1%

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

      3. *-un-lft-identity 57.1%

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

      4. associate--l- 49.2%

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

      5. unpow2 49.2%

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

      6. pow2 49.2%

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

      7. hypot-def 57.2%

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

   3. Applied egg-rr 57.2%

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

      1. div-sub 42.3%

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

      2. div-inv 42.3%

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

      3. fma-neg 43.8%

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

   5. Applied egg-rr 43.8%

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

      1. fma-udef 42.3%

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

      2. unsub-neg 42.3%

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

   7. Simplified 42.3%

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

   8. Taylor expanded in C around inf 11.3%

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

      1. distribute-lft1-in 11.3%

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

      2. metadata-eval 11.3%

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

      3. mul0-lft 42.0%

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

      4. metadata-eval 42.0%

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

   10. Simplified 42.0%

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

   if 6.5000000000000003e-87 < B

   1. Initial program 51.5%

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

   3. Simplified 51.5%

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

   4. Taylor expanded in B around inf 61.9%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.2 \cdot 10^{-204}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 21: 40.6% accurate, 2.5× 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 58.2%

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

   3. Simplified 55.1%

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

   4. Taylor expanded in B around -inf 47.0%

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

   if -4.999999999999985e-310 < B

   1. Initial program 52.7%

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

   3. Simplified 51.2%

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

   4. Taylor expanded in B around inf 40.7%

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

4. Final simplification 43.8%

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

Alternative 22: 21.0% accurate, 2.5× 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 55.4%

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

3. Simplified 53.2%

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

4. Taylor expanded in B around inf 21.5%

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

5. Final simplification 21.5%

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

Reproduce

herbie shell --seed 2023275 
(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)))