ABCF->ab-angle angle

Percentage Accurate: 53.5% → 88.0%

Time: 24.7s

Alternatives: 23

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: 53.5% 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: 88.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_1 := \frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\\ \mathbf{if}\;t_0 \leq -0.02:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} t_1}{\pi}\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(e^{\mathsf{log1p}\left(t_1\right)} + -1\right)}{\pi}\\ \end{array} \end{array} \]

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))))))
        (t_1 (/ (- (- C A) (hypot (- A C) B)) B)))
   (if (<= t_0 -0.02)
     (/ (* 180.0 (atan t_1)) PI)
     (if (<= t_0 0.0)
       (/ (* 180.0 (atan (/ 1.0 (+ (* -2.0 (/ C B)) (* 2.0 (/ A B)))))) PI)
       (* 180.0 (/ (atan (+ (exp (log1p t_1)) -1.0)) 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 t_1 = ((C - A) - hypot((A - C), B)) / B;
	double tmp;
	if (t_0 <= -0.02) {
		tmp = (180.0 * atan(t_1)) / ((double) M_PI);
	} else if (t_0 <= 0.0) {
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((exp(log1p(t_1)) + -1.0)) / ((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 t_1 = ((C - A) - Math.hypot((A - C), B)) / B;
	double tmp;
	if (t_0 <= -0.02) {
		tmp = (180.0 * Math.atan(t_1)) / Math.PI;
	} else if (t_0 <= 0.0) {
		tmp = (180.0 * Math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((Math.exp(Math.log1p(t_1)) + -1.0)) / 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))))
	t_1 = ((C - A) - math.hypot((A - C), B)) / B
	tmp = 0
	if t_0 <= -0.02:
		tmp = (180.0 * math.atan(t_1)) / math.pi
	elif t_0 <= 0.0:
		tmp = (180.0 * math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / math.pi
	else:
		tmp = 180.0 * (math.atan((math.exp(math.log1p(t_1)) + -1.0)) / 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)))))
	t_1 = Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B)
	tmp = 0.0
	if (t_0 <= -0.02)
		tmp = Float64(Float64(180.0 * atan(t_1)) / pi);
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(-2.0 * Float64(C / B)) + Float64(2.0 * Float64(A / B)))))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(exp(log1p(t_1)) + -1.0)) / pi));
	end
	return 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]}, Block[{t$95$1 = N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[t$95$0, -0.02], N[(N[(180.0 * N[ArcTan[t$95$1], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(N[(-2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[Exp[N[Log[1 + t$95$1], $MachinePrecision]], $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $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))))) < -0.0200000000000000004

   1. Initial program 58.2%

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

      1. associate-*r/ 58.2%

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

      2. associate-*l/ 58.2%

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

      3. *-un-lft-identity 58.2%

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

      4. unpow2 58.2%

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

      5. unpow2 58.2%

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

      6. hypot-def 86.7%

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

   3. Applied egg-rr 86.7%

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

   if -0.0200000000000000004 < (*.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 26.2%

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

      1. associate-*r/ 26.2%

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

      2. associate-*l/ 26.2%

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

      3. *-un-lft-identity 26.2%

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

      4. unpow2 26.2%

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

      5. unpow2 26.2%

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

      6. hypot-def 26.2%

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

   3. Applied egg-rr 26.2%

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

      1. clear-num 26.2%

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

      2. inv-pow 26.2%

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

   5. Applied egg-rr 26.2%

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

      1. unpow-1 26.2%

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

      2. associate--r+ 14.9%

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

   7. Simplified 14.9%

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

   8. Taylor expanded in A around -inf 99.3%

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

   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 57.6%

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

      1. *-commutative 57.6%

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

      2. +-commutative 57.6%

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

      3. unpow2 57.6%

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

      4. unpow2 57.6%

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

      5. hypot-udef 90.0%

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

      6. associate--r+ 87.9%

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

      7. div-inv 87.9%

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

      8. expm1-log1p-u 87.9%

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

      9. expm1-udef 89.1%

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

   3. Applied egg-rr 90.0%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.02:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(e^{\mathsf{log1p}\left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)} + -1\right)}{\pi}\\ \end{array} \]

Alternative 2: 81.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.5e+46)
   (/ (* 180.0 (atan (/ 1.0 (+ (* -2.0 (/ C B)) (* 2.0 (/ A B)))))) 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 <= -5.5e+46) {
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / ((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 <= -5.5e+46) {
		tmp = (180.0 * Math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / 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 <= -5.5e+46:
		tmp = (180.0 * math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / 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 <= -5.5e+46)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(-2.0 * Float64(C / B)) + Float64(2.0 * Float64(A / B)))))) / 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 <= -5.5e+46)
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / 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, -5.5e+46], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(N[(-2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]), $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 < -5.4999999999999998e46

   1. Initial program 17.4%

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

      1. associate-*r/ 17.4%

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

      2. associate-*l/ 17.4%

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

      3. *-un-lft-identity 17.4%

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

      4. unpow2 17.4%

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

      5. unpow2 17.4%

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

      6. hypot-def 49.4%

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

   3. Applied egg-rr 49.4%

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

      1. clear-num 49.4%

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

      2. inv-pow 49.4%

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

   5. Applied egg-rr 49.4%

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

      1. unpow-1 49.4%

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

      2. associate--r+ 23.3%

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

   7. Simplified 23.3%

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

   8. Taylor expanded in A around -inf 76.3%

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

   if -5.4999999999999998e46 < A

   1. Initial program 62.5%

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

   3. Simplified 88.6%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3: 81.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.2e+45)
   (/ (* 180.0 (atan (/ 1.0 (+ (* -2.0 (/ C B)) (* 2.0 (/ A B)))))) PI)
   (/ (* 180.0 (atan (/ (- (- C A) (hypot (- A C) B)) B))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.2e+45) {
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / ((double) M_PI);
	} 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 tmp;
	if (A <= -2.2e+45) {
		tmp = (180.0 * Math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan((((C - A) - Math.hypot((A - C), B)) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.2e+45:
		tmp = (180.0 * math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / math.pi
	else:
		tmp = (180.0 * math.atan((((C - A) - math.hypot((A - C), B)) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.2e+45)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(-2.0 * Float64(C / B)) + Float64(2.0 * Float64(A / B)))))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.2e+45)
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / pi;
	else
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.2e+45], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(N[(-2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -2.2e45

   1. Initial program 17.4%

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

      1. associate-*r/ 17.4%

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

      2. associate-*l/ 17.4%

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

      3. *-un-lft-identity 17.4%

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

      4. unpow2 17.4%

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

      5. unpow2 17.4%

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

      6. hypot-def 49.4%

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

   3. Applied egg-rr 49.4%

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

      1. clear-num 49.4%

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

      2. inv-pow 49.4%

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

   5. Applied egg-rr 49.4%

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

      1. unpow-1 49.4%

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

      2. associate--r+ 23.3%

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

   7. Simplified 23.3%

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

   8. Taylor expanded in A around -inf 76.3%

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

   if -2.2e45 < A

   1. Initial program 62.5%

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

      1. associate-*r/ 62.5%

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

      2. associate-*l/ 62.5%

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

      3. *-un-lft-identity 62.5%

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

      4. unpow2 62.5%

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

      5. unpow2 62.5%

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

      6. hypot-def 88.6%

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

   3. Applied egg-rr 88.6%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 76.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.02 \cdot 10^{+40}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{+99}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.02e+40)
   (/ (* 180.0 (atan (/ 1.0 (+ (* -2.0 (/ C B)) (* 2.0 (/ A B)))))) PI)
   (if (<= A 6.8e+99)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.02e+40) {
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / ((double) M_PI);
	} else if (A <= 6.8e+99) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.02e+40) {
		tmp = (180.0 * Math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / Math.PI;
	} else if (A <= 6.8e+99) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.02e+40:
		tmp = (180.0 * math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / math.pi
	elif A <= 6.8e+99:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.02e+40)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(-2.0 * Float64(C / B)) + Float64(2.0 * Float64(A / B)))))) / pi);
	elseif (A <= 6.8e+99)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.02e+40)
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / pi;
	elseif (A <= 6.8e+99)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.02e+40], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(N[(-2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 6.8e+99], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.0200000000000001e40

   1. Initial program 17.4%

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

      1. associate-*r/ 17.4%

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

      2. associate-*l/ 17.4%

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

      3. *-un-lft-identity 17.4%

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

      4. unpow2 17.4%

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

      5. unpow2 17.4%

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

      6. hypot-def 49.4%

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

   3. Applied egg-rr 49.4%

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

      1. clear-num 49.4%

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

      2. inv-pow 49.4%

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

   5. Applied egg-rr 49.4%

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

      1. unpow-1 49.4%

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

      2. associate--r+ 23.3%

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

   7. Simplified 23.3%

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

   8. Taylor expanded in A around -inf 76.3%

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

   if -2.0200000000000001e40 < A < 6.79999999999999968e99

   1. Initial program 54.4%

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

   2. Taylor expanded in A around 0 52.0%

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

      1. unpow2 52.0%

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

      2. unpow2 52.0%

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

      3. hypot-def 82.4%

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

   4. Simplified 82.4%

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

   if 6.79999999999999968e99 < A

   1. Initial program 89.2%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in B around inf 93.9%

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

      1. +-commutative 93.9%

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

   6. Simplified 93.9%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.02 \cdot 10^{+40}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{+99}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 78.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -0.0025:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.75 \cdot 10^{+117}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -0.0025)
   (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
   (if (<= C 1.75e+117)
     (/ (* -180.0 (atan (/ (+ A (hypot A B)) B))) PI)
     (/ (* 180.0 (atan (* -0.5 (/ B C)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -0.0025) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else if (C <= 1.75e+117) {
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((-0.5 * (B / C)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -0.0025) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else if (C <= 1.75e+117) {
		tmp = (-180.0 * Math.atan(((A + Math.hypot(A, B)) / B))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan((-0.5 * (B / C)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -0.0025:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	elif C <= 1.75e+117:
		tmp = (-180.0 * math.atan(((A + math.hypot(A, B)) / B))) / math.pi
	else:
		tmp = (180.0 * math.atan((-0.5 * (B / C)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -0.0025)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	elseif (C <= 1.75e+117)
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(A + hypot(A, B)) / B))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / C)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -0.0025)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	elseif (C <= 1.75e+117)
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / pi;
	else
		tmp = (180.0 * atan((-0.5 * (B / C)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -0.0025], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.75e+117], N[(N[(-180.0 * N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -0.00250000000000000005

   1. Initial program 74.2%

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

   2. Taylor expanded in A around 0 73.8%

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

      1. unpow2 73.8%

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

      2. unpow2 73.8%

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

      3. hypot-def 87.0%

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

   4. Simplified 87.0%

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

   if -0.00250000000000000005 < C < 1.74999999999999991e117

   1. Initial program 54.6%

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

   2. Taylor expanded in C around 0 53.5%

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

      1. associate-*r/ 53.5%

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

      2. mul-1-neg 53.5%

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

      3. +-commutative 53.5%

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

      4. unpow2 53.5%

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

      5. unpow2 53.5%

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

      6. hypot-def 83.8%

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

   4. Simplified 83.8%

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

      1. expm1-log1p-u 43.1%

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

      2. expm1-udef 43.1%

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

   6. Applied egg-rr 43.1%

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

      1. expm1-def 43.1%

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

      2. expm1-log1p 83.8%

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

      3. associate-*r/ 83.8%

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

      4. distribute-rgt-neg-out 83.8%

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

      5. distribute-lft-neg-in 83.8%

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

      6. metadata-eval 83.8%

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

   8. Simplified 83.8%

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

   if 1.74999999999999991e117 < C

   1. Initial program 22.0%

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

      1. associate-*r/ 22.0%

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

      2. associate-*l/ 22.0%

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

      3. *-un-lft-identity 22.0%

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

      4. unpow2 22.0%

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

      5. unpow2 22.0%

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

      6. hypot-def 53.7%

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

   3. Applied egg-rr 53.7%

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

   4. Taylor expanded in C around inf 44.7%

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

      1. +-commutative 44.7%

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

      2. fma-def 44.7%

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

   6. Simplified 61.4%

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

   7. Taylor expanded in B around 0 80.1%

      \[\leadsto \frac{\color{blue}{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, 0\right)\right)}}{\pi} \]
   8. Step-by-step derivation

      1. fma-udef 80.1%

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

      2. +-rgt-identity 80.1%

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

   9. Simplified 80.1%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -0.0025:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.75 \cdot 10^{+117}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 6: 62.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.8 \cdot 10^{+38}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-182}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{B}{B + C}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.8e+38)
   (/ (* 180.0 (atan (/ 1.0 (+ (* -2.0 (/ C B)) (* 2.0 (/ A B)))))) PI)
   (if (<= A 5e-182)
     (/ (* 180.0 (atan (/ 1.0 (/ B (+ B C))))) PI)
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.8e+38) {
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / ((double) M_PI);
	} else if (A <= 5e-182) {
		tmp = (180.0 * atan((1.0 / (B / (B + C))))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.8e+38) {
		tmp = (180.0 * Math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / Math.PI;
	} else if (A <= 5e-182) {
		tmp = (180.0 * Math.atan((1.0 / (B / (B + C))))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.8e+38:
		tmp = (180.0 * math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / math.pi
	elif A <= 5e-182:
		tmp = (180.0 * math.atan((1.0 / (B / (B + C))))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.8e+38)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(-2.0 * Float64(C / B)) + Float64(2.0 * Float64(A / B)))))) / pi);
	elseif (A <= 5e-182)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(B / Float64(B + C))))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.8e+38)
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / pi;
	elseif (A <= 5e-182)
		tmp = (180.0 * atan((1.0 / (B / (B + C))))) / pi;
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.8e+38], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(N[(-2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 5e-182], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(B / N[(B + C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.80000000000000026e38

   1. Initial program 17.4%

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

      1. associate-*r/ 17.4%

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

      2. associate-*l/ 17.4%

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

      3. *-un-lft-identity 17.4%

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

      4. unpow2 17.4%

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

      5. unpow2 17.4%

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

      6. hypot-def 49.4%

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

   3. Applied egg-rr 49.4%

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

      1. clear-num 49.4%

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

      2. inv-pow 49.4%

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

   5. Applied egg-rr 49.4%

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

      1. unpow-1 49.4%

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

      2. associate--r+ 23.3%

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

   7. Simplified 23.3%

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

   8. Taylor expanded in A around -inf 76.3%

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

   if -8.80000000000000026e38 < A < 5.00000000000000024e-182

   1. Initial program 51.2%

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

      1. associate-*r/ 51.2%

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

      2. associate-*l/ 51.2%

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

      3. *-un-lft-identity 51.2%

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

      4. unpow2 51.2%

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

      5. unpow2 51.2%

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

      6. hypot-def 85.7%

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

   3. Applied egg-rr 85.7%

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

      1. clear-num 85.7%

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

      2. inv-pow 85.7%

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

   5. Applied egg-rr 85.7%

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

      1. unpow-1 85.7%

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

      2. associate--r+ 85.7%

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

   7. Simplified 85.7%

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

   8. Taylor expanded in B around -inf 60.0%

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

      1. mul-1-neg 60.0%

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

   10. Simplified 60.0%

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

   if 5.00000000000000024e-182 < A

   1. Initial program 74.3%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in B around inf 75.2%

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

      1. +-commutative 75.2%

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

   6. Simplified 75.2%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.8 \cdot 10^{+38}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-182}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{B}{B + C}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 46.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -9.1 \cdot 10^{-38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -5 \cdot 10^{-106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-242}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.7 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-98}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ (- A) B))) PI)))
   (if (<= B -9.1e-38)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -5e-106)
       t_0
       (if (<= B 6.5e-242)
         (/ (* 180.0 (atan (/ C B))) PI)
         (if (<= B 5.7e-166)
           (* 180.0 (/ (atan (/ 0.0 B)) PI))
           (if (<= B 2.9e-98) 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 <= -9.1e-38) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -5e-106) {
		tmp = t_0;
	} else if (B <= 6.5e-242) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else if (B <= 5.7e-166) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 2.9e-98) {
		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 <= -9.1e-38) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -5e-106) {
		tmp = t_0;
	} else if (B <= 6.5e-242) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else if (B <= 5.7e-166) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 2.9e-98) {
		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 <= -9.1e-38:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -5e-106:
		tmp = t_0
	elif B <= 6.5e-242:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	elif B <= 5.7e-166:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 2.9e-98:
		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 <= -9.1e-38)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -5e-106)
		tmp = t_0;
	elseif (B <= 6.5e-242)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	elseif (B <= 5.7e-166)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 2.9e-98)
		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 <= -9.1e-38)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -5e-106)
		tmp = t_0;
	elseif (B <= 6.5e-242)
		tmp = (180.0 * atan((C / B))) / pi;
	elseif (B <= 5.7e-166)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 2.9e-98)
		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, -9.1e-38], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -5e-106], t$95$0, If[LessEqual[B, 6.5e-242], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 5.7e-166], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.9e-98], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -9.10000000000000012e-38

   1. Initial program 44.4%

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

   2. Taylor expanded in B around -inf 63.6%

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

   if -9.10000000000000012e-38 < B < -4.99999999999999983e-106 or 5.7e-166 < B < 2.9e-98

   1. Initial program 67.0%

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

      1. associate-*r/ 67.0%

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

      2. associate-*l/ 67.0%

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

      3. *-un-lft-identity 67.0%

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

      4. unpow2 67.0%

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

      5. unpow2 67.0%

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

      6. hypot-def 78.3%

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

   3. Applied egg-rr 78.3%

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

   4. Taylor expanded in B around inf 55.5%

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

      1. mul-1-neg 55.5%

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

      2. unsub-neg 55.5%

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

   6. Simplified 55.5%

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

   7. Taylor expanded in A around inf 48.6%

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

      1. associate-*r/ 48.6%

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

      2. neg-mul-1 48.6%

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

   9. Simplified 48.6%

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

   if -4.99999999999999983e-106 < B < 6.4999999999999998e-242

   1. Initial program 78.8%

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

      1. associate-*r/ 78.8%

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

      2. associate-*l/ 78.8%

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

      3. *-un-lft-identity 78.8%

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

      4. unpow2 78.8%

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

      5. unpow2 78.8%

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

      6. hypot-def 92.1%

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

   3. Applied egg-rr 92.1%

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

   4. Taylor expanded in B around inf 62.4%

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

      1. mul-1-neg 62.4%

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

      2. unsub-neg 62.4%

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

   6. Simplified 62.4%

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

   7. Taylor expanded in C around inf 54.1%

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

   if 6.4999999999999998e-242 < B < 5.7e-166

   1. Initial program 36.1%

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

   2. Taylor expanded in C around inf 51.7%

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

      1. associate-*r/ 51.7%

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

      2. distribute-rgt1-in 51.7%

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

      3. metadata-eval 51.7%

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

      4. mul0-lft 51.7%

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

      5. metadata-eval 51.7%

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

   4. Simplified 51.7%

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

   if 2.9e-98 < B

   1. Initial program 50.4%

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

   2. Taylor expanded in B around inf 52.6%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9.1 \cdot 10^{-38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -5 \cdot 10^{-106}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-242}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.7 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-98}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 8: 46.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.75 \cdot 10^{-31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.8 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-241}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.32 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-97}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.75e-31)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -2.8e-106)
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
     (if (<= B 4e-241)
       (/ (* 180.0 (atan (/ C B))) PI)
       (if (<= B 1.32e-166)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 3.7e-97)
           (/ (* 180.0 (atan (/ (- A) B))) PI)
           (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.75e-31) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2.8e-106) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else if (B <= 4e-241) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else if (B <= 1.32e-166) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 3.7e-97) {
		tmp = (180.0 * atan((-A / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.75e-31) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2.8e-106) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else if (B <= 4e-241) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else if (B <= 1.32e-166) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 3.7e-97) {
		tmp = (180.0 * Math.atan((-A / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.75e-31:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2.8e-106:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	elif B <= 4e-241:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	elif B <= 1.32e-166:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 3.7e-97:
		tmp = (180.0 * math.atan((-A / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.75e-31)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2.8e-106)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	elseif (B <= 4e-241)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	elseif (B <= 1.32e-166)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 3.7e-97)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-A) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.75e-31)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2.8e-106)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	elseif (B <= 4e-241)
		tmp = (180.0 * atan((C / B))) / pi;
	elseif (B <= 1.32e-166)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 3.7e-97)
		tmp = (180.0 * atan((-A / B))) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.75e-31], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.8e-106], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4e-241], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.32e-166], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.7e-97], N[(N[(180.0 * N[ArcTan[N[((-A) / 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 < -2.74999999999999979e-31

   1. Initial program 44.4%

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

   2. Taylor expanded in B around -inf 63.6%

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

   if -2.74999999999999979e-31 < B < -2.79999999999999988e-106

   1. Initial program 72.4%

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

   2. Taylor expanded in A around inf 54.8%

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

   if -2.79999999999999988e-106 < B < 3.9999999999999999e-241

   1. Initial program 78.8%

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

      1. associate-*r/ 78.8%

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

      2. associate-*l/ 78.8%

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

      3. *-un-lft-identity 78.8%

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

      4. unpow2 78.8%

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

      5. unpow2 78.8%

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

      6. hypot-def 92.1%

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

   3. Applied egg-rr 92.1%

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

   4. Taylor expanded in B around inf 62.4%

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

      1. mul-1-neg 62.4%

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

      2. unsub-neg 62.4%

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

   6. Simplified 62.4%

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

   7. Taylor expanded in C around inf 54.1%

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

   if 3.9999999999999999e-241 < B < 1.31999999999999998e-166

   1. Initial program 36.1%

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

   2. Taylor expanded in C around inf 51.7%

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

      1. associate-*r/ 51.7%

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

      2. distribute-rgt1-in 51.7%

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

      3. metadata-eval 51.7%

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

      4. mul0-lft 51.7%

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

      5. metadata-eval 51.7%

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

   4. Simplified 51.7%

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

   if 1.31999999999999998e-166 < B < 3.69999999999999976e-97

   1. Initial program 60.1%

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

      1. associate-*r/ 60.1%

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

      2. associate-*l/ 60.1%

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

      3. *-un-lft-identity 60.1%

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

      4. unpow2 60.1%

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

      5. unpow2 60.1%

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

      6. hypot-def 69.1%

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

   3. Applied egg-rr 69.1%

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

   4. Taylor expanded in B around inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. unsub-neg 59.4%

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

   6. Simplified 59.4%

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

   7. Taylor expanded in A around inf 43.3%

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

      1. associate-*r/ 43.3%

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

      2. neg-mul-1 43.3%

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

   9. Simplified 43.3%

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

   if 3.69999999999999976e-97 < B

   1. Initial program 50.4%

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

   2. Taylor expanded in B around inf 52.6%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.75 \cdot 10^{-31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.8 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-241}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.32 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-97}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 9: 47.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.05 \cdot 10^{+40}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.9 \cdot 10^{-39}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.7 \cdot 10^{-70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 2.7 \cdot 10^{-132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.05e+40)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A -1.9e-39)
     (/ (* 180.0 (atan (/ C B))) PI)
     (if (<= A -1.7e-70)
       (* 180.0 (/ (atan -1.0) PI))
       (if (<= A 2.7e-132)
         (* 180.0 (/ (atan 1.0) PI))
         (* 180.0 (/ (atan (* -2.0 (/ A B))) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.05e+40) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= -1.9e-39) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else if (A <= -1.7e-70) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 2.7e-132) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.05e+40) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= -1.9e-39) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else if (A <= -1.7e-70) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 2.7e-132) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.05e+40:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= -1.9e-39:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	elif A <= -1.7e-70:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 2.7e-132:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.05e+40)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= -1.9e-39)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	elseif (A <= -1.7e-70)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 2.7e-132)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.05e+40)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= -1.9e-39)
		tmp = (180.0 * atan((C / B))) / pi;
	elseif (A <= -1.7e-70)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 2.7e-132)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.05e+40], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.9e-39], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -1.7e-70], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.7e-132], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -3.05e40

   1. Initial program 17.4%

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

   2. Taylor expanded in A around -inf 73.1%

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

   if -3.05e40 < A < -1.9000000000000001e-39

   1. Initial program 57.9%

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

      1. associate-*r/ 57.9%

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

      2. associate-*l/ 57.9%

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

      3. *-un-lft-identity 57.9%

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

      4. unpow2 57.9%

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

      5. unpow2 57.9%

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

      6. hypot-def 88.4%

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

   3. Applied egg-rr 88.4%

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

   4. Taylor expanded in B around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

   6. Simplified 63.2%

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

   7. Taylor expanded in C around inf 45.5%

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

   if -1.9000000000000001e-39 < A < -1.69999999999999998e-70

   1. Initial program 44.1%

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

   2. Taylor expanded in B around inf 53.5%

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

   if -1.69999999999999998e-70 < A < 2.6999999999999999e-132

   1. Initial program 53.0%

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

   2. Taylor expanded in B around -inf 44.0%

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

   if 2.6999999999999999e-132 < A

   1. Initial program 74.0%

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

   2. Taylor expanded in A around inf 59.8%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.05 \cdot 10^{+40}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.9 \cdot 10^{-39}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.7 \cdot 10^{-70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 2.7 \cdot 10^{-132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10: 47.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.05 \cdot 10^{+38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7.6 \cdot 10^{-40}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.9 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.3 \cdot 10^{-135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.05e+38)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A -7.6e-40)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= A -1.9e-67)
       (* 180.0 (/ (atan -1.0) PI))
       (if (<= A 1.3e-135)
         (* 180.0 (/ (atan 1.0) PI))
         (* 180.0 (/ (atan (* -2.0 (/ A B))) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.05e+38) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= -7.6e-40) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (A <= -1.9e-67) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 1.3e-135) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.05e+38) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= -7.6e-40) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (A <= -1.9e-67) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 1.3e-135) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.05e+38:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= -7.6e-40:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif A <= -1.9e-67:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 1.3e-135:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.05e+38)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= -7.6e-40)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (A <= -1.9e-67)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 1.3e-135)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.05e+38)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= -7.6e-40)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (A <= -1.9e-67)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 1.3e-135)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.05e+38], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -7.6e-40], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.9e-67], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.3e-135], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -1.05e38

   1. Initial program 17.4%

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

   2. Taylor expanded in A around -inf 73.1%

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

   if -1.05e38 < A < -7.5999999999999998e-40

   1. Initial program 57.9%

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

   2. Taylor expanded in C around -inf 45.5%

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

   if -7.5999999999999998e-40 < A < -1.89999999999999994e-67

   1. Initial program 44.1%

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

   2. Taylor expanded in B around inf 53.5%

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

   if -1.89999999999999994e-67 < A < 1.30000000000000002e-135

   1. Initial program 53.0%

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

   2. Taylor expanded in B around -inf 44.0%

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

   if 1.30000000000000002e-135 < A

   1. Initial program 74.0%

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

   2. Taylor expanded in A around inf 59.8%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.05 \cdot 10^{+38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7.6 \cdot 10^{-40}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.9 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.3 \cdot 10^{-135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 11: 54.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.16 \cdot 10^{-185}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-131}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4e-106)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (if (<= B 1.8e-244)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= B 1.16e-185)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 5.2e-131)
         (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
         (/ (* -180.0 (atan (/ (+ B A) B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4e-106) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= 1.8e-244) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (B <= 1.16e-185) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 5.2e-131) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((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 tmp;
	if (B <= -4e-106) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= 1.8e-244) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (B <= 1.16e-185) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 5.2e-131) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else {
		tmp = (-180.0 * Math.atan(((B + A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4e-106:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= 1.8e-244:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif B <= 1.16e-185:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 5.2e-131:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / 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 (B <= -4e-106)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= 1.8e-244)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (B <= 1.16e-185)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 5.2e-131)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / 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)
	tmp = 0.0;
	if (B <= -4e-106)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= 1.8e-244)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (B <= 1.16e-185)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 5.2e-131)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	else
		tmp = (-180.0 * atan(((B + A) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4e-106], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.8e-244], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.16e-185], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.2e-131], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / 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 5 regimes

2. if B < -3.99999999999999976e-106

   1. Initial program 49.0%

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

   2. Taylor expanded in C around 0 45.3%

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

      1. associate-*r/ 45.3%

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

      2. mul-1-neg 45.3%

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

      3. +-commutative 45.3%

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

      4. unpow2 45.3%

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

      5. unpow2 45.3%

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

      6. hypot-def 73.6%

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

   4. Simplified 73.6%

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

   5. Taylor expanded in B around -inf 71.3%

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

      1. mul-1-neg 71.3%

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

      2. unsub-neg 71.3%

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

   7. Simplified 71.3%

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

   if -3.99999999999999976e-106 < B < 1.79999999999999987e-244

   1. Initial program 78.8%

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

   2. Taylor expanded in C around -inf 54.4%

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

   if 1.79999999999999987e-244 < B < 1.16000000000000008e-185

   1. Initial program 35.6%

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

   2. Taylor expanded in C around inf 59.8%

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

      1. associate-*r/ 59.8%

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

      2. distribute-rgt1-in 59.8%

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

      3. metadata-eval 59.8%

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

      4. mul0-lft 59.8%

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

      5. metadata-eval 59.8%

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

   4. Simplified 59.8%

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

   if 1.16000000000000008e-185 < B < 5.19999999999999993e-131

   1. Initial program 39.6%

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

      1. associate-*r/ 39.6%

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

      2. associate-*l/ 39.6%

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

      3. *-un-lft-identity 39.6%

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

      4. unpow2 39.6%

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

      5. unpow2 39.6%

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

      6. hypot-def 74.8%

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

   3. Applied egg-rr 74.8%

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

   4. Taylor expanded in A around -inf 40.0%

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

   5. Taylor expanded in B around 0 40.0%

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

      1. associate-*r/ 40.0%

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

      2. *-commutative 40.0%

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

      3. associate-*r/ 40.2%

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

   7. Simplified 40.2%

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

   if 5.19999999999999993e-131 < B

   1. Initial program 52.0%

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

   2. Taylor expanded in C around 0 46.1%

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

      1. associate-*r/ 46.1%

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

      2. mul-1-neg 46.1%

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

      3. +-commutative 46.1%

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

      4. unpow2 46.1%

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

      5. unpow2 46.1%

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

      6. hypot-def 68.7%

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

   4. Simplified 68.7%

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

      1. expm1-log1p-u 1.2%

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

      2. expm1-udef 1.2%

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

   6. Applied egg-rr 1.2%

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

      1. expm1-def 1.2%

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

      2. expm1-log1p 68.7%

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

      3. associate-*r/ 68.7%

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

      4. distribute-rgt-neg-out 68.7%

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

      5. distribute-lft-neg-in 68.7%

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

      6. metadata-eval 68.7%

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

   8. Simplified 68.7%

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

   9. Taylor expanded in A around 0 66.9%

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

       1. +-commutative 66.9%

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

   11. Simplified 66.9%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.16 \cdot 10^{-185}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-131}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 12: 54.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.5 \cdot 10^{-106}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A - B}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-242}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-131}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.5e-106)
   (/ (* -180.0 (atan (/ (- A B) B))) PI)
   (if (<= B 2.1e-242)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= B 1.9e-184)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 5.2e-131)
         (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
         (/ (* -180.0 (atan (/ (+ B A) B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.5e-106) {
		tmp = (-180.0 * atan(((A - B) / B))) / ((double) M_PI);
	} else if (B <= 2.1e-242) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (B <= 1.9e-184) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 5.2e-131) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((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 tmp;
	if (B <= -6.5e-106) {
		tmp = (-180.0 * Math.atan(((A - B) / B))) / Math.PI;
	} else if (B <= 2.1e-242) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (B <= 1.9e-184) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 5.2e-131) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else {
		tmp = (-180.0 * Math.atan(((B + A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -6.5e-106:
		tmp = (-180.0 * math.atan(((A - B) / B))) / math.pi
	elif B <= 2.1e-242:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif B <= 1.9e-184:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 5.2e-131:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / 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 (B <= -6.5e-106)
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(A - B) / B))) / pi);
	elseif (B <= 2.1e-242)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (B <= 1.9e-184)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 5.2e-131)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / 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)
	tmp = 0.0;
	if (B <= -6.5e-106)
		tmp = (-180.0 * atan(((A - B) / B))) / pi;
	elseif (B <= 2.1e-242)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (B <= 1.9e-184)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 5.2e-131)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	else
		tmp = (-180.0 * atan(((B + A) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -6.5e-106], N[(N[(-180.0 * N[ArcTan[N[(N[(A - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 2.1e-242], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.9e-184], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.2e-131], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / 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 5 regimes

2. if B < -6.4999999999999997e-106

   1. Initial program 49.0%

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

   2. Taylor expanded in C around 0 45.3%

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

      1. associate-*r/ 45.3%

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

      2. mul-1-neg 45.3%

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

      3. +-commutative 45.3%

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

      4. unpow2 45.3%

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

      5. unpow2 45.3%

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

      6. hypot-def 73.6%

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

   4. Simplified 73.6%

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

      1. expm1-log1p-u 73.1%

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

      2. expm1-udef 73.1%

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

   6. Applied egg-rr 73.1%

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

      1. expm1-def 73.1%

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

      2. expm1-log1p 73.6%

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

      3. associate-*r/ 73.6%

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

      4. distribute-rgt-neg-out 73.6%

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

      5. distribute-lft-neg-in 73.6%

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

      6. metadata-eval 73.6%

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

   8. Simplified 73.6%

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

   9. Taylor expanded in B around -inf 71.3%

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

       1. mul-1-neg 71.3%

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

       2. unsub-neg 71.3%

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

   11. Simplified 71.3%

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

   if -6.4999999999999997e-106 < B < 2.10000000000000019e-242

   1. Initial program 78.8%

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

   2. Taylor expanded in C around -inf 54.4%

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

   if 2.10000000000000019e-242 < B < 1.90000000000000008e-184

   1. Initial program 35.6%

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

   2. Taylor expanded in C around inf 59.8%

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

      1. associate-*r/ 59.8%

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

      2. distribute-rgt1-in 59.8%

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

      3. metadata-eval 59.8%

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

      4. mul0-lft 59.8%

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

      5. metadata-eval 59.8%

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

   4. Simplified 59.8%

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

   if 1.90000000000000008e-184 < B < 5.19999999999999993e-131

   1. Initial program 39.6%

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

      1. associate-*r/ 39.6%

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

      2. associate-*l/ 39.6%

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

      3. *-un-lft-identity 39.6%

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

      4. unpow2 39.6%

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

      5. unpow2 39.6%

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

      6. hypot-def 74.8%

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

   3. Applied egg-rr 74.8%

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

   4. Taylor expanded in A around -inf 40.0%

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

   5. Taylor expanded in B around 0 40.0%

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

      1. associate-*r/ 40.0%

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

      2. *-commutative 40.0%

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

      3. associate-*r/ 40.2%

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

   7. Simplified 40.2%

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

   if 5.19999999999999993e-131 < B

   1. Initial program 52.0%

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

   2. Taylor expanded in C around 0 46.1%

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

      1. associate-*r/ 46.1%

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

      2. mul-1-neg 46.1%

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

      3. +-commutative 46.1%

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

      4. unpow2 46.1%

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

      5. unpow2 46.1%

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

      6. hypot-def 68.7%

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

   4. Simplified 68.7%

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

      1. expm1-log1p-u 1.2%

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

      2. expm1-udef 1.2%

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

   6. Applied egg-rr 1.2%

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

      1. expm1-def 1.2%

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

      2. expm1-log1p 68.7%

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

      3. associate-*r/ 68.7%

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

      4. distribute-rgt-neg-out 68.7%

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

      5. distribute-lft-neg-in 68.7%

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

      6. metadata-eval 68.7%

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

   8. Simplified 68.7%

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

   9. Taylor expanded in A around 0 66.9%

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

       1. +-commutative 66.9%

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

   11. Simplified 66.9%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.5 \cdot 10^{-106}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A - B}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-242}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-131}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 13: 50.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-242}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-169}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-100}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4e-106)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (if (<= B 3.7e-242)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= B 4e-169)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 2e-100)
         (/ (* 180.0 (atan (/ (- A) B))) PI)
         (* 180.0 (/ (atan -1.0) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4e-106) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= 3.7e-242) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (B <= 4e-169) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 2e-100) {
		tmp = (180.0 * atan((-A / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -4e-106) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= 3.7e-242) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (B <= 4e-169) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 2e-100) {
		tmp = (180.0 * Math.atan((-A / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4e-106:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= 3.7e-242:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif B <= 4e-169:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 2e-100:
		tmp = (180.0 * math.atan((-A / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -4e-106)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= 3.7e-242)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (B <= 4e-169)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 2e-100)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-A) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -4e-106)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= 3.7e-242)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (B <= 4e-169)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 2e-100)
		tmp = (180.0 * atan((-A / B))) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4e-106], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.7e-242], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4e-169], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2e-100], N[(N[(180.0 * N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -3.99999999999999976e-106

   1. Initial program 49.0%

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

   2. Taylor expanded in C around 0 45.3%

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

      1. associate-*r/ 45.3%

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

      2. mul-1-neg 45.3%

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

      3. +-commutative 45.3%

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

      4. unpow2 45.3%

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

      5. unpow2 45.3%

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

      6. hypot-def 73.6%

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

   4. Simplified 73.6%

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

   5. Taylor expanded in B around -inf 71.3%

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

      1. mul-1-neg 71.3%

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

      2. unsub-neg 71.3%

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

   7. Simplified 71.3%

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

   if -3.99999999999999976e-106 < B < 3.69999999999999997e-242

   1. Initial program 78.8%

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

   2. Taylor expanded in C around -inf 54.4%

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

   if 3.69999999999999997e-242 < B < 4.00000000000000008e-169

   1. Initial program 36.1%

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

   2. Taylor expanded in C around inf 51.7%

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

      1. associate-*r/ 51.7%

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

      2. distribute-rgt1-in 51.7%

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

      3. metadata-eval 51.7%

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

      4. mul0-lft 51.7%

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

      5. metadata-eval 51.7%

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

   4. Simplified 51.7%

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

   if 4.00000000000000008e-169 < B < 2e-100

   1. Initial program 60.1%

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

      1. associate-*r/ 60.1%

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

      2. associate-*l/ 60.1%

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

      3. *-un-lft-identity 60.1%

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

      4. unpow2 60.1%

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

      5. unpow2 60.1%

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

      6. hypot-def 69.1%

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

   3. Applied egg-rr 69.1%

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

   4. Taylor expanded in B around inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. unsub-neg 59.4%

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

   6. Simplified 59.4%

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

   7. Taylor expanded in A around inf 43.3%

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

      1. associate-*r/ 43.3%

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

      2. neg-mul-1 43.3%

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

   9. Simplified 43.3%

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

   if 2e-100 < B

   1. Initial program 50.4%

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

   2. Taylor expanded in B around inf 52.6%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-242}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-169}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-100}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 14: 45.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.3 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-242}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-186}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-152}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ C B))) PI)))
   (if (<= B -3.3e-63)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 9.5e-242)
       t_0
       (if (<= B 3.1e-186)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 2.1e-152) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan((C / B))) / ((double) M_PI);
	double tmp;
	if (B <= -3.3e-63) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 9.5e-242) {
		tmp = t_0;
	} else if (B <= 3.1e-186) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 2.1e-152) {
		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((C / B))) / Math.PI;
	double tmp;
	if (B <= -3.3e-63) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 9.5e-242) {
		tmp = t_0;
	} else if (B <= 3.1e-186) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 2.1e-152) {
		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((C / B))) / math.pi
	tmp = 0
	if B <= -3.3e-63:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 9.5e-242:
		tmp = t_0
	elif B <= 3.1e-186:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 2.1e-152:
		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(C / B))) / pi)
	tmp = 0.0
	if (B <= -3.3e-63)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 9.5e-242)
		tmp = t_0;
	elseif (B <= 3.1e-186)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 2.1e-152)
		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((C / B))) / pi;
	tmp = 0.0;
	if (B <= -3.3e-63)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 9.5e-242)
		tmp = t_0;
	elseif (B <= 3.1e-186)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 2.1e-152)
		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[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[B, -3.3e-63], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.5e-242], t$95$0, If[LessEqual[B, 3.1e-186], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.1e-152], 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 < -3.29999999999999994e-63

   1. Initial program 46.9%

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

   2. Taylor expanded in B around -inf 60.8%

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

   if -3.29999999999999994e-63 < B < 9.4999999999999997e-242 or 3.10000000000000009e-186 < B < 2.09999999999999999e-152

   1. Initial program 74.0%

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

      1. associate-*r/ 74.0%

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

      2. associate-*l/ 74.0%

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

      3. *-un-lft-identity 74.0%

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

      4. unpow2 74.0%

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

      5. unpow2 74.0%

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

      6. hypot-def 92.7%

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

   3. Applied egg-rr 92.7%

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

   4. Taylor expanded in B around inf 61.8%

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

      1. mul-1-neg 61.8%

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

      2. unsub-neg 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in C around inf 49.7%

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

   if 9.4999999999999997e-242 < B < 3.10000000000000009e-186

   1. Initial program 35.6%

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

   2. Taylor expanded in C around inf 59.8%

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

      1. associate-*r/ 59.8%

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

      2. distribute-rgt1-in 59.8%

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

      3. metadata-eval 59.8%

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

      4. mul0-lft 59.8%

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

      5. metadata-eval 59.8%

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

   4. Simplified 59.8%

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

   if 2.09999999999999999e-152 < B

   1. Initial program 50.6%

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

   2. Taylor expanded in B around inf 49.0%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.3 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-242}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-186}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-152}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 15: 61.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.9 \cdot 10^{+40}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{-182}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.9e+40)
   (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
   (if (<= A 4.4e-182)
     (/ (* 180.0 (atan (/ (+ B C) B))) PI)
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.9e+40) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	} else if (A <= 4.4e-182) {
		tmp = (180.0 * atan(((B + C) / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.9e+40) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else if (A <= 4.4e-182) {
		tmp = (180.0 * Math.atan(((B + C) / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.9e+40:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	elif A <= 4.4e-182:
		tmp = (180.0 * math.atan(((B + C) / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.9e+40)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	elseif (A <= 4.4e-182)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B + C) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.9e+40)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	elseif (A <= 4.4e-182)
		tmp = (180.0 * atan(((B + C) / B))) / pi;
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.9e+40], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.4e-182], N[(N[(180.0 * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.8999999999999999e40

   1. Initial program 17.4%

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

      1. associate-*r/ 17.4%

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

      2. associate-*l/ 17.4%

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

      3. *-un-lft-identity 17.4%

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

      4. unpow2 17.4%

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

      5. unpow2 17.4%

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

      6. hypot-def 49.4%

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

   3. Applied egg-rr 49.4%

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

   4. Taylor expanded in A around -inf 73.2%

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

   5. Taylor expanded in B around 0 73.1%

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

      1. associate-*r/ 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-*r/ 73.4%

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

   7. Simplified 73.4%

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

   if -5.8999999999999999e40 < A < 4.3999999999999999e-182

   1. Initial program 51.2%

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

      1. associate-*r/ 51.2%

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

      2. associate-*l/ 51.2%

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

      3. *-un-lft-identity 51.2%

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

      4. unpow2 51.2%

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

      5. unpow2 51.2%

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

      6. hypot-def 85.7%

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

   3. Applied egg-rr 85.7%

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

   4. Taylor expanded in A around 0 50.4%

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

      1. unpow2 50.4%

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

      2. unpow2 50.4%

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

      3. hypot-def 84.3%

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

   6. Simplified 84.3%

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

   7. Taylor expanded in B around -inf 60.0%

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

   if 4.3999999999999999e-182 < A

   1. Initial program 74.3%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in B around inf 75.2%

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

      1. +-commutative 75.2%

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

   6. Simplified 75.2%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.9 \cdot 10^{+40}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{-182}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 16: 61.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+46}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{-182}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{B}{B + C}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.2e+46)
   (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
   (if (<= A 9e-182)
     (/ (* 180.0 (atan (/ 1.0 (/ B (+ B C))))) PI)
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.2e+46) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	} else if (A <= 9e-182) {
		tmp = (180.0 * atan((1.0 / (B / (B + C))))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.2e+46) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else if (A <= 9e-182) {
		tmp = (180.0 * Math.atan((1.0 / (B / (B + C))))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.2e+46:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	elif A <= 9e-182:
		tmp = (180.0 * math.atan((1.0 / (B / (B + C))))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.2e+46)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	elseif (A <= 9e-182)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(B / Float64(B + C))))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.2e+46)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	elseif (A <= 9e-182)
		tmp = (180.0 * atan((1.0 / (B / (B + C))))) / pi;
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.2e+46], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9e-182], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(B / N[(B + C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.20000000000000027e46

   1. Initial program 17.4%

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

      1. associate-*r/ 17.4%

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

      2. associate-*l/ 17.4%

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

      3. *-un-lft-identity 17.4%

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

      4. unpow2 17.4%

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

      5. unpow2 17.4%

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

      6. hypot-def 49.4%

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

   3. Applied egg-rr 49.4%

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

   4. Taylor expanded in A around -inf 73.2%

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

   5. Taylor expanded in B around 0 73.1%

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

      1. associate-*r/ 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-*r/ 73.4%

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

   7. Simplified 73.4%

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

   if -5.20000000000000027e46 < A < 8.9999999999999998e-182

   1. Initial program 51.2%

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

      1. associate-*r/ 51.2%

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

      2. associate-*l/ 51.2%

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

      3. *-un-lft-identity 51.2%

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

      4. unpow2 51.2%

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

      5. unpow2 51.2%

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

      6. hypot-def 85.7%

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

   3. Applied egg-rr 85.7%

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

      1. clear-num 85.7%

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

      2. inv-pow 85.7%

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

   5. Applied egg-rr 85.7%

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

      1. unpow-1 85.7%

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

      2. associate--r+ 85.7%

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

   7. Simplified 85.7%

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

   8. Taylor expanded in B around -inf 60.0%

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

      1. mul-1-neg 60.0%

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

   10. Simplified 60.0%

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

   if 8.9999999999999998e-182 < A

   1. Initial program 74.3%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in B around inf 75.2%

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

      1. +-commutative 75.2%

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

   6. Simplified 75.2%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+46}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{-182}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{B}{B + C}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 17: 59.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.25 \cdot 10^{+41}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{-180}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-B\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.25e+41)
   (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
   (if (<= A 1.55e-180)
     (/ (* 180.0 (atan (/ (+ B C) B))) PI)
     (* 180.0 (/ (atan (/ (- (- B) A) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.25e+41) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	} else if (A <= 1.55e-180) {
		tmp = (180.0 * atan(((B + C) / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((-B - A) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.25e+41) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else if (A <= 1.55e-180) {
		tmp = (180.0 * Math.atan(((B + C) / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((-B - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.25e+41:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	elif A <= 1.55e-180:
		tmp = (180.0 * math.atan(((B + C) / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((-B - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.25e+41)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	elseif (A <= 1.55e-180)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B + C) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-B) - A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.25e+41)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	elseif (A <= 1.55e-180)
		tmp = (180.0 * atan(((B + C) / B))) / pi;
	else
		tmp = 180.0 * (atan(((-B - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.25e+41], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.55e-180], N[(N[(180.0 * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[((-B) - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.25000000000000006e41

   1. Initial program 17.4%

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

      1. associate-*r/ 17.4%

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

      2. associate-*l/ 17.4%

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

      3. *-un-lft-identity 17.4%

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

      4. unpow2 17.4%

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

      5. unpow2 17.4%

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

      6. hypot-def 49.4%

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

   3. Applied egg-rr 49.4%

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

   4. Taylor expanded in A around -inf 73.2%

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

   5. Taylor expanded in B around 0 73.1%

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

      1. associate-*r/ 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-*r/ 73.4%

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

   7. Simplified 73.4%

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

   if -1.25000000000000006e41 < A < 1.5499999999999999e-180

   1. Initial program 51.7%

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

      1. associate-*r/ 51.7%

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

      2. associate-*l/ 51.7%

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

      3. *-un-lft-identity 51.7%

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

      4. unpow2 51.7%

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

      5. unpow2 51.7%

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

      6. hypot-def 85.9%

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

   3. Applied egg-rr 85.9%

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

   4. Taylor expanded in A around 0 50.9%

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

      1. unpow2 50.9%

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

      2. unpow2 50.9%

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

      3. hypot-def 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in B around -inf 60.4%

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

   if 1.5499999999999999e-180 < A

   1. Initial program 74.1%

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

   2. Taylor expanded in C around 0 68.1%

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

      1. associate-*r/ 68.1%

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

      2. mul-1-neg 68.1%

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

      3. +-commutative 68.1%

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

      4. unpow2 68.1%

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

      5. unpow2 68.1%

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

      6. hypot-def 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in A around 0 69.5%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.25 \cdot 10^{+41}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{-180}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-B\right) - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 18: 56.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -2.25 \cdot 10^{+66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 9.6 \cdot 10^{+99}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -2.25e+66)
   (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
   (if (<= C 9.6e+99)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (* 180.0 (/ (atan (/ (* B -0.5) C)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.25e+66) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= 9.6e+99) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.25e+66) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= 9.6e+99) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -2.25e+66:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= 9.6e+99:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -2.25e+66)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= 9.6e+99)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -2.25e+66)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= 9.6e+99)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -2.25e+66], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 9.6e+99], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -2.2499999999999999e66

   1. Initial program 77.3%

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

   2. Taylor expanded in C around -inf 73.7%

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

   if -2.2499999999999999e66 < C < 9.6000000000000005e99

   1. Initial program 56.5%

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

   2. Taylor expanded in C around 0 52.6%

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

      1. associate-*r/ 52.6%

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

      2. mul-1-neg 52.6%

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

      3. +-commutative 52.6%

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

      4. unpow2 52.6%

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

      5. unpow2 52.6%

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

      6. hypot-def 81.5%

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

   4. Simplified 81.5%

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

   5. Taylor expanded in B around -inf 52.0%

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

      1. mul-1-neg 52.0%

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

      2. unsub-neg 52.0%

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

   7. Simplified 52.0%

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

   if 9.6000000000000005e99 < C

   1. Initial program 22.9%

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

   2. Taylor expanded in C around inf 49.2%

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

   3. Taylor expanded in B around inf 77.3%

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

      1. associate-*r/ 77.3%

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

   5. Simplified 77.3%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.25 \cdot 10^{+66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 9.6 \cdot 10^{+99}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \]

Alternative 19: 56.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.7 \cdot 10^{+65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 9.6 \cdot 10^{+99}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.7e+65)
   (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
   (if (<= C 9.6e+99)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (* (atan (* -0.5 (/ B C))) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.7e+65) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= 9.6e+99) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = atan((-0.5 * (B / C))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.7e+65) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= 9.6e+99) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = Math.atan((-0.5 * (B / C))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.7e+65:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= 9.6e+99:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = math.atan((-0.5 * (B / C))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.7e+65)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= 9.6e+99)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(atan(Float64(-0.5 * Float64(B / C))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.7e+65)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= 9.6e+99)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = atan((-0.5 * (B / C))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.7e+65], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 9.6e+99], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.7e65

   1. Initial program 77.3%

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

   2. Taylor expanded in C around -inf 73.7%

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

   if -1.7e65 < C < 9.6000000000000005e99

   1. Initial program 56.5%

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

   2. Taylor expanded in C around 0 52.6%

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

      1. associate-*r/ 52.6%

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

      2. mul-1-neg 52.6%

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

      3. +-commutative 52.6%

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

      4. unpow2 52.6%

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

      5. unpow2 52.6%

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

      6. hypot-def 81.5%

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

   4. Simplified 81.5%

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

   5. Taylor expanded in B around -inf 52.0%

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

      1. mul-1-neg 52.0%

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

      2. unsub-neg 52.0%

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

   7. Simplified 52.0%

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

   if 9.6000000000000005e99 < C

   1. Initial program 22.9%

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

      1. associate-*r/ 22.9%

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

      2. associate-*l/ 22.9%

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

      3. *-un-lft-identity 22.9%

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

      4. unpow2 22.9%

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

      5. unpow2 22.9%

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

      6. hypot-def 54.7%

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

   3. Applied egg-rr 54.7%

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

   4. Taylor expanded in C around inf 44.4%

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

      1. +-commutative 44.4%

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

      2. fma-def 44.4%

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

   6. Simplified 62.2%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\mathsf{fma}\left(-0.5, \frac{{B}^{2} + 0}{B \cdot C}, 0\right)\right)}}{\pi} \]
   7. Step-by-step derivation

      1. expm1-log1p-u 62.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{{B}^{2} + 0}{B \cdot C}, 0\right)\right)}{\pi}\right)\right)} \]

      2. expm1-udef 34.5%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{{B}^{2} + 0}{B \cdot C}, 0\right)\right)}{\pi}\right)} - 1} \]

   8. Applied egg-rr 36.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, 0\right)\right)}}\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 77.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, 0\right)\right)}}\right)\right)} \]

      2. expm1-log1p 77.4%

         \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, 0\right)\right)}}} \]

      3. associate-/r/ 77.4%

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

      4. fma-udef 77.4%

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

      5. +-rgt-identity 77.4%

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

   10. Simplified 77.4%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.7 \cdot 10^{+65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 9.6 \cdot 10^{+99}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \]

Alternative 20: 59.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.6 \cdot 10^{+45}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-180}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.6e+45)
   (* (atan (* 0.5 (/ B A))) (/ 180.0 PI))
   (if (<= A 2.1e-180)
     (/ (* 180.0 (atan (/ (+ B C) B))) PI)
     (/ (* -180.0 (atan (/ (+ B A) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.6e+45) {
		tmp = atan((0.5 * (B / A))) * (180.0 / ((double) M_PI));
	} else if (A <= 2.1e-180) {
		tmp = (180.0 * atan(((B + C) / B))) / ((double) M_PI);
	} else {
		tmp = (-180.0 * atan(((B + A) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.6e+45) {
		tmp = Math.atan((0.5 * (B / A))) * (180.0 / Math.PI);
	} else if (A <= 2.1e-180) {
		tmp = (180.0 * Math.atan(((B + C) / B))) / Math.PI;
	} else {
		tmp = (-180.0 * Math.atan(((B + A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.6e+45:
		tmp = math.atan((0.5 * (B / A))) * (180.0 / math.pi)
	elif A <= 2.1e-180:
		tmp = (180.0 * math.atan(((B + C) / B))) / math.pi
	else:
		tmp = (-180.0 * math.atan(((B + A) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.6e+45)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(180.0 / pi));
	elseif (A <= 2.1e-180)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(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 <= -5.6e+45)
		tmp = atan((0.5 * (B / A))) * (180.0 / pi);
	elseif (A <= 2.1e-180)
		tmp = (180.0 * atan(((B + C) / B))) / pi;
	else
		tmp = (-180.0 * atan(((B + A) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.6e+45], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.1e-180], N[(N[(180.0 * N[ArcTan[N[(N[(B + C), $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 < -5.5999999999999999e45

   1. Initial program 17.4%

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

      1. associate-*r/ 17.4%

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

      2. associate-*l/ 17.4%

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

      3. *-un-lft-identity 17.4%

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

      4. unpow2 17.4%

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

      5. unpow2 17.4%

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

      6. hypot-def 49.4%

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

   3. Applied egg-rr 49.4%

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

   4. Taylor expanded in A around -inf 73.2%

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

   5. Taylor expanded in B around 0 73.1%

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

      1. associate-*r/ 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-*r/ 73.4%

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

   7. Simplified 73.4%

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

   if -5.5999999999999999e45 < A < 2.0999999999999999e-180

   1. Initial program 51.7%

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

      1. associate-*r/ 51.7%

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

      2. associate-*l/ 51.7%

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

      3. *-un-lft-identity 51.7%

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

      4. unpow2 51.7%

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

      5. unpow2 51.7%

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

      6. hypot-def 85.9%

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

   3. Applied egg-rr 85.9%

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

   4. Taylor expanded in A around 0 50.9%

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

      1. unpow2 50.9%

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

      2. unpow2 50.9%

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

      3. hypot-def 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in B around -inf 60.4%

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

   if 2.0999999999999999e-180 < A

   1. Initial program 74.1%

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

   2. Taylor expanded in C around 0 68.1%

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

      1. associate-*r/ 68.1%

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

      2. mul-1-neg 68.1%

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

      3. +-commutative 68.1%

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

      4. unpow2 68.1%

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

      5. unpow2 68.1%

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

      6. hypot-def 78.5%

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

   4. Simplified 78.5%

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

      1. expm1-log1p-u 30.7%

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

      2. expm1-udef 30.7%

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

   6. Applied egg-rr 30.7%

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

      1. expm1-def 30.7%

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

      2. expm1-log1p 78.5%

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

      3. associate-*r/ 78.5%

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

      4. distribute-rgt-neg-out 78.5%

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

      5. distribute-lft-neg-in 78.5%

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

      6. metadata-eval 78.5%

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

   8. Simplified 78.5%

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

   9. Taylor expanded in A around 0 69.5%

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

       1. +-commutative 69.5%

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

   11. Simplified 69.5%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.6 \cdot 10^{+45}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-180}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 21: 43.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.7 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.7e-216)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 3.6e-176)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.7e-216) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 3.6e-176) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.7e-216) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 3.6e-176) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5.7e-216:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 3.6e-176:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5.7e-216)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 3.6e-176)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5.7e-216)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 3.6e-176)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5.7e-216], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.6e-176], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -5.70000000000000004e-216

   1. Initial program 53.6%

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

   2. Taylor expanded in B around -inf 51.8%

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

   if -5.70000000000000004e-216 < B < 3.6000000000000003e-176

   1. Initial program 66.5%

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

   2. Taylor expanded in C around inf 39.6%

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

      1. associate-*r/ 39.6%

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

      2. distribute-rgt1-in 39.6%

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

      3. metadata-eval 39.6%

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

      4. mul0-lft 39.6%

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

      5. metadata-eval 39.6%

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

   4. Simplified 39.6%

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

   if 3.6000000000000003e-176 < B

   1. Initial program 50.6%

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

   2. Taylor expanded in B around inf 48.5%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.7 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 22: 40.3% 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 55.7%

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

   2. Taylor expanded in B around -inf 47.1%

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

   if -4.999999999999985e-310 < B

   1. Initial program 53.5%

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

   2. Taylor expanded in B around inf 40.6%

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

4. Final simplification 43.7%

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

Alternative 23: 21.4% 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 54.6%

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

2. Taylor expanded in B around inf 21.6%

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

3. Final simplification 21.6%

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

Reproduce

herbie shell --seed 2023338 
(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)))