ABCF->ab-angle angle

Percentage Accurate: 54.1% → 88.5%

Time: 24.5s

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: 54.1% 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: 88.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_1 := \left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{-46}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{t_1}{B}\right)}}\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{B}{t_1}}\right)}{\pi}\\ \end{array} \end{array} \]

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))))
   (if (<= t_0 -5e-46)
     (/ 180.0 (/ PI (atan (/ t_1 B))))
     (if (<= t_0 0.0)
       (/ (* 180.0 (atan (/ 1.0 (+ (* -2.0 (/ C B)) (* 2.0 (/ A B)))))) PI)
       (/ (* 180.0 (atan (/ 1.0 (/ B t_1)))) 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);
	double tmp;
	if (t_0 <= -5e-46) {
		tmp = 180.0 / (((double) M_PI) / atan((t_1 / B)));
	} 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((1.0 / (B / t_1)))) / ((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);
	double tmp;
	if (t_0 <= -5e-46) {
		tmp = 180.0 / (Math.PI / Math.atan((t_1 / B)));
	} 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((1.0 / (B / t_1)))) / 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)
	tmp = 0
	if t_0 <= -5e-46:
		tmp = 180.0 / (math.pi / math.atan((t_1 / B)))
	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((1.0 / (B / t_1)))) / 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(C - A) - hypot(Float64(A - C), B))
	tmp = 0.0
	if (t_0 <= -5e-46)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(t_1 / B))));
	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(Float64(180.0 * atan(Float64(1.0 / Float64(B / t_1)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	t_1 = (C - A) - hypot((A - C), B);
	tmp = 0.0;
	if (t_0 <= -5e-46)
		tmp = 180.0 / (pi / atan((t_1 / B)));
	elseif (t_0 <= 0.0)
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / pi;
	else
		tmp = (180.0 * atan((1.0 / (B / t_1)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e-46], N[(180.0 / N[(Pi / N[ArcTan[N[(t$95$1 / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $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[(N[(180.0 * N[ArcTan[N[(1.0 / N[(B / t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -4.99999999999999992e-46

   1. Initial program 56.4%

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

   3. Applied egg-rr 87.8%

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

   if -4.99999999999999992e-46 < (*.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 12.1%

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

      1. associate-*r/ 12.1%

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

      2. associate-*l/ 12.1%

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

      3. *-un-lft-identity 12.1%

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

      4. unpow2 12.1%

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

      5. unpow2 12.1%

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

      6. hypot-def 12.1%

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

   3. Applied egg-rr 12.1%

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

      1. clear-num 12.1%

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

      2. inv-pow 12.1%

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

      3. associate--l- 12.1%

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

   5. Applied egg-rr 12.1%

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

      1. unpow-1 12.1%

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

      2. associate--r+ 12.1%

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

   7. Simplified 12.1%

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

   8. Taylor expanded in A around -inf 99.0%

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

   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 63.4%

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

      1. associate-*r/ 63.4%

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

      2. associate-*l/ 63.4%

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

      3. *-un-lft-identity 63.4%

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

      4. unpow2 63.4%

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

      5. unpow2 63.4%

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

      6. hypot-def 89.5%

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

   3. Applied egg-rr 89.5%

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

      1. clear-num 89.5%

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

      2. inv-pow 89.5%

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

      3. associate--l- 86.0%

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

   5. Applied egg-rr 86.0%

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

      1. unpow-1 86.0%

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

      2. associate--r+ 89.5%

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

   7. Simplified 89.5%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -5 \cdot 10^{-46}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{\frac{B}{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}}\right)}{\pi}\\ \end{array} \]

Alternative 2: 80.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{+109}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9e+109)
   (/ (* 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 <= -9e+109) {
		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 <= -9e+109) {
		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 <= -9e+109:
		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 <= -9e+109)
		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 <= -9e+109)
		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, -9e+109], 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 < -8.9999999999999992e109

   1. Initial program 11.8%

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

      1. associate-*r/ 11.8%

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

      2. associate-*l/ 11.8%

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

      3. *-un-lft-identity 11.8%

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

      4. unpow2 11.8%

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

      5. unpow2 11.8%

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

      6. hypot-def 49.9%

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

   3. Applied egg-rr 49.9%

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

      1. clear-num 49.9%

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

      2. inv-pow 49.9%

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

      3. associate--l- 27.8%

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

   5. Applied egg-rr 27.8%

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

      1. unpow-1 27.8%

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

      2. associate--r+ 49.9%

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

   7. Simplified 49.9%

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

   8. Taylor expanded in A around -inf 79.2%

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

   if -8.9999999999999992e109 < A

   1. Initial program 62.8%

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

   3. Simplified 86.5%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{+109}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3: 81.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{+109}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.35e+109)
   (/ (* 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 <= -1.35e+109) {
		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 <= -1.35e+109) {
		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 <= -1.35e+109:
		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 <= -1.35e+109)
		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 <= -1.35e+109)
		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, -1.35e+109], 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 < -1.35000000000000001e109

   1. Initial program 11.8%

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

      1. associate-*r/ 11.8%

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

      2. associate-*l/ 11.8%

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

      3. *-un-lft-identity 11.8%

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

      4. unpow2 11.8%

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

      5. unpow2 11.8%

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

      6. hypot-def 49.9%

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

   3. Applied egg-rr 49.9%

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

      1. clear-num 49.9%

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

      2. inv-pow 49.9%

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

      3. associate--l- 27.8%

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

   5. Applied egg-rr 27.8%

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

      1. unpow-1 27.8%

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

      2. associate--r+ 49.9%

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

   7. Simplified 49.9%

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

   8. Taylor expanded in A around -inf 79.2%

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

   if -1.35000000000000001e109 < A

   1. Initial program 62.8%

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

      1. associate-*r/ 62.8%

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

      2. associate-*l/ 62.8%

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

      3. *-un-lft-identity 62.8%

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

      4. unpow2 62.8%

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

      5. unpow2 62.8%

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

      6. hypot-def 86.5%

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

   3. Applied egg-rr 86.5%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{+109}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 77.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3 \cdot 10^{+109}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{+80}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3e+109)
   (/ (* 180.0 (atan (/ 1.0 (+ (* -2.0 (/ C B)) (* 2.0 (/ A B)))))) PI)
   (if (<= A 1.8e+80)
     (/ (* 180.0 (atan (/ (- C (hypot B C)) B))) PI)
     (* 180.0 (/ (atan (/ (- (- A) (hypot B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3e+109) {
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / ((double) M_PI);
	} else if (A <= 1.8e+80) {
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3e+109) {
		tmp = (180.0 * Math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / Math.PI;
	} else if (A <= 1.8e+80) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(B, C)) / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(B, A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3e+109:
		tmp = (180.0 * math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / math.pi
	elif A <= 1.8e+80:
		tmp = (180.0 * math.atan(((C - math.hypot(B, C)) / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((-A - math.hypot(B, A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3e+109)
		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 <= 1.8e+80)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(B, C)) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(B, A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3e+109)
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / pi;
	elseif (A <= 1.8e+80)
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / pi;
	else
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3e+109], 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, 1.8e+80], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.00000000000000015e109

   1. Initial program 11.8%

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

      1. associate-*r/ 11.8%

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

      2. associate-*l/ 11.8%

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

      3. *-un-lft-identity 11.8%

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

      4. unpow2 11.8%

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

      5. unpow2 11.8%

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

      6. hypot-def 49.9%

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

   3. Applied egg-rr 49.9%

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

      1. clear-num 49.9%

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

      2. inv-pow 49.9%

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

      3. associate--l- 27.8%

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

   5. Applied egg-rr 27.8%

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

      1. unpow-1 27.8%

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

      2. associate--r+ 49.9%

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

   7. Simplified 49.9%

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

   8. Taylor expanded in A around -inf 79.2%

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

   if -3.00000000000000015e109 < A < 1.79999999999999997e80

   1. Initial program 56.4%

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

      1. associate-*r/ 56.3%

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

      2. associate-*l/ 56.3%

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

      3. *-un-lft-identity 56.3%

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

      4. unpow2 56.3%

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

      5. unpow2 56.3%

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

      6. hypot-def 83.5%

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

   3. Applied egg-rr 83.5%

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

   4. Taylor expanded in A around 0 52.2%

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

      1. unpow2 52.2%

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

      2. unpow2 52.2%

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

      3. hypot-def 79.6%

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

   6. Simplified 79.6%

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

   if 1.79999999999999997e80 < A

   1. Initial program 83.5%

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

   2. Taylor expanded in C around 0 83.6%

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

      1. associate-*r/ 83.6%

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

      2. mul-1-neg 83.6%

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

      3. +-commutative 83.6%

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

      4. unpow2 83.6%

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

      5. unpow2 83.6%

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

      6. hypot-def 95.9%

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

   4. Simplified 95.9%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3 \cdot 10^{+109}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{+80}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 75.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.05 \cdot 10^{+110}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{+89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.05e+110)
   (/ (* 180.0 (atan (/ 1.0 (+ (* -2.0 (/ C B)) (* 2.0 (/ A B)))))) PI)
   (if (<= A 1.2e+89)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.05e+110) {
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / ((double) M_PI);
	} else if (A <= 1.2e+89) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.05e+110) {
		tmp = (180.0 * Math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / Math.PI;
	} else if (A <= 1.2e+89) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.05e+110:
		tmp = (180.0 * math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / math.pi
	elif A <= 1.2e+89:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.05e+110)
		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 <= 1.2e+89)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.05e+110)
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / pi;
	elseif (A <= 1.2e+89)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.05e+110], 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, 1.2e+89], 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[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.05000000000000007e110

   1. Initial program 11.8%

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

      1. associate-*r/ 11.8%

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

      2. associate-*l/ 11.8%

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

      3. *-un-lft-identity 11.8%

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

      4. unpow2 11.8%

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

      5. unpow2 11.8%

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

      6. hypot-def 49.9%

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

   3. Applied egg-rr 49.9%

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

      1. clear-num 49.9%

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

      2. inv-pow 49.9%

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

      3. associate--l- 27.8%

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

   5. Applied egg-rr 27.8%

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

      1. unpow-1 27.8%

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

      2. associate--r+ 49.9%

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

   7. Simplified 49.9%

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

   8. Taylor expanded in A around -inf 79.2%

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

   if -1.05000000000000007e110 < A < 1.20000000000000002e89

   1. Initial program 56.4%

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

   2. Taylor expanded in A around 0 52.2%

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

      1. unpow2 52.2%

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

      2. unpow2 52.2%

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

      3. hypot-def 79.6%

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

   4. Simplified 79.6%

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

   if 1.20000000000000002e89 < A

   1. Initial program 83.5%

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

   2. Taylor expanded in C around 0 83.6%

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

      1. associate-*r/ 83.6%

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

      2. mul-1-neg 83.6%

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

      3. +-commutative 83.6%

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

      4. unpow2 83.6%

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

      5. unpow2 83.6%

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

      6. hypot-def 95.9%

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

   4. Simplified 95.9%

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

   5. Taylor expanded in B around -inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. unsub-neg 89.7%

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

   7. Simplified 89.7%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.05 \cdot 10^{+110}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{+89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 6: 75.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.1 \cdot 10^{+109}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{+81}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.1e+109)
   (/ (* 180.0 (atan (/ 1.0 (+ (* -2.0 (/ C B)) (* 2.0 (/ A B)))))) PI)
   (if (<= A 1.35e+81)
     (/ (* 180.0 (atan (/ (- C (hypot B C)) B))) PI)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.1e+109) {
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / ((double) M_PI);
	} else if (A <= 1.35e+81) {
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.1e+109) {
		tmp = (180.0 * Math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / Math.PI;
	} else if (A <= 1.35e+81) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(B, C)) / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.1e+109:
		tmp = (180.0 * math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / math.pi
	elif A <= 1.35e+81:
		tmp = (180.0 * math.atan(((C - math.hypot(B, C)) / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.1e+109)
		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 <= 1.35e+81)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(B, C)) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.1e+109)
		tmp = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / pi;
	elseif (A <= 1.35e+81)
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / pi;
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.1e+109], 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, 1.35e+81], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.1e109

   1. Initial program 11.8%

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

      1. associate-*r/ 11.8%

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

      2. associate-*l/ 11.8%

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

      3. *-un-lft-identity 11.8%

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

      4. unpow2 11.8%

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

      5. unpow2 11.8%

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

      6. hypot-def 49.9%

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

   3. Applied egg-rr 49.9%

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

      1. clear-num 49.9%

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

      2. inv-pow 49.9%

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

      3. associate--l- 27.8%

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

   5. Applied egg-rr 27.8%

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

      1. unpow-1 27.8%

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

      2. associate--r+ 49.9%

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

   7. Simplified 49.9%

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

   8. Taylor expanded in A around -inf 79.2%

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

   if -1.1e109 < A < 1.35e81

   1. Initial program 56.4%

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

      1. associate-*r/ 56.3%

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

      2. associate-*l/ 56.3%

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

      3. *-un-lft-identity 56.3%

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

      4. unpow2 56.3%

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

      5. unpow2 56.3%

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

      6. hypot-def 83.5%

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

   3. Applied egg-rr 83.5%

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

   4. Taylor expanded in A around 0 52.2%

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

      1. unpow2 52.2%

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

      2. unpow2 52.2%

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

      3. hypot-def 79.6%

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

   6. Simplified 79.6%

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

   if 1.35e81 < A

   1. Initial program 83.5%

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

   2. Taylor expanded in C around 0 83.6%

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

      1. associate-*r/ 83.6%

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

      2. mul-1-neg 83.6%

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

      3. +-commutative 83.6%

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

      4. unpow2 83.6%

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

      5. unpow2 83.6%

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

      6. hypot-def 95.9%

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

   4. Simplified 95.9%

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

   5. Taylor expanded in B around -inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. unsub-neg 89.7%

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

   7. Simplified 89.7%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.1 \cdot 10^{+109}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{+81}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 65.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ t_1 := \frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.9 \cdot 10^{-127}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.34 \cdot 10^{-291}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-275}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{1 + \frac{A - C}{B}}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-169}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))
        (t_1
         (/ (* 180.0 (atan (/ 1.0 (+ (* -2.0 (/ C B)) (* 2.0 (/ A B)))))) PI)))
   (if (<= B -1.9e-127)
     (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
     (if (<= B -3e-173)
       t_1
       (if (<= B 1.34e-291)
         t_0
         (if (<= B 7.8e-275)
           (/ (* 180.0 (atan (/ 1.0 (+ 1.0 (/ (- A C) B))))) PI)
           (if (<= B 3.3e-169)
             t_0
             (if (<= B 1.55e-138)
               t_1
               (/ 180.0 (/ PI (atan (/ (- (- C B) A) B))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	double t_1 = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / ((double) M_PI);
	double tmp;
	if (B <= -1.9e-127) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else if (B <= -3e-173) {
		tmp = t_1;
	} else if (B <= 1.34e-291) {
		tmp = t_0;
	} else if (B <= 7.8e-275) {
		tmp = (180.0 * atan((1.0 / (1.0 + ((A - C) / B))))) / ((double) M_PI);
	} else if (B <= 3.3e-169) {
		tmp = t_0;
	} else if (B <= 1.55e-138) {
		tmp = t_1;
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((C - B) - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	double t_1 = (180.0 * Math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / Math.PI;
	double tmp;
	if (B <= -1.9e-127) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else if (B <= -3e-173) {
		tmp = t_1;
	} else if (B <= 1.34e-291) {
		tmp = t_0;
	} else if (B <= 7.8e-275) {
		tmp = (180.0 * Math.atan((1.0 / (1.0 + ((A - C) / B))))) / Math.PI;
	} else if (B <= 3.3e-169) {
		tmp = t_0;
	} else if (B <= 1.55e-138) {
		tmp = t_1;
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((C - B) - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	t_1 = (180.0 * math.atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / math.pi
	tmp = 0
	if B <= -1.9e-127:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	elif B <= -3e-173:
		tmp = t_1
	elif B <= 1.34e-291:
		tmp = t_0
	elif B <= 7.8e-275:
		tmp = (180.0 * math.atan((1.0 / (1.0 + ((A - C) / B))))) / math.pi
	elif B <= 3.3e-169:
		tmp = t_0
	elif B <= 1.55e-138:
		tmp = t_1
	else:
		tmp = 180.0 / (math.pi / math.atan((((C - B) - A) / B)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi))
	t_1 = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(Float64(-2.0 * Float64(C / B)) + Float64(2.0 * Float64(A / B)))))) / pi)
	tmp = 0.0
	if (B <= -1.9e-127)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	elseif (B <= -3e-173)
		tmp = t_1;
	elseif (B <= 1.34e-291)
		tmp = t_0;
	elseif (B <= 7.8e-275)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(1.0 + Float64(Float64(A - C) / B))))) / pi);
	elseif (B <= 3.3e-169)
		tmp = t_0;
	elseif (B <= 1.55e-138)
		tmp = t_1;
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C - B) - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	t_1 = (180.0 * atan((1.0 / ((-2.0 * (C / B)) + (2.0 * (A / B)))))) / pi;
	tmp = 0.0;
	if (B <= -1.9e-127)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	elseif (B <= -3e-173)
		tmp = t_1;
	elseif (B <= 1.34e-291)
		tmp = t_0;
	elseif (B <= 7.8e-275)
		tmp = (180.0 * atan((1.0 / (1.0 + ((A - C) / B))))) / pi;
	elseif (B <= 3.3e-169)
		tmp = t_0;
	elseif (B <= 1.55e-138)
		tmp = t_1;
	else
		tmp = 180.0 / (pi / atan((((C - B) - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = 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[B, -1.9e-127], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3e-173], t$95$1, If[LessEqual[B, 1.34e-291], t$95$0, If[LessEqual[B, 7.8e-275], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(1.0 + N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 3.3e-169], t$95$0, If[LessEqual[B, 1.55e-138], t$95$1, N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.90000000000000001e-127

   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

   3. Simplified 82.0%

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

   4. Taylor expanded in B around -inf 76.5%

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

      1. neg-mul-1 76.5%

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

      2. unsub-neg 76.5%

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

   6. Simplified 76.5%

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

   if -1.90000000000000001e-127 < B < -3.0000000000000001e-173 or 3.30000000000000026e-169 < B < 1.5499999999999999e-138

   1. Initial program 17.1%

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

      1. associate-*r/ 17.1%

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

      2. associate-*l/ 17.1%

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

      3. *-un-lft-identity 17.1%

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

      4. unpow2 17.1%

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

      5. unpow2 17.1%

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

      6. hypot-def 54.8%

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

   3. Applied egg-rr 54.8%

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

      1. clear-num 54.8%

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

      2. inv-pow 54.8%

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

      3. associate--l- 36.9%

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

   5. Applied egg-rr 36.9%

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

      1. unpow-1 36.9%

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

      2. associate--r+ 54.8%

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

   7. Simplified 54.8%

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

   8. Taylor expanded in A around -inf 83.9%

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

   if -3.0000000000000001e-173 < B < 1.34e-291 or 7.79999999999999945e-275 < B < 3.30000000000000026e-169

   1. Initial program 69.7%

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

   3. Simplified 87.6%

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

   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%

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

   if 1.34e-291 < B < 7.79999999999999945e-275

   1. Initial program 44.5%

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

      1. associate-*r/ 44.5%

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

      2. associate-*l/ 44.5%

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

      3. *-un-lft-identity 44.5%

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

      4. unpow2 44.5%

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

      5. unpow2 44.5%

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

      6. hypot-def 86.3%

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

   3. Applied egg-rr 86.3%

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

      1. clear-num 86.3%

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

      2. inv-pow 86.3%

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

      3. associate--l- 86.6%

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

   5. Applied egg-rr 86.6%

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

      1. unpow-1 86.6%

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

      2. associate--r+ 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in B around -inf 74.6%

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

      1. associate-*r/ 74.6%

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

      2. neg-mul-1 74.6%

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

      3. sub-neg 74.6%

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

      4. distribute-neg-in 74.6%

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

      5. mul-1-neg 74.6%

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

      6. remove-double-neg 74.6%

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

      7. +-commutative 74.6%

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

      8. mul-1-neg 74.6%

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

      9. sub-neg 74.6%

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

   10. Simplified 74.6%

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

   if 1.5499999999999999e-138 < B

   1. Initial program 52.2%

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

   3. Applied egg-rr 78.9%

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

   4. Taylor expanded in B around inf 76.1%

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

      1. mul-1-neg 76.1%

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

      2. unsub-neg 76.1%

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

   6. Simplified 76.1%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.9 \cdot 10^{-127}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-173}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.34 \cdot 10^{-291}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-275}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{1 + \frac{A - C}{B}}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-169}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-138}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{-2 \cdot \frac{C}{B} + 2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}}\\ \end{array} \]

Alternative 8: 54.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.02 \cdot 10^{-128}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.25 \cdot 10^{-191}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7.4 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-275}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-74} \lor \neg \left(B \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (* (/ B C) -0.5))) PI))
        (t_1 (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))))
   (if (<= B -1.02e-128)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (if (<= B -2.25e-191)
       t_0
       (if (<= B 7.4e-298)
         t_1
         (if (<= B 9.5e-275)
           t_0
           (if (<= B 4.6e-228)
             t_1
             (if (or (<= B 1.8e-74) (not (<= B 1.4e-18)))
               (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
               (/ 180.0 (/ PI (atan (/ (* B 0.5) A))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan(((B / C) * -0.5))) / ((double) M_PI);
	double t_1 = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	double tmp;
	if (B <= -1.02e-128) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= -2.25e-191) {
		tmp = t_0;
	} else if (B <= 7.4e-298) {
		tmp = t_1;
	} else if (B <= 9.5e-275) {
		tmp = t_0;
	} else if (B <= 4.6e-228) {
		tmp = t_1;
	} else if ((B <= 1.8e-74) || !(B <= 1.4e-18)) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((B * 0.5) / A)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan(((B / C) * -0.5))) / Math.PI;
	double t_1 = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	double tmp;
	if (B <= -1.02e-128) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= -2.25e-191) {
		tmp = t_0;
	} else if (B <= 7.4e-298) {
		tmp = t_1;
	} else if (B <= 9.5e-275) {
		tmp = t_0;
	} else if (B <= 4.6e-228) {
		tmp = t_1;
	} else if ((B <= 1.8e-74) || !(B <= 1.4e-18)) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((B * 0.5) / A)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan(((B / C) * -0.5))) / math.pi
	t_1 = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	tmp = 0
	if B <= -1.02e-128:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= -2.25e-191:
		tmp = t_0
	elif B <= 7.4e-298:
		tmp = t_1
	elif B <= 9.5e-275:
		tmp = t_0
	elif B <= 4.6e-228:
		tmp = t_1
	elif (B <= 1.8e-74) or not (B <= 1.4e-18):
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan(((B * 0.5) / A)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(Float64(B / C) * -0.5))) / pi)
	t_1 = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi))
	tmp = 0.0
	if (B <= -1.02e-128)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= -2.25e-191)
		tmp = t_0;
	elseif (B <= 7.4e-298)
		tmp = t_1;
	elseif (B <= 9.5e-275)
		tmp = t_0;
	elseif (B <= 4.6e-228)
		tmp = t_1;
	elseif ((B <= 1.8e-74) || !(B <= 1.4e-18))
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(B * 0.5) / A))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan(((B / C) * -0.5))) / pi;
	t_1 = 180.0 * (atan((2.0 * (C / B))) / pi);
	tmp = 0.0;
	if (B <= -1.02e-128)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= -2.25e-191)
		tmp = t_0;
	elseif (B <= 7.4e-298)
		tmp = t_1;
	elseif (B <= 9.5e-275)
		tmp = t_0;
	elseif (B <= 4.6e-228)
		tmp = t_1;
	elseif ((B <= 1.8e-74) || ~((B <= 1.4e-18)))
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	else
		tmp = 180.0 / (pi / atan(((B * 0.5) / A)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.02e-128], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.25e-191], t$95$0, If[LessEqual[B, 7.4e-298], t$95$1, If[LessEqual[B, 9.5e-275], t$95$0, If[LessEqual[B, 4.6e-228], t$95$1, If[Or[LessEqual[B, 1.8e-74], N[Not[LessEqual[B, 1.4e-18]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.02e-128

   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. Taylor expanded in C around 0 50.9%

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

      1. associate-*r/ 50.9%

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

      2. mul-1-neg 50.9%

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

      3. +-commutative 50.9%

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

      4. unpow2 50.9%

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

      5. unpow2 50.9%

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

      6. hypot-def 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in B around -inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unsub-neg 66.7%

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

   7. Simplified 66.7%

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

   if -1.02e-128 < B < -2.25000000000000004e-191 or 7.3999999999999996e-298 < B < 9.49999999999999961e-275

   1. Initial program 33.0%

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

      1. associate-*r/ 33.0%

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

      2. associate-*l/ 33.0%

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

      3. *-un-lft-identity 33.0%

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

      4. unpow2 33.0%

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

      5. unpow2 33.0%

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

      6. hypot-def 64.5%

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

   3. Applied egg-rr 64.5%

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

   4. Taylor expanded in C around inf 42.7%

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

      1. +-commutative 42.7%

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

      2. associate-*r/ 42.7%

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

      3. associate--l+ 42.7%

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

      4. unpow2 42.7%

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

      5. mul-1-neg 42.7%

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

      6. mul-1-neg 42.7%

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

      7. sqr-neg 42.7%

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

      8. unpow2 42.7%

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

      9. distribute-rgt1-in 42.7%

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

      10. metadata-eval 42.7%

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

      11. mul0-lft 42.7%

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

      12. metadata-eval 42.7%

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

   6. Simplified 42.7%

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

   7. Taylor expanded in A around 0 58.7%

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

      1. *-commutative 58.7%

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

   9. Simplified 58.7%

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

   if -2.25000000000000004e-191 < B < 7.3999999999999996e-298 or 9.49999999999999961e-275 < B < 4.5999999999999998e-228

   1. Initial program 76.7%

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

   2. Taylor expanded in C around -inf 70.6%

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

   if 4.5999999999999998e-228 < B < 1.8000000000000001e-74 or 1.40000000000000006e-18 < B

   1. Initial program 49.6%

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

   2. Taylor expanded in C around 0 44.3%

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

      1. associate-*r/ 44.3%

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

      2. mul-1-neg 44.3%

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

      3. +-commutative 44.3%

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

      4. unpow2 44.3%

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

      5. unpow2 44.3%

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

      6. hypot-def 70.9%

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

   4. Simplified 70.9%

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

   5. Taylor expanded in A around 0 65.8%

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

   6. Taylor expanded in B around -inf 65.8%

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

      1. div-sub 65.8%

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

      2. neg-mul-1 65.8%

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

      3. neg-sub0 65.8%

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

      4. div-sub 65.8%

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

      5. div0 65.8%

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

      6. *-inverses 65.8%

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

      7. metadata-eval 65.8%

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

   8. Simplified 65.8%

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

   if 1.8000000000000001e-74 < B < 1.40000000000000006e-18

   1. Initial program 44.0%

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

   3. Applied egg-rr 45.4%

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

   4. Taylor expanded in A around -inf 68.1%

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

      1. associate-*r/ 68.1%

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

   6. Simplified 68.1%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.02 \cdot 10^{-128}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.25 \cdot 10^{-191}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.4 \cdot 10^{-298}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-275}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-228}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-74} \lor \neg \left(B \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}}\\ \end{array} \]

Alternative 9: 54.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{-128}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5 \cdot 10^{-175}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.12 \cdot 10^{-274}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-74} \lor \neg \left(B \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (* (/ B C) -0.5))) PI))
        (t_1 (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))))
   (if (<= B -1.55e-128)
     (* 180.0 (/ (atan (/ (- B A) B)) PI))
     (if (<= B -5e-175)
       t_0
       (if (<= B 1.45e-299)
         t_1
         (if (<= B 1.12e-274)
           t_0
           (if (<= B 4e-229)
             t_1
             (if (or (<= B 3.5e-74) (not (<= B 1.4e-18)))
               (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
               (/ 180.0 (/ PI (atan (/ (* B 0.5) A))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan(((B / C) * -0.5))) / ((double) M_PI);
	double t_1 = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	double tmp;
	if (B <= -1.55e-128) {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	} else if (B <= -5e-175) {
		tmp = t_0;
	} else if (B <= 1.45e-299) {
		tmp = t_1;
	} else if (B <= 1.12e-274) {
		tmp = t_0;
	} else if (B <= 4e-229) {
		tmp = t_1;
	} else if ((B <= 3.5e-74) || !(B <= 1.4e-18)) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((B * 0.5) / A)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan(((B / C) * -0.5))) / Math.PI;
	double t_1 = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	double tmp;
	if (B <= -1.55e-128) {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	} else if (B <= -5e-175) {
		tmp = t_0;
	} else if (B <= 1.45e-299) {
		tmp = t_1;
	} else if (B <= 1.12e-274) {
		tmp = t_0;
	} else if (B <= 4e-229) {
		tmp = t_1;
	} else if ((B <= 3.5e-74) || !(B <= 1.4e-18)) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((B * 0.5) / A)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan(((B / C) * -0.5))) / math.pi
	t_1 = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	tmp = 0
	if B <= -1.55e-128:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	elif B <= -5e-175:
		tmp = t_0
	elif B <= 1.45e-299:
		tmp = t_1
	elif B <= 1.12e-274:
		tmp = t_0
	elif B <= 4e-229:
		tmp = t_1
	elif (B <= 3.5e-74) or not (B <= 1.4e-18):
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan(((B * 0.5) / A)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(Float64(B / C) * -0.5))) / pi)
	t_1 = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi))
	tmp = 0.0
	if (B <= -1.55e-128)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	elseif (B <= -5e-175)
		tmp = t_0;
	elseif (B <= 1.45e-299)
		tmp = t_1;
	elseif (B <= 1.12e-274)
		tmp = t_0;
	elseif (B <= 4e-229)
		tmp = t_1;
	elseif ((B <= 3.5e-74) || !(B <= 1.4e-18))
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(B * 0.5) / A))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan(((B / C) * -0.5))) / pi;
	t_1 = 180.0 * (atan((2.0 * (C / B))) / pi);
	tmp = 0.0;
	if (B <= -1.55e-128)
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	elseif (B <= -5e-175)
		tmp = t_0;
	elseif (B <= 1.45e-299)
		tmp = t_1;
	elseif (B <= 1.12e-274)
		tmp = t_0;
	elseif (B <= 4e-229)
		tmp = t_1;
	elseif ((B <= 3.5e-74) || ~((B <= 1.4e-18)))
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	else
		tmp = 180.0 / (pi / atan(((B * 0.5) / A)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.55e-128], N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -5e-175], t$95$0, If[LessEqual[B, 1.45e-299], t$95$1, If[LessEqual[B, 1.12e-274], t$95$0, If[LessEqual[B, 4e-229], t$95$1, If[Or[LessEqual[B, 3.5e-74], N[Not[LessEqual[B, 1.4e-18]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.55000000000000001e-128

   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. Taylor expanded in C around 0 50.9%

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

      1. associate-*r/ 50.9%

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

      2. mul-1-neg 50.9%

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

      3. +-commutative 50.9%

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

      4. unpow2 50.9%

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

      5. unpow2 50.9%

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

      6. hypot-def 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in B around -inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unsub-neg 66.7%

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

   7. Simplified 66.7%

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

   if -1.55000000000000001e-128 < B < -5e-175 or 1.45000000000000013e-299 < B < 1.11999999999999998e-274

   1. Initial program 33.0%

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

      1. associate-*r/ 33.0%

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

      2. associate-*l/ 33.0%

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

      3. *-un-lft-identity 33.0%

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

      4. unpow2 33.0%

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

      5. unpow2 33.0%

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

      6. hypot-def 64.5%

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

   3. Applied egg-rr 64.5%

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

   4. Taylor expanded in C around inf 42.7%

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

      1. +-commutative 42.7%

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

      2. associate-*r/ 42.7%

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

      3. associate--l+ 42.7%

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

      4. unpow2 42.7%

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

      5. mul-1-neg 42.7%

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

      6. mul-1-neg 42.7%

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

      7. sqr-neg 42.7%

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

      8. unpow2 42.7%

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

      9. distribute-rgt1-in 42.7%

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

      10. metadata-eval 42.7%

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

      11. mul0-lft 42.7%

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

      12. metadata-eval 42.7%

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

   6. Simplified 42.7%

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

   7. Taylor expanded in A around 0 58.7%

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

      1. *-commutative 58.7%

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

   9. Simplified 58.7%

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

   if -5e-175 < B < 1.45000000000000013e-299 or 1.11999999999999998e-274 < B < 4.00000000000000028e-229

   1. Initial program 76.7%

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

   2. Taylor expanded in C around -inf 70.6%

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

   if 4.00000000000000028e-229 < B < 3.50000000000000015e-74 or 1.40000000000000006e-18 < B

   1. Initial program 49.6%

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

   2. Taylor expanded in C around 0 44.3%

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

      1. associate-*r/ 44.3%

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

      2. mul-1-neg 44.3%

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

      3. +-commutative 44.3%

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

      4. unpow2 44.3%

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

      5. unpow2 44.3%

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

      6. hypot-def 70.9%

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

   4. Simplified 70.9%

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

   5. Taylor expanded in A around 0 65.8%

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

   6. Taylor expanded in B around -inf 65.8%

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

      1. div-sub 65.8%

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

      2. neg-mul-1 65.8%

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

      3. neg-sub0 65.8%

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

      4. div-sub 65.8%

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

      5. div0 65.8%

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

      6. *-inverses 65.8%

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

      7. metadata-eval 65.8%

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

   8. Simplified 65.8%

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

   if 3.50000000000000015e-74 < B < 1.40000000000000006e-18

   1. Initial program 44.0%

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

   3. Applied egg-rr 45.4%

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

   4. Taylor expanded in A around -inf 68.1%

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

      1. associate-*r/ 68.1%

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

   6. Simplified 68.1%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.55 \cdot 10^{-128}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5 \cdot 10^{-175}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-299}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.12 \cdot 10^{-274}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-229}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-74} \lor \neg \left(B \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}}\\ \end{array} \]

Alternative 10: 54.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.45 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-299}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-274}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-229}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-74} \lor \neg \left(B \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))))
   (if (<= B -2.45e-166)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (if (<= B 6e-299)
       t_0
       (if (<= B 3.6e-274)
         (/ (* 180.0 (atan 0.0)) PI)
         (if (<= B 2e-229)
           t_0
           (if (or (<= B 1.15e-74) (not (<= B 1.4e-18)))
             (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
             (* 180.0 (/ (atan (* 0.5 (/ B A))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	double tmp;
	if (B <= -2.45e-166) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= 6e-299) {
		tmp = t_0;
	} else if (B <= 3.6e-274) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (B <= 2e-229) {
		tmp = t_0;
	} else if ((B <= 1.15e-74) || !(B <= 1.4e-18)) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	double tmp;
	if (B <= -2.45e-166) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= 6e-299) {
		tmp = t_0;
	} else if (B <= 3.6e-274) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (B <= 2e-229) {
		tmp = t_0;
	} else if ((B <= 1.15e-74) || !(B <= 1.4e-18)) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	tmp = 0
	if B <= -2.45e-166:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= 6e-299:
		tmp = t_0
	elif B <= 3.6e-274:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif B <= 2e-229:
		tmp = t_0
	elif (B <= 1.15e-74) or not (B <= 1.4e-18):
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi))
	tmp = 0.0
	if (B <= -2.45e-166)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= 6e-299)
		tmp = t_0;
	elseif (B <= 3.6e-274)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (B <= 2e-229)
		tmp = t_0;
	elseif ((B <= 1.15e-74) || !(B <= 1.4e-18))
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((2.0 * (C / B))) / pi);
	tmp = 0.0;
	if (B <= -2.45e-166)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= 6e-299)
		tmp = t_0;
	elseif (B <= 3.6e-274)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (B <= 2e-229)
		tmp = t_0;
	elseif ((B <= 1.15e-74) || ~((B <= 1.4e-18)))
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.45e-166], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6e-299], t$95$0, If[LessEqual[B, 3.6e-274], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 2e-229], t$95$0, If[Or[LessEqual[B, 1.15e-74], N[Not[LessEqual[B, 1.4e-18]], $MachinePrecision]], 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[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.4499999999999999e-166

   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 46.6%

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

      1. associate-*r/ 46.6%

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

      2. mul-1-neg 46.6%

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

      3. +-commutative 46.6%

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

      4. unpow2 46.6%

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

      5. unpow2 46.6%

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

      6. hypot-def 67.1%

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

   4. Simplified 67.1%

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

   5. Taylor expanded in B around -inf 60.5%

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

      1. mul-1-neg 60.5%

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

      2. unsub-neg 60.5%

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

   7. Simplified 60.5%

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

   if -2.4499999999999999e-166 < B < 5.99999999999999969e-299 or 3.59999999999999983e-274 < B < 2.00000000000000014e-229

   1. Initial program 73.4%

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

   2. Taylor expanded in C around -inf 67.6%

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

   if 5.99999999999999969e-299 < B < 3.59999999999999983e-274

   1. Initial program 56.8%

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

      1. associate-*r/ 56.8%

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

      2. associate-*l/ 56.8%

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

      3. *-un-lft-identity 56.8%

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

      4. unpow2 56.8%

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

      5. unpow2 56.8%

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

      6. hypot-def 89.3%

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

   3. Applied egg-rr 89.3%

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

      1. clear-num 89.3%

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

      2. inv-pow 89.3%

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

      3. associate--l- 89.5%

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

   5. Applied egg-rr 89.5%

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

      1. unpow-1 89.5%

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

      2. associate--r+ 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in C around inf 57.0%

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

      1. distribute-rgt1-in 57.0%

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

      2. metadata-eval 57.0%

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

      3. mul0-lft 57.0%

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

      4. div0 57.0%

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

      5. metadata-eval 57.0%

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

   10. Simplified 57.0%

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

   if 2.00000000000000014e-229 < B < 1.1499999999999999e-74 or 1.40000000000000006e-18 < B

   1. Initial program 49.6%

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

   2. Taylor expanded in C around 0 44.3%

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

      1. associate-*r/ 44.3%

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

      2. mul-1-neg 44.3%

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

      3. +-commutative 44.3%

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

      4. unpow2 44.3%

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

      5. unpow2 44.3%

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

      6. hypot-def 70.9%

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

   4. Simplified 70.9%

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

   5. Taylor expanded in A around 0 65.8%

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

   6. Taylor expanded in B around -inf 65.8%

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

      1. div-sub 65.8%

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

      2. neg-mul-1 65.8%

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

      3. neg-sub0 65.8%

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

      4. div-sub 65.8%

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

      5. div0 65.8%

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

      6. *-inverses 65.8%

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

      7. metadata-eval 65.8%

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

   8. Simplified 65.8%

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

   if 1.1499999999999999e-74 < B < 1.40000000000000006e-18

   1. Initial program 44.0%

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

   2. Taylor expanded in A around -inf 68.0%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.45 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-299}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-274}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-229}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-74} \lor \neg \left(B \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \end{array} \]

Alternative 11: 54.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.35 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{-298}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.02 \cdot 10^{-274}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-229}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-76} \lor \neg \left(B \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))))
   (if (<= B -2.35e-166)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (if (<= B 5.6e-298)
       t_0
       (if (<= B 1.02e-274)
         (/ (* 180.0 (atan 0.0)) PI)
         (if (<= B 5.2e-229)
           t_0
           (if (or (<= B 3.7e-76) (not (<= B 1.4e-18)))
             (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
             (/ 180.0 (/ PI (atan (/ (* B 0.5) A)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	double tmp;
	if (B <= -2.35e-166) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= 5.6e-298) {
		tmp = t_0;
	} else if (B <= 1.02e-274) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (B <= 5.2e-229) {
		tmp = t_0;
	} else if ((B <= 3.7e-76) || !(B <= 1.4e-18)) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((B * 0.5) / A)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	double tmp;
	if (B <= -2.35e-166) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= 5.6e-298) {
		tmp = t_0;
	} else if (B <= 1.02e-274) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (B <= 5.2e-229) {
		tmp = t_0;
	} else if ((B <= 3.7e-76) || !(B <= 1.4e-18)) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((B * 0.5) / A)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	tmp = 0
	if B <= -2.35e-166:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= 5.6e-298:
		tmp = t_0
	elif B <= 1.02e-274:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif B <= 5.2e-229:
		tmp = t_0
	elif (B <= 3.7e-76) or not (B <= 1.4e-18):
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan(((B * 0.5) / A)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi))
	tmp = 0.0
	if (B <= -2.35e-166)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= 5.6e-298)
		tmp = t_0;
	elseif (B <= 1.02e-274)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (B <= 5.2e-229)
		tmp = t_0;
	elseif ((B <= 3.7e-76) || !(B <= 1.4e-18))
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(B * 0.5) / A))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((2.0 * (C / B))) / pi);
	tmp = 0.0;
	if (B <= -2.35e-166)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= 5.6e-298)
		tmp = t_0;
	elseif (B <= 1.02e-274)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (B <= 5.2e-229)
		tmp = t_0;
	elseif ((B <= 3.7e-76) || ~((B <= 1.4e-18)))
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	else
		tmp = 180.0 / (pi / atan(((B * 0.5) / A)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.35e-166], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.6e-298], t$95$0, If[LessEqual[B, 1.02e-274], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 5.2e-229], t$95$0, If[Or[LessEqual[B, 3.7e-76], N[Not[LessEqual[B, 1.4e-18]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.35000000000000007e-166

   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 46.6%

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

      1. associate-*r/ 46.6%

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

      2. mul-1-neg 46.6%

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

      3. +-commutative 46.6%

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

      4. unpow2 46.6%

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

      5. unpow2 46.6%

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

      6. hypot-def 67.1%

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

   4. Simplified 67.1%

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

   5. Taylor expanded in B around -inf 60.5%

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

      1. mul-1-neg 60.5%

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

      2. unsub-neg 60.5%

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

   7. Simplified 60.5%

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

   if -2.35000000000000007e-166 < B < 5.59999999999999985e-298 or 1.01999999999999997e-274 < B < 5.2000000000000003e-229

   1. Initial program 73.4%

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

   2. Taylor expanded in C around -inf 67.6%

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

   if 5.59999999999999985e-298 < B < 1.01999999999999997e-274

   1. Initial program 56.8%

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

      1. associate-*r/ 56.8%

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

      2. associate-*l/ 56.8%

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

      3. *-un-lft-identity 56.8%

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

      4. unpow2 56.8%

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

      5. unpow2 56.8%

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

      6. hypot-def 89.3%

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

   3. Applied egg-rr 89.3%

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

      1. clear-num 89.3%

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

      2. inv-pow 89.3%

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

      3. associate--l- 89.5%

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

   5. Applied egg-rr 89.5%

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

      1. unpow-1 89.5%

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

      2. associate--r+ 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in C around inf 57.0%

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

      1. distribute-rgt1-in 57.0%

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

      2. metadata-eval 57.0%

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

      3. mul0-lft 57.0%

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

      4. div0 57.0%

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

      5. metadata-eval 57.0%

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

   10. Simplified 57.0%

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

   if 5.2000000000000003e-229 < B < 3.70000000000000011e-76 or 1.40000000000000006e-18 < B

   1. Initial program 49.6%

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

   2. Taylor expanded in C around 0 44.3%

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

      1. associate-*r/ 44.3%

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

      2. mul-1-neg 44.3%

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

      3. +-commutative 44.3%

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

      4. unpow2 44.3%

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

      5. unpow2 44.3%

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

      6. hypot-def 70.9%

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

   4. Simplified 70.9%

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

   5. Taylor expanded in A around 0 65.8%

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

   6. Taylor expanded in B around -inf 65.8%

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

      1. div-sub 65.8%

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

      2. neg-mul-1 65.8%

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

      3. neg-sub0 65.8%

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

      4. div-sub 65.8%

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

      5. div0 65.8%

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

      6. *-inverses 65.8%

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

      7. metadata-eval 65.8%

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

   8. Simplified 65.8%

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

   if 3.70000000000000011e-76 < B < 1.40000000000000006e-18

   1. Initial program 44.0%

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

   3. Applied egg-rr 45.4%

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

   4. Taylor expanded in A around -inf 68.1%

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

      1. associate-*r/ 68.1%

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

   6. Simplified 68.1%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.35 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{-298}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.02 \cdot 10^{-274}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-229}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-76} \lor \neg \left(B \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}}\\ \end{array} \]

Alternative 12: 65.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.05 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-174}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-274}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{1 + \frac{A - C}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.05e-129)
   (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
   (if (<= B -1.5e-174)
     (/ (* 180.0 (atan (* (/ B C) -0.5))) PI)
     (if (<= B 5e-292)
       (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI))
       (if (<= B 7e-274)
         (/ (* 180.0 (atan (/ 1.0 (+ 1.0 (/ (- A C) B))))) PI)
         (/ 180.0 (/ PI (atan (/ (- (- C B) A) B)))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.05e-129) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else if (B <= -1.5e-174) {
		tmp = (180.0 * atan(((B / C) * -0.5))) / ((double) M_PI);
	} else if (B <= 5e-292) {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	} else if (B <= 7e-274) {
		tmp = (180.0 * atan((1.0 / (1.0 + ((A - C) / B))))) / ((double) M_PI);
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((C - B) - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.05e-129) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else if (B <= -1.5e-174) {
		tmp = (180.0 * Math.atan(((B / C) * -0.5))) / Math.PI;
	} else if (B <= 5e-292) {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	} else if (B <= 7e-274) {
		tmp = (180.0 * Math.atan((1.0 / (1.0 + ((A - C) / B))))) / Math.PI;
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((C - B) - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.05e-129:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	elif B <= -1.5e-174:
		tmp = (180.0 * math.atan(((B / C) * -0.5))) / math.pi
	elif B <= 5e-292:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	elif B <= 7e-274:
		tmp = (180.0 * math.atan((1.0 / (1.0 + ((A - C) / B))))) / math.pi
	else:
		tmp = 180.0 / (math.pi / math.atan((((C - B) - A) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.05e-129)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	elseif (B <= -1.5e-174)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / C) * -0.5))) / pi);
	elseif (B <= 5e-292)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	elseif (B <= 7e-274)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 / Float64(1.0 + Float64(Float64(A - C) / B))))) / pi);
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C - B) - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.05e-129)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	elseif (B <= -1.5e-174)
		tmp = (180.0 * atan(((B / C) * -0.5))) / pi;
	elseif (B <= 5e-292)
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	elseif (B <= 7e-274)
		tmp = (180.0 * atan((1.0 / (1.0 + ((A - C) / B))))) / pi;
	else
		tmp = 180.0 / (pi / atan((((C - B) - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.05e-129], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.5e-174], N[(N[(180.0 * N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 5e-292], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7e-274], N[(N[(180.0 * N[ArcTan[N[(1.0 / N[(1.0 + N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.05e-129

   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

   3. Simplified 82.0%

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

   4. Taylor expanded in B around -inf 76.5%

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

      1. neg-mul-1 76.5%

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

      2. unsub-neg 76.5%

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

   6. Simplified 76.5%

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

   if -2.05e-129 < B < -1.50000000000000011e-174

   1. Initial program 17.6%

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

      1. associate-*r/ 17.6%

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

      2. associate-*l/ 17.6%

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

      3. *-un-lft-identity 17.6%

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

      4. unpow2 17.6%

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

      5. unpow2 17.6%

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

      6. hypot-def 48.6%

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

   3. Applied egg-rr 48.6%

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

   4. Taylor expanded in C around inf 33.9%

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

      1. +-commutative 33.9%

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

      2. associate-*r/ 33.9%

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

      3. associate--l+ 33.9%

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

      4. unpow2 33.9%

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

      5. mul-1-neg 33.9%

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

      6. mul-1-neg 33.9%

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

      7. sqr-neg 33.9%

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

      8. unpow2 33.9%

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

      9. distribute-rgt1-in 33.9%

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

      10. metadata-eval 33.9%

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

      11. mul0-lft 33.9%

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

      12. metadata-eval 33.9%

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

   6. Simplified 33.9%

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

   7. Taylor expanded in A around 0 59.5%

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

      1. *-commutative 59.5%

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

   9. Simplified 59.5%

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

   if -1.50000000000000011e-174 < B < 4.99999999999999981e-292

   1. Initial program 84.5%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in B around inf 84.5%

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

      1. +-commutative 84.5%

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

   6. Simplified 84.5%

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

   if 4.99999999999999981e-292 < B < 6.99999999999999963e-274

   1. Initial program 44.5%

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

      1. associate-*r/ 44.5%

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

      2. associate-*l/ 44.5%

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

      3. *-un-lft-identity 44.5%

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

      4. unpow2 44.5%

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

      5. unpow2 44.5%

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

      6. hypot-def 86.3%

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

   3. Applied egg-rr 86.3%

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

      1. clear-num 86.3%

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

      2. inv-pow 86.3%

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

      3. associate--l- 86.6%

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

   5. Applied egg-rr 86.6%

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

      1. unpow-1 86.6%

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

      2. associate--r+ 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in B around -inf 74.6%

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

      1. associate-*r/ 74.6%

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

      2. neg-mul-1 74.6%

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

      3. sub-neg 74.6%

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

      4. distribute-neg-in 74.6%

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

      5. mul-1-neg 74.6%

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

      6. remove-double-neg 74.6%

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

      7. +-commutative 74.6%

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

      8. mul-1-neg 74.6%

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

      9. sub-neg 74.6%

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

   10. Simplified 74.6%

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

   if 6.99999999999999963e-274 < B

   1. Initial program 50.0%

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

   3. Applied egg-rr 78.8%

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

   4. Taylor expanded in B around inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. unsub-neg 70.2%

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

   6. Simplified 70.2%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.05 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-174}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-274}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{1}{1 + \frac{A - C}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}}\\ \end{array} \]

Alternative 13: 51.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{-154}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.26 \cdot 10^{-225} \lor \neg \left(A \leq 4 \cdot 10^{-133}\right) \land A \leq 4 \cdot 10^{-48}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.5e-154)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (or (<= A -1.26e-225) (and (not (<= A 4e-133)) (<= A 4e-48)))
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e-154) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if ((A <= -1.26e-225) || (!(A <= 4e-133) && (A <= 4e-48))) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e-154) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if ((A <= -1.26e-225) || (!(A <= 4e-133) && (A <= 4e-48))) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.5e-154:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif (A <= -1.26e-225) or (not (A <= 4e-133) and (A <= 4e-48)):
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.5e-154)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif ((A <= -1.26e-225) || (!(A <= 4e-133) && (A <= 4e-48)))
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.5e-154)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif ((A <= -1.26e-225) || (~((A <= 4e-133)) && (A <= 4e-48)))
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.5e-154], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[A, -1.26e-225], And[N[Not[LessEqual[A, 4e-133]], $MachinePrecision], LessEqual[A, 4e-48]]], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.4999999999999996e-154

   1. Initial program 35.9%

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

   2. Taylor expanded in A around -inf 53.2%

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

   if -8.4999999999999996e-154 < A < -1.2599999999999999e-225 or 4.0000000000000003e-133 < A < 3.9999999999999999e-48

   1. Initial program 76.8%

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

   2. Taylor expanded in C around -inf 56.8%

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

   if -1.2599999999999999e-225 < A < 4.0000000000000003e-133 or 3.9999999999999999e-48 < A

   1. Initial program 62.0%

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

   2. Taylor expanded in C around 0 58.2%

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

      1. associate-*r/ 58.2%

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

      2. mul-1-neg 58.2%

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

      3. +-commutative 58.2%

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

      4. unpow2 58.2%

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

      5. unpow2 58.2%

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

      6. hypot-def 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in A around 0 67.8%

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

   6. Taylor expanded in B around -inf 67.8%

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

      1. div-sub 67.8%

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

      2. neg-mul-1 67.8%

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

      3. neg-sub0 67.8%

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

      4. div-sub 67.8%

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

      5. div0 67.8%

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

      6. *-inverses 67.8%

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

      7. metadata-eval 67.8%

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

   8. Simplified 67.8%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{-154}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.26 \cdot 10^{-225} \lor \neg \left(A \leq 4 \cdot 10^{-133}\right) \land A \leq 4 \cdot 10^{-48}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 14: 47.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -8.6 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-292}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 6.1 \cdot 10^{-264}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 11.5:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))))
   (if (<= B -8.6e-54)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 8.5e-292)
       t_0
       (if (<= B 6.1e-264)
         (/ (* 180.0 (atan 0.0)) PI)
         (if (<= B 11.5) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	double tmp;
	if (B <= -8.6e-54) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 8.5e-292) {
		tmp = t_0;
	} else if (B <= 6.1e-264) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (B <= 11.5) {
		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((-2.0 * (A / B))) / Math.PI);
	double tmp;
	if (B <= -8.6e-54) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 8.5e-292) {
		tmp = t_0;
	} else if (B <= 6.1e-264) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (B <= 11.5) {
		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((-2.0 * (A / B))) / math.pi)
	tmp = 0
	if B <= -8.6e-54:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 8.5e-292:
		tmp = t_0
	elif B <= 6.1e-264:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif B <= 11.5:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi))
	tmp = 0.0
	if (B <= -8.6e-54)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 8.5e-292)
		tmp = t_0;
	elseif (B <= 6.1e-264)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (B <= 11.5)
		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((-2.0 * (A / B))) / pi);
	tmp = 0.0;
	if (B <= -8.6e-54)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 8.5e-292)
		tmp = t_0;
	elseif (B <= 6.1e-264)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (B <= 11.5)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -8.6e-54], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.5e-292], t$95$0, If[LessEqual[B, 6.1e-264], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 11.5], 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 < -8.5999999999999999e-54

   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 57.7%

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

   if -8.5999999999999999e-54 < B < 8.50000000000000066e-292 or 6.10000000000000025e-264 < B < 11.5

   1. Initial program 63.1%

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

   2. Taylor expanded in A around inf 40.6%

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

   if 8.50000000000000066e-292 < B < 6.10000000000000025e-264

   1. Initial program 46.0%

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

      1. associate-*r/ 46.0%

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

      2. associate-*l/ 46.0%

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

      3. *-un-lft-identity 46.0%

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

      4. unpow2 46.0%

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

      5. unpow2 46.0%

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

      6. hypot-def 89.3%

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

   3. Applied egg-rr 89.3%

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

      1. clear-num 89.3%

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

      2. inv-pow 89.3%

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

      3. associate--l- 89.5%

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

   5. Applied egg-rr 89.5%

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

      1. unpow-1 89.5%

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

      2. associate--r+ 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in C around inf 67.8%

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

      1. distribute-rgt1-in 67.8%

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

      2. metadata-eval 67.8%

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

      3. mul0-lft 67.8%

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

      4. div0 67.8%

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

      5. metadata-eval 67.8%

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

   10. Simplified 67.8%

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

   if 11.5 < B

   1. Initial program 42.6%

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

   2. Taylor expanded in B around inf 63.3%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.6 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.1 \cdot 10^{-264}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 11.5:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 15: 47.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -5.5 \cdot 10^{-154}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.3 \cdot 10^{-218}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 7.2 \cdot 10^{-189}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 3.05 \cdot 10^{+32}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))))
   (if (<= A -5.5e-154)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (if (<= A -1.3e-218)
       t_0
       (if (<= A 7.2e-189)
         (* 180.0 (/ (atan -1.0) PI))
         (if (<= A 3.05e+32) t_0 (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	double tmp;
	if (A <= -5.5e-154) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= -1.3e-218) {
		tmp = t_0;
	} else if (A <= 7.2e-189) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 3.05e+32) {
		tmp = t_0;
	} 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 t_0 = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	double tmp;
	if (A <= -5.5e-154) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= -1.3e-218) {
		tmp = t_0;
	} else if (A <= 7.2e-189) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 3.05e+32) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	tmp = 0
	if A <= -5.5e-154:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= -1.3e-218:
		tmp = t_0
	elif A <= 7.2e-189:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 3.05e+32:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi))
	tmp = 0.0
	if (A <= -5.5e-154)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= -1.3e-218)
		tmp = t_0;
	elseif (A <= 7.2e-189)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 3.05e+32)
		tmp = t_0;
	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)
	t_0 = 180.0 * (atan((2.0 * (C / B))) / pi);
	tmp = 0.0;
	if (A <= -5.5e-154)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= -1.3e-218)
		tmp = t_0;
	elseif (A <= 7.2e-189)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 3.05e+32)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -5.5e-154], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.3e-218], t$95$0, If[LessEqual[A, 7.2e-189], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.05e+32], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -5.50000000000000002e-154

   1. Initial program 35.9%

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

   2. Taylor expanded in A around -inf 53.2%

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

   if -5.50000000000000002e-154 < A < -1.29999999999999992e-218 or 7.20000000000000034e-189 < A < 3.05000000000000014e32

   1. Initial program 67.1%

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

   2. Taylor expanded in C around -inf 46.1%

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

   if -1.29999999999999992e-218 < A < 7.20000000000000034e-189

   1. Initial program 40.6%

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

   2. Taylor expanded in B around inf 56.0%

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

   if 3.05000000000000014e32 < A

   1. Initial program 80.0%

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

   2. Taylor expanded in A around inf 76.6%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.5 \cdot 10^{-154}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.3 \cdot 10^{-218}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.2 \cdot 10^{-189}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 3.05 \cdot 10^{+32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 16: 60.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.3 \cdot 10^{+35} \lor \neg \left(A \leq 2.25 \cdot 10^{+191}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.7e-95)
   (/ (* 180.0 (atan (/ (* B 0.5) A))) PI)
   (if (or (<= A 6.3e+35) (not (<= A 2.25e+191)))
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI))
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.7e-95) {
		tmp = (180.0 * atan(((B * 0.5) / A))) / ((double) M_PI);
	} else if ((A <= 6.3e+35) || !(A <= 2.25e+191)) {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.7e-95) {
		tmp = (180.0 * Math.atan(((B * 0.5) / A))) / Math.PI;
	} else if ((A <= 6.3e+35) || !(A <= 2.25e+191)) {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.7e-95:
		tmp = (180.0 * math.atan(((B * 0.5) / A))) / math.pi
	elif (A <= 6.3e+35) or not (A <= 2.25e+191):
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.7e-95)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * 0.5) / A))) / pi);
	elseif ((A <= 6.3e+35) || !(A <= 2.25e+191))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.7e-95)
		tmp = (180.0 * atan(((B * 0.5) / A))) / pi;
	elseif ((A <= 6.3e+35) || ~((A <= 2.25e+191)))
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.7e-95], N[(N[(180.0 * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[Or[LessEqual[A, 6.3e+35], N[Not[LessEqual[A, 2.25e+191]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -4.6999999999999998e-95

   1. Initial program 30.6%

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

      1. associate-*r/ 30.6%

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

      2. associate-*l/ 30.6%

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

      3. *-un-lft-identity 30.6%

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

      4. unpow2 30.6%

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

      5. unpow2 30.6%

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

      6. hypot-def 56.6%

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

   3. Applied egg-rr 56.6%

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

   4. Taylor expanded in A around -inf 58.8%

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

      1. associate-*r/ 58.7%

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

   6. Simplified 58.8%

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

   if -4.6999999999999998e-95 < A < 6.29999999999999969e35 or 2.2500000000000001e191 < A

   1. Initial program 64.8%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in B around inf 70.1%

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

      1. +-commutative 70.1%

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

   6. Simplified 70.1%

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

   if 6.29999999999999969e35 < A < 2.2500000000000001e191

   1. Initial program 69.9%

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

   2. Taylor expanded in C around 0 70.0%

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

      1. associate-*r/ 70.0%

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

      2. mul-1-neg 70.0%

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

      3. +-commutative 70.0%

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

      4. unpow2 70.0%

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

      5. unpow2 70.0%

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

      6. hypot-def 86.8%

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

   4. Simplified 86.8%

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

   5. Taylor expanded in B around -inf 83.4%

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

      1. mul-1-neg 83.4%

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

      2. unsub-neg 83.4%

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

   7. Simplified 83.4%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.7 \cdot 10^{-95}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.3 \cdot 10^{+35} \lor \neg \left(A \leq 2.25 \cdot 10^{+191}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 17: 47.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -4.8 \cdot 10^{-53}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-294}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-266}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 19:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- A) B)) PI))))
   (if (<= B -4.8e-53)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 8.5e-294)
       t_0
       (if (<= B 1.25e-266)
         (/ (* 180.0 (atan 0.0)) PI)
         (if (<= B 19.0) 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 <= -4.8e-53) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 8.5e-294) {
		tmp = t_0;
	} else if (B <= 1.25e-266) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else if (B <= 19.0) {
		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 <= -4.8e-53) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 8.5e-294) {
		tmp = t_0;
	} else if (B <= 1.25e-266) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else if (B <= 19.0) {
		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 <= -4.8e-53:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 8.5e-294:
		tmp = t_0
	elif B <= 1.25e-266:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	elif B <= 19.0:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi))
	tmp = 0.0
	if (B <= -4.8e-53)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 8.5e-294)
		tmp = t_0;
	elseif (B <= 1.25e-266)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	elseif (B <= 19.0)
		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 <= -4.8e-53)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 8.5e-294)
		tmp = t_0;
	elseif (B <= 1.25e-266)
		tmp = (180.0 * atan(0.0)) / pi;
	elseif (B <= 19.0)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -4.8e-53], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.5e-294], t$95$0, If[LessEqual[B, 1.25e-266], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 19.0], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -4.80000000000000015e-53

   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 57.7%

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

   if -4.80000000000000015e-53 < B < 8.4999999999999999e-294 or 1.24999999999999998e-266 < B < 19

   1. Initial program 63.1%

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

   2. Taylor expanded in C around 0 49.6%

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

      1. associate-*r/ 49.6%

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

      2. mul-1-neg 49.6%

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

      3. +-commutative 49.6%

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

      4. unpow2 49.6%

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

      5. unpow2 49.6%

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

      6. hypot-def 59.1%

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

   4. Simplified 59.1%

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

   5. Taylor expanded in A around 0 46.9%

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

   6. Taylor expanded in A around inf 40.5%

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

      1. associate-*r/ 40.5%

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

      2. neg-mul-1 40.5%

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

   8. Simplified 40.5%

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

   if 8.4999999999999999e-294 < B < 1.24999999999999998e-266

   1. Initial program 46.0%

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

      1. associate-*r/ 46.0%

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

      2. associate-*l/ 46.0%

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

      3. *-un-lft-identity 46.0%

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

      4. unpow2 46.0%

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

      5. unpow2 46.0%

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

      6. hypot-def 89.3%

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

   3. Applied egg-rr 89.3%

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

      1. clear-num 89.3%

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

      2. inv-pow 89.3%

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

      3. associate--l- 89.5%

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

   5. Applied egg-rr 89.5%

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

      1. unpow-1 89.5%

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

      2. associate--r+ 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in C around inf 67.8%

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

      1. distribute-rgt1-in 67.8%

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

      2. metadata-eval 67.8%

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

      3. mul0-lft 67.8%

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

      4. div0 67.8%

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

      5. metadata-eval 67.8%

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

   10. Simplified 67.8%

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

   if 19 < B

   1. Initial program 42.6%

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

   2. Taylor expanded in B around inf 63.3%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.8 \cdot 10^{-53}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-266}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 19:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 18: 65.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.6e-129)
   (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
   (if (<= B -6.2e-169)
     (/ (* 180.0 (atan (* (/ B C) -0.5))) PI)
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.6e-129) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else if (B <= -6.2e-169) {
		tmp = (180.0 * atan(((B / C) * -0.5))) / ((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 (B <= -2.6e-129) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else if (B <= -6.2e-169) {
		tmp = (180.0 * Math.atan(((B / C) * -0.5))) / 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 B <= -2.6e-129:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	elif B <= -6.2e-169:
		tmp = (180.0 * math.atan(((B / C) * -0.5))) / 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 (B <= -2.6e-129)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	elseif (B <= -6.2e-169)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / C) * -0.5))) / 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 (B <= -2.6e-129)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	elseif (B <= -6.2e-169)
		tmp = (180.0 * atan(((B / C) * -0.5))) / pi;
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.6e-129], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6.2e-169], N[(N[(180.0 * N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $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 B < -2.6000000000000001e-129

   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

   3. Simplified 82.0%

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

   4. Taylor expanded in B around -inf 76.5%

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

      1. neg-mul-1 76.5%

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

      2. unsub-neg 76.5%

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

   6. Simplified 76.5%

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

   if -2.6000000000000001e-129 < B < -6.2000000000000004e-169

   1. Initial program 17.6%

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

      1. associate-*r/ 17.6%

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

      2. associate-*l/ 17.6%

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

      3. *-un-lft-identity 17.6%

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

      4. unpow2 17.6%

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

      5. unpow2 17.6%

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

      6. hypot-def 48.6%

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

   3. Applied egg-rr 48.6%

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

   4. Taylor expanded in C around inf 33.9%

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

      1. +-commutative 33.9%

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

      2. associate-*r/ 33.9%

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

      3. associate--l+ 33.9%

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

      4. unpow2 33.9%

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

      5. mul-1-neg 33.9%

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

      6. mul-1-neg 33.9%

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

      7. sqr-neg 33.9%

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

      8. unpow2 33.9%

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

      9. distribute-rgt1-in 33.9%

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

      10. metadata-eval 33.9%

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

      11. mul0-lft 33.9%

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

      12. metadata-eval 33.9%

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

   6. Simplified 33.9%

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

   7. Taylor expanded in A around 0 59.5%

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

      1. *-commutative 59.5%

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

   9. Simplified 59.5%

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

   if -6.2000000000000004e-169 < B

   1. Initial program 55.3%

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

   3. Simplified 78.7%

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

   4. Taylor expanded in B around inf 70.1%

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

      1. +-commutative 70.1%

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

   6. Simplified 70.1%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 19: 65.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.8 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.3 \cdot 10^{-169}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.8e-129)
   (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
   (if (<= B -3.3e-169)
     (/ (* 180.0 (atan (* (/ B C) -0.5))) PI)
     (/ 180.0 (/ PI (atan (/ (- (- C B) A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.8e-129) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else if (B <= -3.3e-169) {
		tmp = (180.0 * atan(((B / C) * -0.5))) / ((double) M_PI);
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((C - B) - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.8e-129) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else if (B <= -3.3e-169) {
		tmp = (180.0 * Math.atan(((B / C) * -0.5))) / Math.PI;
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((C - B) - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.8e-129:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	elif B <= -3.3e-169:
		tmp = (180.0 * math.atan(((B / C) * -0.5))) / math.pi
	else:
		tmp = 180.0 / (math.pi / math.atan((((C - B) - A) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.8e-129)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	elseif (B <= -3.3e-169)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / C) * -0.5))) / pi);
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C - B) - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.8e-129)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	elseif (B <= -3.3e-169)
		tmp = (180.0 * atan(((B / C) * -0.5))) / pi;
	else
		tmp = 180.0 / (pi / atan((((C - B) - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.8e-129], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.3e-169], N[(N[(180.0 * N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.8e-129

   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

   3. Simplified 82.0%

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

   4. Taylor expanded in B around -inf 76.5%

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

      1. neg-mul-1 76.5%

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

      2. unsub-neg 76.5%

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

   6. Simplified 76.5%

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

   if -1.8e-129 < B < -3.30000000000000026e-169

   1. Initial program 17.6%

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

      1. associate-*r/ 17.6%

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

      2. associate-*l/ 17.6%

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

      3. *-un-lft-identity 17.6%

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

      4. unpow2 17.6%

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

      5. unpow2 17.6%

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

      6. hypot-def 48.6%

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

   3. Applied egg-rr 48.6%

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

   4. Taylor expanded in C around inf 33.9%

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

      1. +-commutative 33.9%

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

      2. associate-*r/ 33.9%

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

      3. associate--l+ 33.9%

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

      4. unpow2 33.9%

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

      5. mul-1-neg 33.9%

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

      6. mul-1-neg 33.9%

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

      7. sqr-neg 33.9%

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

      8. unpow2 33.9%

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

      9. distribute-rgt1-in 33.9%

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

      10. metadata-eval 33.9%

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

      11. mul0-lft 33.9%

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

      12. metadata-eval 33.9%

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

   6. Simplified 33.9%

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

   7. Taylor expanded in A around 0 59.5%

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

      1. *-commutative 59.5%

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

   9. Simplified 59.5%

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

   if -3.30000000000000026e-169 < B

   1. Initial program 55.3%

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

   3. Applied egg-rr 82.5%

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

   4. Taylor expanded in B around inf 70.1%

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

      1. mul-1-neg 70.1%

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

      2. unsub-neg 70.1%

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

   6. Simplified 70.1%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.8 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.3 \cdot 10^{-169}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}}\\ \end{array} \]

Alternative 20: 47.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.25 \cdot 10^{-94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-190}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.25e-94)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 5e-190)
     (* 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 <= -1.25e-94) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 5e-190) {
		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 <= -1.25e-94) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 5e-190) {
		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 <= -1.25e-94:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 5e-190:
		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 <= -1.25e-94)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 5e-190)
		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 <= -1.25e-94)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 5e-190)
		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, -1.25e-94], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5e-190], 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 3 regimes

2. if A < -1.2499999999999999e-94

   1. Initial program 30.9%

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

   2. Taylor expanded in A around -inf 59.4%

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

   if -1.2499999999999999e-94 < A < 5.00000000000000034e-190

   1. Initial program 52.5%

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

   2. Taylor expanded in B around inf 42.7%

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

   if 5.00000000000000034e-190 < A

   1. Initial program 73.6%

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

   2. Taylor expanded in A around inf 55.3%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.25 \cdot 10^{-94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-190}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 21: 44.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.3 \cdot 10^{-134}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-136}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.3e-134)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.25e-136)
     (/ (* 180.0 (atan 0.0)) PI)
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.3e-134) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.25e-136) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.3e-134) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.25e-136) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.3e-134:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.25e-136:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.3e-134)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.25e-136)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.3e-134)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.25e-136)
		tmp = (180.0 * atan(0.0)) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.3e-134], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.25e-136], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.3e-134

   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. Taylor expanded in B around -inf 49.5%

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

   if -2.3e-134 < B < 1.25e-136

   1. Initial program 54.1%

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

      1. associate-*r/ 54.1%

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

      2. associate-*l/ 54.1%

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

      3. *-un-lft-identity 54.1%

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

      4. unpow2 54.1%

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

      5. unpow2 54.1%

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

      6. hypot-def 83.9%

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

   3. Applied egg-rr 83.9%

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

      1. clear-num 83.9%

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

      2. inv-pow 83.9%

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

      3. associate--l- 75.7%

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

   5. Applied egg-rr 75.7%

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

      1. unpow-1 75.7%

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

      2. associate--r+ 83.9%

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

   7. Simplified 83.9%

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

   8. Taylor expanded in C around inf 32.1%

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

      1. distribute-rgt1-in 32.1%

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

      2. metadata-eval 32.1%

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

      3. mul0-lft 32.1%

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

      4. div0 32.1%

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

      5. metadata-eval 32.1%

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

   10. Simplified 32.1%

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

   if 1.25e-136 < B

   1. Initial program 52.2%

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

   2. Taylor expanded in B around inf 51.2%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.3 \cdot 10^{-134}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-136}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 22: 39.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-309}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e-309) (* 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 <= -1e-309) {
		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 <= -1e-309) {
		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 <= -1e-309:
		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 <= -1e-309)
		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 <= -1e-309)
		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, -1e-309], 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 < -1.000000000000002e-309

   1. Initial program 57.8%

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

   2. Taylor expanded in B around -inf 40.2%

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

   if -1.000000000000002e-309 < B

   1. Initial program 52.3%

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

   2. Taylor expanded in B around inf 40.4%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-309}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 23: 20.7% 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 54.8%

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

2. Taylor expanded in B around inf 22.7%

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

3. Final simplification 22.7%

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

Reproduce

herbie shell --seed 2023334 
(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)))