ABCF->ab-angle angle

Percentage Accurate: 54.3% → 82.1%

Time: 18.9s

Alternatives: 18

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: 54.3% 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: 82.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (atan
          (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))))
   (if (or (<= t_0 -0.5) (not (<= t_0 0.0)))
     (/ 180.0 (/ PI (atan (/ (- (- C A) (hypot (- A C) B)) B))))
     (/ (* 180.0 (atan (* 0.5 (+ (/ B A) (/ B (/ (pow A 2.0) C)))))) PI))))

C

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

Java

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

Python

def code(A, B, C):
	t_0 = math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))))
	tmp = 0
	if (t_0 <= -0.5) or not (t_0 <= 0.0):
		tmp = 180.0 / (math.pi / math.atan((((C - A) - math.hypot((A - C), B)) / B)))
	else:
		tmp = (180.0 * math.atan((0.5 * ((B / A) + (B / (math.pow(A, 2.0) / C)))))) / math.pi
	return tmp

Julia

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

MATLAB

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

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, If[Or[LessEqual[t$95$0, -0.5], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(B / N[(N[Power[A, 2.0], $MachinePrecision] / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 58.6%

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

   3. Applied egg-rr 89.1%

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

   if -0.5 < (atan.f64 (*.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 25.4%

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

      1. associate-*r/ 25.4%

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

      2. associate-*l/ 25.4%

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

      3. *-un-lft-identity 25.4%

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

      4. unpow2 25.4%

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

      5. unpow2 25.4%

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

      6. hypot-def 25.4%

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

   3. Applied egg-rr 25.4%

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

   4. Taylor expanded in A around -inf 63.9%

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

      1. distribute-lft-out 63.9%

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

      2. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

4. Final simplification 85.5%

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

Alternative 2: 80.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8000000000:\\ \;\;\;\;\tan^{-1} \left(\frac{B}{\frac{A}{0.5}}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8000000000.0)
   (* (atan (/ B (/ A 0.5))) (/ 180.0 PI))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8000000000.0) {
		tmp = atan((B / (A / 0.5))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8000000000.0) {
		tmp = Math.atan((B / (A / 0.5))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8000000000.0:
		tmp = math.atan((B / (A / 0.5))) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8000000000.0)
		tmp = Float64(atan(Float64(B / Float64(A / 0.5))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8000000000.0)
		tmp = atan((B / (A / 0.5))) * (180.0 / pi);
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8000000000.0], N[(N[ArcTan[N[(B / N[(A / 0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -8e9

   1. Initial program 25.1%

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

   2. Taylor expanded in A around -inf 74.4%

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

      1. associate-*r/ 74.6%

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

   4. Applied egg-rr 74.6%

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

   5. Taylor expanded in B around 0 74.4%

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

      1. associate-*r/ 74.6%

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

      2. associate-*r/ 74.6%

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

      3. associate-*l/ 74.7%

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

      4. *-commutative 74.7%

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

      5. *-commutative 74.7%

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

      6. associate-/l* 74.7%

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

   7. Simplified 74.7%

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

   if -8e9 < A

   1. Initial program 64.0%

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

   3. Simplified 85.8%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8000000000:\\ \;\;\;\;\tan^{-1} \left(\frac{B}{\frac{A}{0.5}}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3: 82.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.4 \cdot 10^{+128}:\\ \;\;\;\;\tan^{-1} \left(\frac{B}{\frac{A}{0.5}}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.4e+128)
   (* (atan (/ B (/ A 0.5))) (/ 180.0 PI))
   (/ 180.0 (/ PI (atan (/ (- (- C A) (hypot (- A C) B)) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.4e+128) {
		tmp = atan((B / (A / 0.5))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((C - A) - hypot((A - C), B)) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.4e+128) {
		tmp = Math.atan((B / (A / 0.5))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((C - A) - Math.hypot((A - C), B)) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.4e+128:
		tmp = math.atan((B / (A / 0.5))) * (180.0 / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((((C - A) - math.hypot((A - C), B)) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.4e+128)
		tmp = Float64(atan(Float64(B / Float64(A / 0.5))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.4e+128)
		tmp = atan((B / (A / 0.5))) * (180.0 / pi);
	else
		tmp = 180.0 / (pi / atan((((C - A) - hypot((A - C), B)) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.4e+128], N[(N[ArcTan[N[(B / N[(A / 0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -6.39999999999999971e128

   1. Initial program 17.9%

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

   2. Taylor expanded in A around -inf 86.8%

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

      1. associate-*r/ 86.9%

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

   4. Applied egg-rr 86.9%

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

   5. Taylor expanded in B around 0 86.8%

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

      1. associate-*r/ 86.9%

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

      2. associate-*r/ 86.9%

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

      3. associate-*l/ 87.0%

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

      4. *-commutative 87.0%

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

      5. *-commutative 87.0%

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

      6. associate-/l* 87.0%

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

   7. Simplified 87.0%

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

   if -6.39999999999999971e128 < A

   1. Initial program 60.1%

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

   3. Applied egg-rr 83.0%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.4 \cdot 10^{+128}:\\ \;\;\;\;\tan^{-1} \left(\frac{B}{\frac{A}{0.5}}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}\\ \end{array} \]

Alternative 4: 75.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -7.1 \cdot 10^{+28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.85 \cdot 10^{+132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -7.1e+28)
   (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
   (if (<= C 1.85e+132)
     (* 180.0 (/ (atan (/ (- (- A) (hypot B A)) B)) PI))
     (/ 180.0 (/ PI (atan (/ (* B -0.5) C)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -7.1e+28) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else if (C <= 1.85e+132) {
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((B * -0.5) / C)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -7.1e+28) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else if (C <= 1.85e+132) {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(B, A)) / B)) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((B * -0.5) / C)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -7.1e+28:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	elif C <= 1.85e+132:
		tmp = 180.0 * (math.atan(((-A - math.hypot(B, A)) / B)) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan(((B * -0.5) / C)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -7.1e+28)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	elseif (C <= 1.85e+132)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(B, A)) / B)) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(B * -0.5) / C))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -7.1e+28)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	elseif (C <= 1.85e+132)
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / pi);
	else
		tmp = 180.0 / (pi / atan(((B * -0.5) / C)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -7.1e+28], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.85e+132], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -7.0999999999999999e28

   1. Initial program 82.8%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in B around -inf 88.2%

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

      1. neg-mul-1 88.2%

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

      2. unsub-neg 88.2%

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

   6. Simplified 88.2%

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

   if -7.0999999999999999e28 < C < 1.85000000000000005e132

   1. Initial program 51.1%

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

   2. Taylor expanded in C around 0 48.9%

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

      1. associate-*r/ 48.9%

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

      2. mul-1-neg 48.9%

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

      3. +-commutative 48.9%

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

      4. unpow2 48.9%

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

      5. unpow2 48.9%

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

      6. hypot-def 74.2%

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

   4. Simplified 74.2%

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

   if 1.85000000000000005e132 < C

   1. Initial program 13.7%

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

   3. Applied egg-rr 63.4%

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

   4. Taylor expanded in C around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. associate-*r/ 59.1%

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

      3. associate--l+ 59.1%

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

      4. unpow2 59.1%

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

      5. mul-1-neg 59.1%

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

      6. mul-1-neg 59.1%

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

      7. sqr-neg 59.1%

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

      8. unpow2 59.1%

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

      9. distribute-rgt1-in 59.1%

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

      10. metadata-eval 59.1%

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

      11. mul0-lft 59.1%

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

      12. metadata-eval 59.1%

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

   6. Simplified 59.1%

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

   7. Taylor expanded in A around 0 87.9%

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

      1. *-commutative 87.9%

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

      2. associate-*l/ 87.9%

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

   9. Simplified 87.9%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -7.1 \cdot 10^{+28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.85 \cdot 10^{+132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}}\\ \end{array} \]

Alternative 5: 75.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.2 \cdot 10^{+28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.5 \cdot 10^{+130}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.2e+28)
   (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
   (if (<= C 5.5e+130)
     (/ 180.0 (/ PI (atan (/ (- (- A) (hypot A B)) B))))
     (/ 180.0 (/ PI (atan (/ (* B -0.5) C)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.2e+28) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else if (C <= 5.5e+130) {
		tmp = 180.0 / (((double) M_PI) / atan(((-A - hypot(A, B)) / B)));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((B * -0.5) / C)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.2e+28) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else if (C <= 5.5e+130) {
		tmp = 180.0 / (Math.PI / Math.atan(((-A - Math.hypot(A, B)) / B)));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((B * -0.5) / C)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.2e+28:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	elif C <= 5.5e+130:
		tmp = 180.0 / (math.pi / math.atan(((-A - math.hypot(A, B)) / B)))
	else:
		tmp = 180.0 / (math.pi / math.atan(((B * -0.5) / C)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.2e+28)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	elseif (C <= 5.5e+130)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(-A) - hypot(A, B)) / B))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(B * -0.5) / C))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.2e+28)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	elseif (C <= 5.5e+130)
		tmp = 180.0 / (pi / atan(((-A - hypot(A, B)) / B)));
	else
		tmp = 180.0 / (pi / atan(((B * -0.5) / C)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.2e+28], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 5.5e+130], N[(180.0 / N[(Pi / N[ArcTan[N[(N[((-A) - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.19999999999999991e28

   1. Initial program 82.8%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in B around -inf 88.2%

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

      1. neg-mul-1 88.2%

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

      2. unsub-neg 88.2%

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

   6. Simplified 88.2%

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

   if -1.19999999999999991e28 < C < 5.4999999999999997e130

   1. Initial program 51.1%

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

   3. Applied egg-rr 75.8%

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

   4. Taylor expanded in C around 0 48.9%

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

      1. mul-1-neg 48.9%

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

      2. unpow2 48.9%

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

      3. unpow2 48.9%

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

      4. hypot-def 74.2%

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

   6. Simplified 74.2%

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

   if 5.4999999999999997e130 < C

   1. Initial program 13.7%

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

   3. Applied egg-rr 63.4%

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

   4. Taylor expanded in C around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. associate-*r/ 59.1%

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

      3. associate--l+ 59.1%

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

      4. unpow2 59.1%

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

      5. mul-1-neg 59.1%

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

      6. mul-1-neg 59.1%

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

      7. sqr-neg 59.1%

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

      8. unpow2 59.1%

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

      9. distribute-rgt1-in 59.1%

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

      10. metadata-eval 59.1%

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

      11. mul0-lft 59.1%

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

      12. metadata-eval 59.1%

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

   6. Simplified 59.1%

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

   7. Taylor expanded in A around 0 87.9%

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

      1. *-commutative 87.9%

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

      2. associate-*l/ 87.9%

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

   9. Simplified 87.9%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.2 \cdot 10^{+28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.5 \cdot 10^{+130}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}}\\ \end{array} \]

Alternative 6: 52.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{-190}:\\ \;\;\;\;\tan^{-1} \left(\frac{B}{\frac{A}{0.5}}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq -6 \cdot 10^{-245}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq -1.75 \cdot 10^{-303}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-236} \lor \neg \left(A \leq 1.02 \cdot 10^{+39}\right) \land A \leq 4.7 \cdot 10^{+67}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(-B\right) - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.1e-190)
   (* (atan (/ B (/ A 0.5))) (/ 180.0 PI))
   (if (<= A -6e-245)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= A -1.75e-303)
       (* 180.0 (/ (atan -1.0) PI))
       (if (or (<= A 5.2e-236) (and (not (<= A 1.02e+39)) (<= A 4.7e+67)))
         (/ 180.0 (/ PI (atan (/ (* B -0.5) C))))
         (/ 180.0 (/ PI (atan (/ (- (- B) A) B)))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.1e-190) {
		tmp = atan((B / (A / 0.5))) * (180.0 / ((double) M_PI));
	} else if (A <= -6e-245) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= -1.75e-303) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if ((A <= 5.2e-236) || (!(A <= 1.02e+39) && (A <= 4.7e+67))) {
		tmp = 180.0 / (((double) M_PI) / atan(((B * -0.5) / C)));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((-B - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.1e-190) {
		tmp = Math.atan((B / (A / 0.5))) * (180.0 / Math.PI);
	} else if (A <= -6e-245) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= -1.75e-303) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if ((A <= 5.2e-236) || (!(A <= 1.02e+39) && (A <= 4.7e+67))) {
		tmp = 180.0 / (Math.PI / Math.atan(((B * -0.5) / C)));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((-B - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.1e-190:
		tmp = math.atan((B / (A / 0.5))) * (180.0 / math.pi)
	elif A <= -6e-245:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= -1.75e-303:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif (A <= 5.2e-236) or (not (A <= 1.02e+39) and (A <= 4.7e+67)):
		tmp = 180.0 / (math.pi / math.atan(((B * -0.5) / C)))
	else:
		tmp = 180.0 / (math.pi / math.atan(((-B - A) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.1e-190)
		tmp = Float64(atan(Float64(B / Float64(A / 0.5))) * Float64(180.0 / pi));
	elseif (A <= -6e-245)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= -1.75e-303)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif ((A <= 5.2e-236) || (!(A <= 1.02e+39) && (A <= 4.7e+67)))
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(B * -0.5) / C))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(-B) - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.1e-190)
		tmp = atan((B / (A / 0.5))) * (180.0 / pi);
	elseif (A <= -6e-245)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= -1.75e-303)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif ((A <= 5.2e-236) || (~((A <= 1.02e+39)) && (A <= 4.7e+67)))
		tmp = 180.0 / (pi / atan(((B * -0.5) / C)));
	else
		tmp = 180.0 / (pi / atan(((-B - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.1e-190], N[(N[ArcTan[N[(B / N[(A / 0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -6e-245], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.75e-303], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[A, 5.2e-236], And[N[Not[LessEqual[A, 1.02e+39]], $MachinePrecision], LessEqual[A, 4.7e+67]]], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[((-B) - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -2.09999999999999991e-190

   1. Initial program 34.6%

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

   2. Taylor expanded in A around -inf 61.9%

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

      1. associate-*r/ 62.0%

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

   4. Applied egg-rr 62.0%

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

   5. Taylor expanded in B around 0 61.9%

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

      1. associate-*r/ 62.0%

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

      2. associate-*r/ 62.0%

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

      3. associate-*l/ 62.1%

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

      4. *-commutative 62.1%

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

      5. *-commutative 62.1%

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

      6. associate-/l* 62.1%

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

   7. Simplified 62.1%

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

   if -2.09999999999999991e-190 < A < -6.0000000000000004e-245

   1. Initial program 42.5%

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

   2. Taylor expanded in B around -inf 54.8%

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

   if -6.0000000000000004e-245 < A < -1.75e-303

   1. Initial program 67.5%

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

   2. Taylor expanded in B around inf 55.9%

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

   if -1.75e-303 < A < 5.2000000000000001e-236 or 1.02e39 < A < 4.70000000000000017e67

   1. Initial program 41.4%

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

   3. Applied egg-rr 72.9%

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

   4. Taylor expanded in C around inf 37.9%

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

      1. +-commutative 37.9%

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

      2. associate-*r/ 37.9%

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

      3. associate--l+ 37.9%

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

      4. unpow2 37.9%

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

      5. mul-1-neg 37.9%

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

      6. mul-1-neg 37.9%

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

      7. sqr-neg 37.9%

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

      8. unpow2 37.9%

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

      9. distribute-rgt1-in 37.9%

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

      10. metadata-eval 37.9%

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

      11. mul0-lft 37.9%

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

      12. metadata-eval 37.9%

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

   6. Simplified 37.9%

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

   7. Taylor expanded in A around 0 53.2%

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

      1. *-commutative 53.2%

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

      2. associate-*l/ 53.2%

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

   9. Simplified 53.2%

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

   if 5.2000000000000001e-236 < A < 1.02e39 or 4.70000000000000017e67 < A

   1. Initial program 77.6%

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

   3. Applied egg-rr 92.3%

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

   4. Taylor expanded in C around 0 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unpow2 74.1%

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

      3. unpow2 74.1%

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

      4. hypot-def 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in A around 0 73.2%

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

      1. +-commutative 73.2%

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

   9. Simplified 73.2%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{-190}:\\ \;\;\;\;\tan^{-1} \left(\frac{B}{\frac{A}{0.5}}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq -6 \cdot 10^{-245}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq -1.75 \cdot 10^{-303}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-236} \lor \neg \left(A \leq 1.02 \cdot 10^{+39}\right) \land A \leq 4.7 \cdot 10^{+67}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(-B\right) - A}{B}\right)}}\\ \end{array} \]

Alternative 7: 47.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.15 \cdot 10^{-12}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.95 \cdot 10^{-250}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 4.8 \cdot 10^{-200}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 8.6 \cdot 10^{-9}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= C -1.15e-12)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= C -1.95e-250)
       t_0
       (if (<= C 4.8e-200)
         (* 180.0 (/ (atan -1.0) PI))
         (if (<= C 8.6e-9) t_0 (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (C <= -1.15e-12) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= -1.95e-250) {
		tmp = t_0;
	} else if (C <= 4.8e-200) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (C <= 8.6e-9) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (C <= -1.15e-12) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= -1.95e-250) {
		tmp = t_0;
	} else if (C <= 4.8e-200) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (C <= 8.6e-9) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	tmp = 0
	if C <= -1.15e-12:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= -1.95e-250:
		tmp = t_0
	elif C <= 4.8e-200:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif C <= 8.6e-9:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (C <= -1.15e-12)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= -1.95e-250)
		tmp = t_0;
	elseif (C <= 4.8e-200)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (C <= 8.6e-9)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (C <= -1.15e-12)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= -1.95e-250)
		tmp = t_0;
	elseif (C <= 4.8e-200)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (C <= 8.6e-9)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.15e-12], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -1.95e-250], t$95$0, If[LessEqual[C, 4.8e-200], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 8.6e-9], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.14999999999999995e-12

   1. Initial program 83.1%

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

   2. Taylor expanded in C around -inf 69.8%

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

   if -1.14999999999999995e-12 < C < -1.95000000000000014e-250 or 4.80000000000000003e-200 < C < 8.59999999999999925e-9

   1. Initial program 52.1%

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

   2. Taylor expanded in A around -inf 42.5%

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

   if -1.95000000000000014e-250 < C < 4.80000000000000003e-200

   1. Initial program 46.8%

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

   2. Taylor expanded in B around inf 43.1%

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

   if 8.59999999999999925e-9 < C

   1. Initial program 28.3%

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

   3. Applied egg-rr 68.5%

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

   4. Taylor expanded in C around inf 42.8%

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

      1. +-commutative 42.8%

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

      2. associate-*r/ 42.8%

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

      3. associate--l+ 42.8%

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

      4. unpow2 42.8%

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

      5. mul-1-neg 42.8%

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

      6. mul-1-neg 42.8%

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

      7. sqr-neg 42.8%

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

      8. unpow2 42.8%

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

      9. distribute-rgt1-in 42.8%

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

      10. metadata-eval 42.8%

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

      11. mul0-lft 42.8%

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

      12. metadata-eval 42.8%

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

   6. Simplified 42.8%

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

   7. Taylor expanded in A around 0 60.3%

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

      1. associate-*r/ 60.3%

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

      2. +-rgt-identity 60.3%

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

      3. +-inverses 49.3%

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

      4. sub-neg 49.3%

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

      5. +-commutative 49.3%

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

      6. associate-+l+ 42.8%

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

      7. sub-neg 42.8%

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

      8. +-commutative 42.8%

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

      9. unpow2 42.8%

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

      10. fma-udef 35.2%

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

      11. associate-*l/ 35.2%

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

      12. *-commutative 35.2%

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

   9. Simplified 60.2%

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

   10. Taylor expanded in B around 0 69.9%

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

       1. *-commutative 69.9%

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

       2. associate-*l/ 69.9%

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

   12. Simplified 69.9%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.15 \cdot 10^{-12}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -1.95 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.8 \cdot 10^{-200}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 8.6 \cdot 10^{-9}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \]

Alternative 8: 47.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{B}{\frac{A}{0.5}}\right) \cdot \frac{180}{\pi}\\ \mathbf{if}\;C \leq -1.4 \cdot 10^{-12}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.2 \cdot 10^{-250}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 5.6 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 9.2 \cdot 10^{-9}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (atan (/ B (/ A 0.5))) (/ 180.0 PI))))
   (if (<= C -1.4e-12)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= C -2.2e-250)
       t_0
       (if (<= C 5.6e-197)
         (* 180.0 (/ (atan -1.0) PI))
         (if (<= C 9.2e-9) t_0 (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan((B / (A / 0.5))) * (180.0 / ((double) M_PI));
	double tmp;
	if (C <= -1.4e-12) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= -2.2e-250) {
		tmp = t_0;
	} else if (C <= 5.6e-197) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (C <= 9.2e-9) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan((B / (A / 0.5))) * (180.0 / Math.PI);
	double tmp;
	if (C <= -1.4e-12) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= -2.2e-250) {
		tmp = t_0;
	} else if (C <= 5.6e-197) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (C <= 9.2e-9) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan((B / (A / 0.5))) * (180.0 / math.pi)
	tmp = 0
	if C <= -1.4e-12:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= -2.2e-250:
		tmp = t_0
	elif C <= 5.6e-197:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif C <= 9.2e-9:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(atan(Float64(B / Float64(A / 0.5))) * Float64(180.0 / pi))
	tmp = 0.0
	if (C <= -1.4e-12)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= -2.2e-250)
		tmp = t_0;
	elseif (C <= 5.6e-197)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (C <= 9.2e-9)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan((B / (A / 0.5))) * (180.0 / pi);
	tmp = 0.0;
	if (C <= -1.4e-12)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= -2.2e-250)
		tmp = t_0;
	elseif (C <= 5.6e-197)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (C <= 9.2e-9)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[ArcTan[N[(B / N[(A / 0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.4e-12], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -2.2e-250], t$95$0, If[LessEqual[C, 5.6e-197], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 9.2e-9], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.4000000000000001e-12

   1. Initial program 83.1%

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

   2. Taylor expanded in C around -inf 69.8%

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

   if -1.4000000000000001e-12 < C < -2.2e-250 or 5.6000000000000004e-197 < C < 9.1999999999999997e-9

   1. Initial program 52.1%

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

   2. Taylor expanded in A around -inf 42.5%

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

      1. associate-*r/ 42.6%

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

   4. Applied egg-rr 42.6%

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

   5. Taylor expanded in B around 0 42.5%

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

      1. associate-*r/ 42.6%

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

      2. associate-*r/ 42.6%

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

      3. associate-*l/ 42.6%

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

      4. *-commutative 42.6%

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

      5. *-commutative 42.6%

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

      6. associate-/l* 42.6%

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

   7. Simplified 42.6%

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

   if -2.2e-250 < C < 5.6000000000000004e-197

   1. Initial program 46.8%

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

   2. Taylor expanded in B around inf 43.1%

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

   if 9.1999999999999997e-9 < C

   1. Initial program 28.3%

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

   3. Applied egg-rr 68.5%

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

   4. Taylor expanded in C around inf 42.8%

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

      1. +-commutative 42.8%

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

      2. associate-*r/ 42.8%

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

      3. associate--l+ 42.8%

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

      4. unpow2 42.8%

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

      5. mul-1-neg 42.8%

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

      6. mul-1-neg 42.8%

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

      7. sqr-neg 42.8%

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

      8. unpow2 42.8%

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

      9. distribute-rgt1-in 42.8%

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

      10. metadata-eval 42.8%

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

      11. mul0-lft 42.8%

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

      12. metadata-eval 42.8%

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

   6. Simplified 42.8%

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

   7. Taylor expanded in A around 0 60.3%

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

      1. associate-*r/ 60.3%

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

      2. +-rgt-identity 60.3%

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

      3. +-inverses 49.3%

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

      4. sub-neg 49.3%

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

      5. +-commutative 49.3%

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

      6. associate-+l+ 42.8%

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

      7. sub-neg 42.8%

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

      8. +-commutative 42.8%

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

      9. unpow2 42.8%

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

      10. fma-udef 35.2%

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

      11. associate-*l/ 35.2%

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

      12. *-commutative 35.2%

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

   9. Simplified 60.2%

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

   10. Taylor expanded in B around 0 69.9%

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

       1. *-commutative 69.9%

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

       2. associate-*l/ 69.9%

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

   12. Simplified 69.9%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.4 \cdot 10^{-12}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.2 \cdot 10^{-250}:\\ \;\;\;\;\tan^{-1} \left(\frac{B}{\frac{A}{0.5}}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq 5.6 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 9.2 \cdot 10^{-9}:\\ \;\;\;\;\tan^{-1} \left(\frac{B}{\frac{A}{0.5}}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \]

Alternative 9: 51.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-207}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 - \frac{A}{B}\right)}}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e-207)
   (/ 180.0 (/ PI (atan (- 1.0 (/ A B)))))
   (if (<= B 6.5e-173)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (if (<= B 2.5e-38)
       (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-207) {
		tmp = 180.0 / (((double) M_PI) / atan((1.0 - (A / B))));
	} else if (B <= 6.5e-173) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 2.5e-38) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-207) {
		tmp = 180.0 / (Math.PI / Math.atan((1.0 - (A / B))));
	} else if (B <= 6.5e-173) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 2.5e-38) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1e-207:
		tmp = 180.0 / (math.pi / math.atan((1.0 - (A / B))))
	elif B <= 6.5e-173:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 2.5e-38:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1e-207)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(1.0 - Float64(A / B)))));
	elseif (B <= 6.5e-173)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 2.5e-38)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1e-207)
		tmp = 180.0 / (pi / atan((1.0 - (A / B))));
	elseif (B <= 6.5e-173)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 2.5e-38)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1e-207], N[(180.0 / N[(Pi / N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.5e-173], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.5e-38], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -9.99999999999999925e-208

   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 72.5%

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

   4. Taylor expanded in C around 0 44.9%

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

      1. mul-1-neg 44.9%

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

      2. unpow2 44.9%

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

      3. unpow2 44.9%

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

      4. hypot-def 64.0%

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

   6. Simplified 64.0%

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

   7. Taylor expanded in B around -inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. unsub-neg 60.7%

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

   9. Simplified 60.7%

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

   if -9.99999999999999925e-208 < B < 6.4999999999999995e-173

   1. Initial program 52.1%

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

   2. Taylor expanded in C around inf 55.7%

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

      1. associate-*r/ 55.7%

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

      2. distribute-rgt1-in 55.7%

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

      3. metadata-eval 55.7%

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

      4. mul0-lft 55.7%

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

      5. metadata-eval 55.7%

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

   4. Simplified 55.7%

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

   if 6.4999999999999995e-173 < B < 2.50000000000000017e-38

   1. Initial program 61.5%

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

   2. Taylor expanded in C around -inf 46.8%

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

   if 2.50000000000000017e-38 < B

   1. Initial program 58.0%

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

   2. Taylor expanded in B around inf 59.6%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-207}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 - \frac{A}{B}\right)}}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 10: 59.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.65 \cdot 10^{-209}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 - \frac{A}{B}\right)}}\\ \mathbf{elif}\;B \leq 1.08 \cdot 10^{-172}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.65e-209)
   (/ 180.0 (/ PI (atan (- 1.0 (/ A B)))))
   (if (<= B 1.08e-172)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.65e-209) {
		tmp = 180.0 / (((double) M_PI) / atan((1.0 - (A / B))));
	} else if (B <= 1.08e-172) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.65e-209) {
		tmp = 180.0 / (Math.PI / Math.atan((1.0 - (A / B))));
	} else if (B <= 1.08e-172) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.65e-209:
		tmp = 180.0 / (math.pi / math.atan((1.0 - (A / B))))
	elif B <= 1.08e-172:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.65e-209)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(1.0 - Float64(A / B)))));
	elseif (B <= 1.08e-172)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.65e-209)
		tmp = 180.0 / (pi / atan((1.0 - (A / B))));
	elseif (B <= 1.08e-172)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.65e-209], N[(180.0 / N[(Pi / N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.08e-172], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.64999999999999987e-209

   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 72.5%

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

   4. Taylor expanded in C around 0 44.9%

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

      1. mul-1-neg 44.9%

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

      2. unpow2 44.9%

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

      3. unpow2 44.9%

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

      4. hypot-def 64.0%

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

   6. Simplified 64.0%

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

   7. Taylor expanded in B around -inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. unsub-neg 60.7%

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

   9. Simplified 60.7%

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

   if -1.64999999999999987e-209 < B < 1.08e-172

   1. Initial program 52.1%

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

   2. Taylor expanded in C around inf 55.7%

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

      1. associate-*r/ 55.7%

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

      2. distribute-rgt1-in 55.7%

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

      3. metadata-eval 55.7%

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

      4. mul0-lft 55.7%

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

      5. metadata-eval 55.7%

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

   4. Simplified 55.7%

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

   if 1.08e-172 < B

   1. Initial program 58.7%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in B around inf 77.9%

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

      1. +-commutative 77.9%

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

   6. Simplified 77.9%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.65 \cdot 10^{-209}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 - \frac{A}{B}\right)}}\\ \mathbf{elif}\;B \leq 1.08 \cdot 10^{-172}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 11: 63.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-237}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.6e-237)
   (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
   (if (<= B 3.5e-173)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.6e-237) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else if (B <= 3.5e-173) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.6e-237) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else if (B <= 3.5e-173) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.6e-237:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	elif B <= 3.5e-173:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.6e-237)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	elseif (B <= 3.5e-173)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.6e-237)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	elseif (B <= 3.5e-173)
		tmp = 180.0 * (atan((0.0 / B)) / 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-237], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.5e-173], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.6000000000000002e-237

   1. Initial program 50.1%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in B around -inf 65.5%

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

      1. neg-mul-1 65.5%

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

      2. unsub-neg 65.5%

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

   6. Simplified 65.5%

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

   if -2.6000000000000002e-237 < B < 3.50000000000000014e-173

   1. Initial program 52.1%

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

   2. Taylor expanded in C around inf 58.2%

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

      1. associate-*r/ 58.2%

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

      2. distribute-rgt1-in 58.2%

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

      3. metadata-eval 58.2%

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

      4. mul0-lft 58.2%

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

      5. metadata-eval 58.2%

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

   4. Simplified 58.2%

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

   if 3.50000000000000014e-173 < B

   1. Initial program 58.7%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in B around inf 77.9%

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

      1. +-commutative 77.9%

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

   6. Simplified 77.9%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-237}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 12: 63.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.2 \cdot 10^{-236}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-172}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.2e-236)
   (/ 180.0 (/ PI (atan (/ (- (+ B C) A) B))))
   (if (<= B 3.8e-172)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.2e-236) {
		tmp = 180.0 / (((double) M_PI) / atan((((B + C) - A) / B)));
	} else if (B <= 3.8e-172) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.2e-236) {
		tmp = 180.0 / (Math.PI / Math.atan((((B + C) - A) / B)));
	} else if (B <= 3.8e-172) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5.2e-236:
		tmp = 180.0 / (math.pi / math.atan((((B + C) - A) / B)))
	elif B <= 3.8e-172:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5.2e-236)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(B + C) - A) / B))));
	elseif (B <= 3.8e-172)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5.2e-236)
		tmp = 180.0 / (pi / atan((((B + C) - A) / B)));
	elseif (B <= 3.8e-172)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5.2e-236], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.8e-172], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -5.2000000000000001e-236

   1. Initial program 50.1%

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

   3. Applied egg-rr 73.2%

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

   4. Taylor expanded in B around -inf 65.5%

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

   if -5.2000000000000001e-236 < B < 3.79999999999999987e-172

   1. Initial program 52.1%

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

   2. Taylor expanded in C around inf 58.2%

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

      1. associate-*r/ 58.2%

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

      2. distribute-rgt1-in 58.2%

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

      3. metadata-eval 58.2%

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

      4. mul0-lft 58.2%

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

      5. metadata-eval 58.2%

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

   4. Simplified 58.2%

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

   if 3.79999999999999987e-172 < B

   1. Initial program 58.7%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in B around inf 77.9%

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

      1. +-commutative 77.9%

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

   6. Simplified 77.9%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.2 \cdot 10^{-236}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-172}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 13: 63.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -9.5 \cdot 10^{-237}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-172}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -9.5e-237)
   (/ 180.0 (/ PI (atan (/ (- (+ B C) A) B))))
   (if (<= B 3.8e-172)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (/ 180.0 (/ PI (atan (/ (- (- C B) A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -9.5e-237) {
		tmp = 180.0 / (((double) M_PI) / atan((((B + C) - A) / B)));
	} else if (B <= 3.8e-172) {
		tmp = 180.0 * (atan((0.0 / 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 <= -9.5e-237) {
		tmp = 180.0 / (Math.PI / Math.atan((((B + C) - A) / B)));
	} else if (B <= 3.8e-172) {
		tmp = 180.0 * (Math.atan((0.0 / 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 <= -9.5e-237:
		tmp = 180.0 / (math.pi / math.atan((((B + C) - A) / B)))
	elif B <= 3.8e-172:
		tmp = 180.0 * (math.atan((0.0 / 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 <= -9.5e-237)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(B + C) - A) / B))));
	elseif (B <= 3.8e-172)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / 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 <= -9.5e-237)
		tmp = 180.0 / (pi / atan((((B + C) - A) / B)));
	elseif (B <= 3.8e-172)
		tmp = 180.0 * (atan((0.0 / 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, -9.5e-237], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.8e-172], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $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 < -9.4999999999999998e-237

   1. Initial program 50.1%

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

   3. Applied egg-rr 73.2%

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

   4. Taylor expanded in B around -inf 65.5%

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

   if -9.4999999999999998e-237 < B < 3.79999999999999987e-172

   1. Initial program 52.1%

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

   2. Taylor expanded in C around inf 58.2%

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

      1. associate-*r/ 58.2%

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

      2. distribute-rgt1-in 58.2%

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

      3. metadata-eval 58.2%

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

      4. mul0-lft 58.2%

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

      5. metadata-eval 58.2%

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

   4. Simplified 58.2%

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

   if 3.79999999999999987e-172 < B

   1. Initial program 58.7%

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

   3. Applied egg-rr 81.9%

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

   4. Taylor expanded in B around inf 77.9%

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

      1. mul-1-neg 77.9%

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

      2. unsub-neg 77.9%

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

   6. Simplified 77.9%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9.5 \cdot 10^{-237}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-172}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}}\\ \end{array} \]

Alternative 14: 46.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{-70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -5.4 \cdot 10^{-207}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.7 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.8e-70)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -5.4e-207)
     (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
     (if (<= B 5.7e-95)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.8e-70) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -5.4e-207) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 5.7e-95) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.8e-70) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -5.4e-207) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 5.7e-95) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -6.8e-70:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -5.4e-207:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 5.7e-95:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -6.8e-70)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -5.4e-207)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 5.7e-95)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -6.8e-70)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -5.4e-207)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 5.7e-95)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -6.8e-70], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -5.4e-207], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.7e-95], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -6.79999999999999991e-70

   1. Initial program 49.0%

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

   2. Taylor expanded in B around -inf 55.9%

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

   if -6.79999999999999991e-70 < B < -5.4e-207

   1. Initial program 52.4%

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

   2. Taylor expanded in A around inf 45.2%

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

   if -5.4e-207 < B < 5.7e-95

   1. Initial program 55.9%

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

   2. Taylor expanded in C around inf 51.3%

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

      1. associate-*r/ 51.3%

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

      2. distribute-rgt1-in 51.3%

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

      3. metadata-eval 51.3%

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

      4. mul0-lft 51.3%

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

      5. metadata-eval 51.3%

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

   4. Simplified 51.3%

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

   if 5.7e-95 < B

   1. Initial program 56.6%

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

   2. Taylor expanded in B around inf 54.4%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{-70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -5.4 \cdot 10^{-207}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.7 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 15: 47.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -7 \cdot 10^{-213}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-139}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -7e-213)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 6.5e-139)
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (* (/ A B) -2.0)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -7e-213) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 6.5e-139) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -7e-213) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 6.5e-139) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -7e-213:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 6.5e-139:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -7e-213)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 6.5e-139)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -7e-213)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 6.5e-139)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -7e-213], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6.5e-139], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -7.00000000000000034e-213

   1. Initial program 36.0%

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

   2. Taylor expanded in A around -inf 60.2%

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

   if -7.00000000000000034e-213 < A < 6.5e-139

   1. Initial program 54.9%

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

   2. Taylor expanded in B around inf 37.6%

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

   if 6.5e-139 < A

   1. Initial program 73.9%

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

   2. Taylor expanded in A around inf 57.6%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7 \cdot 10^{-213}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.5 \cdot 10^{-139}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \]

Alternative 16: 45.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.8 \cdot 10^{-134}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-96}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.8e-134)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 6.2e-96)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.8e-134) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 6.2e-96) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.8e-134) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 6.2e-96) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5.8e-134:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 6.2e-96:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5.8e-134)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 6.2e-96)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5.8e-134)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 6.2e-96)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5.8e-134], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.2e-96], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -5.79999999999999986e-134

   1. Initial program 49.3%

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

   2. Taylor expanded in B around -inf 51.8%

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

   if -5.79999999999999986e-134 < B < 6.1999999999999998e-96

   1. Initial program 55.0%

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

   2. Taylor expanded in C around inf 44.7%

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

      1. associate-*r/ 44.7%

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

      2. distribute-rgt1-in 44.7%

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

      3. metadata-eval 44.7%

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

      4. mul0-lft 44.7%

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

      5. metadata-eval 44.7%

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

   4. Simplified 44.7%

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

   if 6.1999999999999998e-96 < B

   1. Initial program 56.6%

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

   2. Taylor expanded in B around inf 54.4%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.8 \cdot 10^{-134}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-96}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 17: 40.2% accurate, 2.5× speedup

Math

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

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -9.999999999999969e-311

   1. Initial program 50.3%

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

   2. Taylor expanded in B around -inf 36.5%

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

   if -9.999999999999969e-311 < B

   1. Initial program 57.3%

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

   2. Taylor expanded in B around inf 41.3%

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

4. Final simplification 38.8%

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

Alternative 18: 21.4% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 53.7%

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

2. Taylor expanded in B around inf 20.9%

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

3. Final simplification 20.9%

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

Reproduce

herbie shell --seed 2023318 
(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)))