ABCF->ab-angle angle

Percentage Accurate: 54.5% → 88.3%

Time: 21.0s

Alternatives: 20

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: 54.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -0.5 \lor \neg \left(t_0 \leq 5 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (or (<= t_0 -0.5) (not (<= t_0 5e-6)))
     (* (/ 180.0 PI) (atan (/ (- (- C A) (hypot B (- C A))) B)))
     (/ (atan (/ B (/ (- C A) -0.5))) (* PI 0.005555555555555556)))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -0.5) || !(t_0 <= 5e-6)) {
		tmp = (180.0 / ((double) M_PI)) * atan((((C - A) - hypot(B, (C - A))) / B));
	} else {
		tmp = atan((B / ((C - A) / -0.5))) / (((double) M_PI) * 0.005555555555555556);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -0.5) || !(t_0 <= 5e-6)) {
		tmp = (180.0 / Math.PI) * Math.atan((((C - A) - Math.hypot(B, (C - A))) / B));
	} else {
		tmp = Math.atan((B / ((C - A) / -0.5))) / (Math.PI * 0.005555555555555556);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if (t_0 <= -0.5) or not (t_0 <= 5e-6):
		tmp = (180.0 / math.pi) * math.atan((((C - A) - math.hypot(B, (C - A))) / B))
	else:
		tmp = math.atan((B / ((C - A) / -0.5))) / (math.pi * 0.005555555555555556)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if ((t_0 <= -0.5) || !(t_0 <= 5e-6))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(C - A))) / B)));
	else
		tmp = Float64(atan(Float64(B / Float64(Float64(C - A) / -0.5))) / Float64(pi * 0.005555555555555556));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if ((t_0 <= -0.5) || ~((t_0 <= 5e-6)))
		tmp = (180.0 / pi) * atan((((C - A) - hypot(B, (C - A))) / B));
	else
		tmp = atan((B / ((C - A) / -0.5))) / (pi * 0.005555555555555556);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -0.5], N[Not[LessEqual[t$95$0, 5e-6]], $MachinePrecision]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(B / N[(N[(C - A), $MachinePrecision] / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.5 or 5.00000000000000041e-6 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 55.4%

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

   3. Simplified 85.9%

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

   if -0.5 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 5.00000000000000041e-6

   1. Initial program 17.8%

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

   3. Simplified 17.8%

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

   4. Taylor expanded in B around 0 98.6%

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

      1. associate-*r/ 98.6%

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

   6. Simplified 98.6%

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

      1. *-commutative 98.6%

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

      2. clear-num 98.6%

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

      3. un-div-inv 98.7%

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

      4. div-inv 98.7%

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

      5. associate-/r* 98.6%

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

   8. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{\frac{\frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}}{0.005555555555555556}} \]

   9. Taylor expanded in A around -inf 98.5%

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

       1. associate-*r/ 98.5%

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

       2. *-commutative 98.5%

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

       3. mul-1-neg 98.5%

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

       4. sub-neg 98.5%

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

       5. associate-*r/ 98.5%

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

       6. /-rgt-identity 98.5%

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

       7. associate-*r/ 98.4%

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

       8. *-commutative 98.4%

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

       9. associate-*r/ 98.5%

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

       10. associate-/l* 98.6%

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

       11. associate-*r/ 98.7%

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

       12. associate-/l* 98.7%

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

       13. associate-/r/ 98.7%

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

       14. metadata-eval 98.7%

           \[\leadsto \frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\color{blue}{0.005555555555555556} \cdot \pi} \]

       15. *-commutative 98.7%

           \[\leadsto \frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\color{blue}{\pi \cdot 0.005555555555555556}} \]

   11. Simplified 98.7%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.5 \lor \neg \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 5 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 2: 78.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+96}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 1.4:\\ \;\;\;\;\frac{180}{\frac{-1}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)} \cdot \left(-\pi\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot -0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.8e+96)
   (/ (atan (/ B (/ (- C A) -0.5))) (* PI 0.005555555555555556))
   (if (<= A 1.4)
     (/ 180.0 (* (/ -1.0 (atan (/ (- C (hypot C B)) B))) (- PI)))
     (/ (atan (/ (+ A (hypot A B)) B)) (* PI -0.005555555555555556)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+96) {
		tmp = atan((B / ((C - A) / -0.5))) / (((double) M_PI) * 0.005555555555555556);
	} else if (A <= 1.4) {
		tmp = 180.0 / ((-1.0 / atan(((C - hypot(C, B)) / B))) * -((double) M_PI));
	} else {
		tmp = atan(((A + hypot(A, B)) / B)) / (((double) M_PI) * -0.005555555555555556);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+96) {
		tmp = Math.atan((B / ((C - A) / -0.5))) / (Math.PI * 0.005555555555555556);
	} else if (A <= 1.4) {
		tmp = 180.0 / ((-1.0 / Math.atan(((C - Math.hypot(C, B)) / B))) * -Math.PI);
	} else {
		tmp = Math.atan(((A + Math.hypot(A, B)) / B)) / (Math.PI * -0.005555555555555556);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.8e+96:
		tmp = math.atan((B / ((C - A) / -0.5))) / (math.pi * 0.005555555555555556)
	elif A <= 1.4:
		tmp = 180.0 / ((-1.0 / math.atan(((C - math.hypot(C, B)) / B))) * -math.pi)
	else:
		tmp = math.atan(((A + math.hypot(A, B)) / B)) / (math.pi * -0.005555555555555556)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.8e+96)
		tmp = Float64(atan(Float64(B / Float64(Float64(C - A) / -0.5))) / Float64(pi * 0.005555555555555556));
	elseif (A <= 1.4)
		tmp = Float64(180.0 / Float64(Float64(-1.0 / atan(Float64(Float64(C - hypot(C, B)) / B))) * Float64(-pi)));
	else
		tmp = Float64(atan(Float64(Float64(A + hypot(A, B)) / B)) / Float64(pi * -0.005555555555555556));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.8e+96)
		tmp = atan((B / ((C - A) / -0.5))) / (pi * 0.005555555555555556);
	elseif (A <= 1.4)
		tmp = 180.0 / ((-1.0 / atan(((C - hypot(C, B)) / B))) * -pi);
	else
		tmp = atan(((A + hypot(A, B)) / B)) / (pi * -0.005555555555555556);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.8e+96], N[(N[ArcTan[N[(B / N[(N[(C - A), $MachinePrecision] / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.4], N[(180.0 / N[(N[(-1.0 / N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * (-Pi)), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / N[(Pi * -0.005555555555555556), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.80000000000000007e96

   1. Initial program 17.8%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in B around 0 85.9%

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

      1. associate-*r/ 85.9%

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

   6. Simplified 85.9%

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

      1. *-commutative 85.9%

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

      2. clear-num 85.9%

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

      3. un-div-inv 85.9%

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

      4. div-inv 85.9%

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

      5. associate-/r* 85.9%

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

   8. Applied egg-rr 85.9%

      \[\leadsto \color{blue}{\frac{\frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}}{0.005555555555555556}} \]

   9. Taylor expanded in A around -inf 85.8%

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

       1. associate-*r/ 85.8%

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

       2. *-commutative 85.8%

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

       3. mul-1-neg 85.8%

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

       4. sub-neg 85.8%

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

       5. associate-*r/ 85.8%

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

       6. /-rgt-identity 85.8%

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

       7. associate-*r/ 85.7%

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

       8. *-commutative 85.7%

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

       9. associate-*r/ 85.8%

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

       10. associate-/l* 85.8%

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

       11. associate-*r/ 85.9%

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

       12. associate-/l* 85.9%

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

       13. associate-/r/ 85.9%

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

       14. metadata-eval 85.9%

           \[\leadsto \frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\color{blue}{0.005555555555555556} \cdot \pi} \]

       15. *-commutative 85.9%

           \[\leadsto \frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\color{blue}{\pi \cdot 0.005555555555555556}} \]

   11. Simplified 85.9%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}} \]

   if -1.80000000000000007e96 < A < 1.3999999999999999

   1. Initial program 52.6%

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

   3. Simplified 52.4%

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

   4. Taylor expanded in A around 0 51.3%

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

      1. unpow2 51.3%

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

      2. unpow2 51.3%

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

      3. hypot-def 75.3%

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

   6. Simplified 75.3%

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

      1. clear-num 75.2%

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

      2. inv-pow 75.2%

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

      3. div-inv 75.3%

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

      4. unpow-prod-down 75.3%

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

      5. inv-pow 75.3%

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

   8. Applied egg-rr 75.3%

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

      1. associate-*r* 75.2%

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

      2. unpow-1 75.2%

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

      3. associate-*r/ 75.2%

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

      4. *-commutative 75.2%

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

      5. associate-*l/ 75.2%

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

      6. frac-2neg 75.2%

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

      7. metadata-eval 75.2%

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

      8. div-inv 75.2%

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

      9. associate-/r* 75.2%

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

      10. metadata-eval 75.2%

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

      11. frac-2neg 75.2%

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

      12. metadata-eval 75.2%

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

      13. associate-*r/ 75.2%

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

   10. Applied egg-rr 75.3%

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

   if 1.3999999999999999 < A

   1. Initial program 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in C around 0 71.6%

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

      1. associate-*r/ 71.6%

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

      2. mul-1-neg 71.6%

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

      3. +-commutative 71.6%

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

      4. unpow2 71.6%

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

      5. unpow2 71.6%

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

      6. hypot-def 83.8%

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

   6. Simplified 83.8%

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

      1. *-commutative 83.8%

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

      2. frac-2neg 83.8%

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

      3. associate-*l/ 83.8%

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

      4. associate-/l* 83.8%

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

      5. distribute-frac-neg 83.8%

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

      6. atan-neg 83.8%

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

      7. remove-double-neg 83.8%

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

      8. hypot-udef 71.6%

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

      9. +-commutative 71.6%

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

      10. hypot-def 83.8%

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

      11. distribute-neg-frac 83.8%

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

      12. div-inv 83.8%

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

      13. distribute-rgt-neg-in 83.8%

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

      14. metadata-eval 83.8%

          \[\leadsto \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot \left(-\color{blue}{0.005555555555555556}\right)} \]

      15. metadata-eval 83.8%

          \[\leadsto \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot \color{blue}{-0.005555555555555556}} \]

   8. Applied egg-rr 83.8%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot -0.005555555555555556}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+96}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 1.4:\\ \;\;\;\;\frac{180}{\frac{-1}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)} \cdot \left(-\pi\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot -0.005555555555555556}\\ \end{array} \]

Alternative 3: 81.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.55 \cdot 10^{+96}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.55e+96)
   (/ (atan (/ B (/ (- C A) -0.5))) (* PI 0.005555555555555556))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.55e+96) {
		tmp = atan((B / ((C - A) / -0.5))) / (((double) M_PI) * 0.005555555555555556);
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.55e+96) {
		tmp = Math.atan((B / ((C - A) / -0.5))) / (Math.PI * 0.005555555555555556);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.55e+96:
		tmp = math.atan((B / ((C - A) / -0.5))) / (math.pi * 0.005555555555555556)
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.55e+96)
		tmp = Float64(atan(Float64(B / Float64(Float64(C - A) / -0.5))) / Float64(pi * 0.005555555555555556));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.55e+96)
		tmp = atan((B / ((C - A) / -0.5))) / (pi * 0.005555555555555556);
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.55e+96], N[(N[ArcTan[N[(B / N[(N[(C - A), $MachinePrecision] / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $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 < -1.5499999999999999e96

   1. Initial program 17.8%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in B around 0 85.9%

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

      1. associate-*r/ 85.9%

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

   6. Simplified 85.9%

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

      1. *-commutative 85.9%

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

      2. clear-num 85.9%

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

      3. un-div-inv 85.9%

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

      4. div-inv 85.9%

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

      5. associate-/r* 85.9%

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

   8. Applied egg-rr 85.9%

      \[\leadsto \color{blue}{\frac{\frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}}{0.005555555555555556}} \]

   9. Taylor expanded in A around -inf 85.8%

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

       1. associate-*r/ 85.8%

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

       2. *-commutative 85.8%

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

       3. mul-1-neg 85.8%

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

       4. sub-neg 85.8%

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

       5. associate-*r/ 85.8%

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

       6. /-rgt-identity 85.8%

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

       7. associate-*r/ 85.7%

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

       8. *-commutative 85.7%

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

       9. associate-*r/ 85.8%

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

       10. associate-/l* 85.8%

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

       11. associate-*r/ 85.9%

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

       12. associate-/l* 85.9%

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

       13. associate-/r/ 85.9%

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

       14. metadata-eval 85.9%

           \[\leadsto \frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\color{blue}{0.005555555555555556} \cdot \pi} \]

       15. *-commutative 85.9%

           \[\leadsto \frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\color{blue}{\pi \cdot 0.005555555555555556}} \]

   11. Simplified 85.9%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}} \]

   if -1.5499999999999999e96 < A

   1. Initial program 58.9%

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

   3. Simplified 81.5%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.55 \cdot 10^{+96}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 76.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.6 \cdot 10^{+97}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{+88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.6e+97)
   (/ (atan (/ B (/ (- C A) -0.5))) (* PI 0.005555555555555556))
   (if (<= A 6.8e+88)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (/ (* -180.0 (atan (/ (+ B A) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.6e+97) {
		tmp = atan((B / ((C - A) / -0.5))) / (((double) M_PI) * 0.005555555555555556);
	} else if (A <= 6.8e+88) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = (-180.0 * atan(((B + A) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.6e+97) {
		tmp = Math.atan((B / ((C - A) / -0.5))) / (Math.PI * 0.005555555555555556);
	} else if (A <= 6.8e+88) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = (-180.0 * Math.atan(((B + A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.6e+97:
		tmp = math.atan((B / ((C - A) / -0.5))) / (math.pi * 0.005555555555555556)
	elif A <= 6.8e+88:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = (-180.0 * math.atan(((B + A) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.6e+97)
		tmp = Float64(atan(Float64(B / Float64(Float64(C - A) / -0.5))) / Float64(pi * 0.005555555555555556));
	elseif (A <= 6.8e+88)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(B + A) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.6e+97)
		tmp = atan((B / ((C - A) / -0.5))) / (pi * 0.005555555555555556);
	elseif (A <= 6.8e+88)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = (-180.0 * atan(((B + A) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.6e+97], N[(N[ArcTan[N[(B / N[(N[(C - A), $MachinePrecision] / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6.8e+88], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(-180.0 * N[ArcTan[N[(N[(B + A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.59999999999999966e97

   1. Initial program 17.8%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in B around 0 85.9%

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

      1. associate-*r/ 85.9%

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

   6. Simplified 85.9%

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

      1. *-commutative 85.9%

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

      2. clear-num 85.9%

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

      3. un-div-inv 85.9%

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

      4. div-inv 85.9%

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

      5. associate-/r* 85.9%

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

   8. Applied egg-rr 85.9%

      \[\leadsto \color{blue}{\frac{\frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}}{0.005555555555555556}} \]

   9. Taylor expanded in A around -inf 85.8%

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

       1. associate-*r/ 85.8%

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

       2. *-commutative 85.8%

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

       3. mul-1-neg 85.8%

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

       4. sub-neg 85.8%

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

       5. associate-*r/ 85.8%

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

       6. /-rgt-identity 85.8%

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

       7. associate-*r/ 85.7%

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

       8. *-commutative 85.7%

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

       9. associate-*r/ 85.8%

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

       10. associate-/l* 85.8%

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

       11. associate-*r/ 85.9%

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

       12. associate-/l* 85.9%

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

       13. associate-/r/ 85.9%

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

       14. metadata-eval 85.9%

           \[\leadsto \frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\color{blue}{0.005555555555555556} \cdot \pi} \]

       15. *-commutative 85.9%

           \[\leadsto \frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\color{blue}{\pi \cdot 0.005555555555555556}} \]

   11. Simplified 85.9%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}} \]

   if -3.59999999999999966e97 < A < 6.80000000000000008e88

   1. Initial program 55.4%

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

   3. Simplified 55.3%

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

   4. Taylor expanded in A around 0 52.0%

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

      1. unpow2 52.0%

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

      2. unpow2 52.0%

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

      3. hypot-def 75.0%

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

   6. Simplified 75.0%

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

   if 6.80000000000000008e88 < A

   1. Initial program 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in C around 0 70.4%

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

      1. associate-*r/ 70.4%

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

      2. mul-1-neg 70.4%

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

      3. +-commutative 70.4%

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

      4. unpow2 70.4%

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

      5. unpow2 70.4%

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

      6. hypot-def 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in A around 0 77.9%

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

      1. +-commutative 77.9%

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

   9. Simplified 77.9%

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

       1. *-commutative 77.9%

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

       2. frac-2neg 77.9%

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

       3. associate-*l/ 77.9%

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

       4. clear-num 77.9%

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

       5. *-commutative 77.9%

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

       6. distribute-frac-neg 77.9%

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

       7. atan-neg 77.9%

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

       8. remove-double-neg 77.9%

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

       9. +-commutative 77.9%

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

   11. Applied egg-rr 77.9%

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

       1. associate-/r* 77.9%

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

       2. associate-/l* 77.9%

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

       3. *-lft-identity 77.9%

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

       4. associate-/l* 77.9%

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

       5. *-commutative 77.9%

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

       6. neg-mul-1 77.9%

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

       7. associate-/r* 77.9%

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

       8. associate-/l* 77.9%

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

       9. associate-/r/ 77.9%

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

       10. metadata-eval 77.9%

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

       11. +-commutative 77.9%

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

   13. Simplified 77.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.6 \cdot 10^{+97}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{+88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 78.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 0.9:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot -0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.2e+98)
   (/ (atan (/ B (/ (- C A) -0.5))) (* PI 0.005555555555555556))
   (if (<= A 0.9)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (/ (atan (/ (+ A (hypot A B)) B)) (* PI -0.005555555555555556)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.2e+98) {
		tmp = atan((B / ((C - A) / -0.5))) / (((double) M_PI) * 0.005555555555555556);
	} else if (A <= 0.9) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = atan(((A + hypot(A, B)) / B)) / (((double) M_PI) * -0.005555555555555556);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.2e+98) {
		tmp = Math.atan((B / ((C - A) / -0.5))) / (Math.PI * 0.005555555555555556);
	} else if (A <= 0.9) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = Math.atan(((A + Math.hypot(A, B)) / B)) / (Math.PI * -0.005555555555555556);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.2e+98:
		tmp = math.atan((B / ((C - A) / -0.5))) / (math.pi * 0.005555555555555556)
	elif A <= 0.9:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = math.atan(((A + math.hypot(A, B)) / B)) / (math.pi * -0.005555555555555556)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.2e+98)
		tmp = Float64(atan(Float64(B / Float64(Float64(C - A) / -0.5))) / Float64(pi * 0.005555555555555556));
	elseif (A <= 0.9)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(atan(Float64(Float64(A + hypot(A, B)) / B)) / Float64(pi * -0.005555555555555556));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.2e+98)
		tmp = atan((B / ((C - A) / -0.5))) / (pi * 0.005555555555555556);
	elseif (A <= 0.9)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = atan(((A + hypot(A, B)) / B)) / (pi * -0.005555555555555556);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.2e+98], N[(N[ArcTan[N[(B / N[(N[(C - A), $MachinePrecision] / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 0.9], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / N[(Pi * -0.005555555555555556), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.2000000000000002e98

   1. Initial program 17.8%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in B around 0 85.9%

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

      1. associate-*r/ 85.9%

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

   6. Simplified 85.9%

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

      1. *-commutative 85.9%

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

      2. clear-num 85.9%

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

      3. un-div-inv 85.9%

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

      4. div-inv 85.9%

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

      5. associate-/r* 85.9%

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

   8. Applied egg-rr 85.9%

      \[\leadsto \color{blue}{\frac{\frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}}{0.005555555555555556}} \]

   9. Taylor expanded in A around -inf 85.8%

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

       1. associate-*r/ 85.8%

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

       2. *-commutative 85.8%

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

       3. mul-1-neg 85.8%

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

       4. sub-neg 85.8%

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

       5. associate-*r/ 85.8%

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

       6. /-rgt-identity 85.8%

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

       7. associate-*r/ 85.7%

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

       8. *-commutative 85.7%

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

       9. associate-*r/ 85.8%

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

       10. associate-/l* 85.8%

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

       11. associate-*r/ 85.9%

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

       12. associate-/l* 85.9%

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

       13. associate-/r/ 85.9%

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

       14. metadata-eval 85.9%

           \[\leadsto \frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\color{blue}{0.005555555555555556} \cdot \pi} \]

       15. *-commutative 85.9%

           \[\leadsto \frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\color{blue}{\pi \cdot 0.005555555555555556}} \]

   11. Simplified 85.9%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}} \]

   if -3.2000000000000002e98 < A < 0.900000000000000022

   1. Initial program 52.6%

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

   3. Simplified 52.4%

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

   4. Taylor expanded in A around 0 51.3%

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

      1. unpow2 51.3%

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

      2. unpow2 51.3%

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

      3. hypot-def 75.3%

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

   6. Simplified 75.3%

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

   if 0.900000000000000022 < A

   1. Initial program 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in C around 0 71.6%

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

      1. associate-*r/ 71.6%

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

      2. mul-1-neg 71.6%

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

      3. +-commutative 71.6%

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

      4. unpow2 71.6%

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

      5. unpow2 71.6%

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

      6. hypot-def 83.8%

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

   6. Simplified 83.8%

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

      1. *-commutative 83.8%

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

      2. frac-2neg 83.8%

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

      3. associate-*l/ 83.8%

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

      4. associate-/l* 83.8%

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

      5. distribute-frac-neg 83.8%

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

      6. atan-neg 83.8%

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

      7. remove-double-neg 83.8%

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

      8. hypot-udef 71.6%

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

      9. +-commutative 71.6%

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

      10. hypot-def 83.8%

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

      11. distribute-neg-frac 83.8%

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

      12. div-inv 83.8%

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

      13. distribute-rgt-neg-in 83.8%

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

      14. metadata-eval 83.8%

          \[\leadsto \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot \left(-\color{blue}{0.005555555555555556}\right)} \]

      15. metadata-eval 83.8%

          \[\leadsto \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot \color{blue}{-0.005555555555555556}} \]

   8. Applied egg-rr 83.8%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot -0.005555555555555556}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 0.9:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot -0.005555555555555556}\\ \end{array} \]

Alternative 6: 44.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.2 \cdot 10^{-59}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-157}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.4 \cdot 10^{-209}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.2 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-55}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ 0.0 B)) PI))))
   (if (<= B -1.2e-59)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -8.8e-157)
       (* 180.0 (/ (atan (/ (- A) B)) PI))
       (if (<= B -4.4e-209)
         t_0
         (if (<= B -1.2e-290)
           (* 180.0 (/ (atan (/ C B)) PI))
           (if (<= B 1.85e-55) t_0 (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double tmp;
	if (B <= -1.2e-59) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -8.8e-157) {
		tmp = 180.0 * (atan((-A / B)) / ((double) M_PI));
	} else if (B <= -4.4e-209) {
		tmp = t_0;
	} else if (B <= -1.2e-290) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= 1.85e-55) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double tmp;
	if (B <= -1.2e-59) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -8.8e-157) {
		tmp = 180.0 * (Math.atan((-A / B)) / Math.PI);
	} else if (B <= -4.4e-209) {
		tmp = t_0;
	} else if (B <= -1.2e-290) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= 1.85e-55) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	tmp = 0
	if B <= -1.2e-59:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -8.8e-157:
		tmp = 180.0 * (math.atan((-A / B)) / math.pi)
	elif B <= -4.4e-209:
		tmp = t_0
	elif B <= -1.2e-290:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= 1.85e-55:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi))
	tmp = 0.0
	if (B <= -1.2e-59)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -8.8e-157)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi));
	elseif (B <= -4.4e-209)
		tmp = t_0;
	elseif (B <= -1.2e-290)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= 1.85e-55)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((0.0 / B)) / pi);
	tmp = 0.0;
	if (B <= -1.2e-59)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -8.8e-157)
		tmp = 180.0 * (atan((-A / B)) / pi);
	elseif (B <= -4.4e-209)
		tmp = t_0;
	elseif (B <= -1.2e-290)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= 1.85e-55)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.2e-59], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.8e-157], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4.4e-209], t$95$0, If[LessEqual[B, -1.2e-290], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.85e-55], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.20000000000000008e-59

   1. Initial program 53.5%

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

   3. Simplified 53.5%

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

   4. Taylor expanded in B around -inf 54.0%

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

   if -1.20000000000000008e-59 < B < -8.80000000000000041e-157

   1. Initial program 60.5%

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

   3. Simplified 60.4%

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

   4. Taylor expanded in C around 0 55.1%

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

      1. associate-*r/ 55.1%

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

      2. mul-1-neg 55.1%

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

      3. +-commutative 55.1%

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

      4. unpow2 55.1%

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

      5. unpow2 55.1%

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

      6. hypot-def 55.5%

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

   6. Simplified 55.5%

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

   7. Taylor expanded in A around 0 47.4%

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

      1. +-commutative 47.4%

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

   9. Simplified 47.4%

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

   10. Taylor expanded in B around 0 48.6%

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

       1. associate-*r/ 48.6%

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

       2. mul-1-neg 48.6%

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

   12. Simplified 48.6%

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

   if -8.80000000000000041e-157 < B < -4.40000000000000019e-209 or -1.2e-290 < B < 1.84999999999999993e-55

   1. Initial program 42.4%

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

   3. Simplified 38.4%

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

   4. Taylor expanded in C around inf 47.2%

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

      1. associate-*r/ 47.2%

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

      2. distribute-rgt1-in 47.2%

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

      3. metadata-eval 47.2%

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

      4. mul0-lft 47.2%

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

      5. metadata-eval 47.2%

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

   6. Simplified 47.2%

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

   if -4.40000000000000019e-209 < B < -1.2e-290

   1. Initial program 64.1%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in A around 0 58.5%

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

      1. unpow2 58.5%

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

      2. unpow2 58.5%

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

      3. hypot-def 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in B around -inf 57.6%

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

   8. Taylor expanded in B around 0 58.0%

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

   if 1.84999999999999993e-55 < B

   1. Initial program 50.3%

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

   3. Simplified 50.2%

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

   4. Taylor expanded in B around inf 53.1%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.2 \cdot 10^{-59}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -8.8 \cdot 10^{-157}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.4 \cdot 10^{-209}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.2 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 7: 48.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.16 \cdot 10^{-156}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -9.2 \cdot 10^{-212}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-291}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-55}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ 0.0 B)) PI))))
   (if (<= B -1.16e-156)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (if (<= B -9.2e-212)
       t_0
       (if (<= B -3.5e-291)
         (* 180.0 (/ (atan (/ C B)) PI))
         (if (<= B 2.2e-55) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double tmp;
	if (B <= -1.16e-156) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= -9.2e-212) {
		tmp = t_0;
	} else if (B <= -3.5e-291) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= 2.2e-55) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double tmp;
	if (B <= -1.16e-156) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= -9.2e-212) {
		tmp = t_0;
	} else if (B <= -3.5e-291) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= 2.2e-55) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	tmp = 0
	if B <= -1.16e-156:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= -9.2e-212:
		tmp = t_0
	elif B <= -3.5e-291:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= 2.2e-55:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi))
	tmp = 0.0
	if (B <= -1.16e-156)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= -9.2e-212)
		tmp = t_0;
	elseif (B <= -3.5e-291)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= 2.2e-55)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((0.0 / B)) / pi);
	tmp = 0.0;
	if (B <= -1.16e-156)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= -9.2e-212)
		tmp = t_0;
	elseif (B <= -3.5e-291)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= 2.2e-55)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.16e-156], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -9.2e-212], t$95$0, If[LessEqual[B, -3.5e-291], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.2e-55], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.15999999999999995e-156

   1. Initial program 54.8%

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

   3. Simplified 54.8%

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

   4. Taylor expanded in C around 0 50.0%

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

      1. associate-*r/ 50.0%

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

      2. mul-1-neg 50.0%

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

      3. +-commutative 50.0%

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

      4. unpow2 50.0%

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

      5. unpow2 50.0%

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

      6. hypot-def 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in B around -inf 61.0%

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

      1. mul-1-neg 61.0%

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

      2. unsub-neg 61.0%

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

   9. Simplified 61.0%

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

   if -1.15999999999999995e-156 < B < -9.2000000000000004e-212 or -3.49999999999999996e-291 < B < 2.2e-55

   1. Initial program 42.4%

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

   3. Simplified 38.4%

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

   4. Taylor expanded in C around inf 47.2%

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

      1. associate-*r/ 47.2%

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

      2. distribute-rgt1-in 47.2%

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

      3. metadata-eval 47.2%

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

      4. mul0-lft 47.2%

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

      5. metadata-eval 47.2%

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

   6. Simplified 47.2%

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

   if -9.2000000000000004e-212 < B < -3.49999999999999996e-291

   1. Initial program 64.1%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in A around 0 58.5%

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

      1. unpow2 58.5%

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

      2. unpow2 58.5%

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

      3. hypot-def 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in B around -inf 57.6%

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

   8. Taylor expanded in B around 0 58.0%

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

   if 2.2e-55 < B

   1. Initial program 50.3%

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

   3. Simplified 50.2%

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

   4. Taylor expanded in B around inf 53.1%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.16 \cdot 10^{-156}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -9.2 \cdot 10^{-212}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-291}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 8: 58.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{+85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.06 \cdot 10^{-274}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 26:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.9e+85)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A -1.06e-274)
     (* 180.0 (/ (atan (/ (- C B) B)) PI))
     (if (<= A 26.0)
       (* 180.0 (/ (atan (/ (+ B C) B)) PI))
       (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e+85) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= -1.06e-274) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (A <= 26.0) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e+85) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= -1.06e-274) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (A <= 26.0) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.9e+85:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= -1.06e-274:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif A <= 26.0:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.9e+85)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= -1.06e-274)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (A <= 26.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.9e+85)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= -1.06e-274)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (A <= 26.0)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.9e+85], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.06e-274], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 26.0], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -2.89999999999999997e85

   1. Initial program 17.6%

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

   3. Simplified 12.2%

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

   4. Taylor expanded in A around -inf 81.8%

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

      1. associate-*r/ 81.8%

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

   6. Simplified 81.8%

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

   if -2.89999999999999997e85 < A < -1.05999999999999997e-274

   1. Initial program 46.4%

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

   3. Simplified 46.1%

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

   4. Taylor expanded in A around 0 46.5%

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

      1. unpow2 46.5%

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

      2. unpow2 46.5%

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

      3. hypot-def 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in C around 0 49.3%

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

      1. mul-1-neg 49.3%

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

      2. unsub-neg 49.3%

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

   9. Simplified 49.3%

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

   if -1.05999999999999997e-274 < A < 26

   1. Initial program 59.8%

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

   3. Simplified 59.8%

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

   4. Taylor expanded in A around 0 57.1%

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

      1. unpow2 57.1%

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

      2. unpow2 57.1%

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

      3. hypot-def 82.7%

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

   6. Simplified 82.7%

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

   7. Taylor expanded in B around -inf 59.7%

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

   if 26 < A

   1. Initial program 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in C around 0 71.6%

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

      1. associate-*r/ 71.6%

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

      2. mul-1-neg 71.6%

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

      3. +-commutative 71.6%

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

      4. unpow2 71.6%

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

      5. unpow2 71.6%

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

      6. hypot-def 83.8%

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

   6. Simplified 83.8%

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

   7. Taylor expanded in B around -inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. unsub-neg 70.2%

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

   9. Simplified 70.2%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{+85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.06 \cdot 10^{-274}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 26:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9: 58.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.4 \cdot 10^{+77}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{A}{-0.5}}\right)}{\pi \cdot -0.005555555555555556}\\ \mathbf{elif}\;A \leq -1.5 \cdot 10^{-274}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 0.16:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.4e+77)
   (/ (atan (/ B (/ A -0.5))) (* PI -0.005555555555555556))
   (if (<= A -1.5e-274)
     (* 180.0 (/ (atan (/ (- C B) B)) PI))
     (if (<= A 0.16)
       (* 180.0 (/ (atan (/ (+ B C) B)) PI))
       (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.4e+77) {
		tmp = atan((B / (A / -0.5))) / (((double) M_PI) * -0.005555555555555556);
	} else if (A <= -1.5e-274) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (A <= 0.16) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.4e+77) {
		tmp = Math.atan((B / (A / -0.5))) / (Math.PI * -0.005555555555555556);
	} else if (A <= -1.5e-274) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (A <= 0.16) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.4e+77:
		tmp = math.atan((B / (A / -0.5))) / (math.pi * -0.005555555555555556)
	elif A <= -1.5e-274:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif A <= 0.16:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.4e+77)
		tmp = Float64(atan(Float64(B / Float64(A / -0.5))) / Float64(pi * -0.005555555555555556));
	elseif (A <= -1.5e-274)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (A <= 0.16)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.4e+77)
		tmp = atan((B / (A / -0.5))) / (pi * -0.005555555555555556);
	elseif (A <= -1.5e-274)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (A <= 0.16)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.4e+77], N[(N[ArcTan[N[(B / N[(A / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * -0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.5e-274], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 0.16], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -2.3999999999999999e77

   1. Initial program 17.6%

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

   3. Simplified 12.2%

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

   4. Taylor expanded in C around 0 17.6%

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

      1. associate-*r/ 17.6%

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

      2. mul-1-neg 17.6%

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

      3. +-commutative 17.6%

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

      4. unpow2 17.6%

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

      5. unpow2 17.6%

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

      6. hypot-def 52.6%

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

   6. Simplified 52.6%

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

      1. *-commutative 52.6%

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

      2. frac-2neg 52.6%

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

      3. associate-*l/ 52.6%

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

      4. associate-/l* 52.6%

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

      5. distribute-frac-neg 52.6%

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

      6. atan-neg 52.6%

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

      7. remove-double-neg 52.6%

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

      8. hypot-udef 17.6%

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

      9. +-commutative 17.6%

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

      10. hypot-def 52.6%

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

      11. distribute-neg-frac 52.6%

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

      12. div-inv 52.6%

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

      13. distribute-rgt-neg-in 52.6%

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

      14. metadata-eval 52.6%

          \[\leadsto \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot \left(-\color{blue}{0.005555555555555556}\right)} \]

      15. metadata-eval 52.6%

          \[\leadsto \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot \color{blue}{-0.005555555555555556}} \]

   8. Applied egg-rr 52.6%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot -0.005555555555555556}} \]

   9. Taylor expanded in A around -inf 81.9%

      \[\leadsto \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{A}\right)}}{\pi \cdot -0.005555555555555556} \]
   10. Step-by-step derivation

       1. *-commutative 81.9%

          \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{A} \cdot -0.5\right)}}{\pi \cdot -0.005555555555555556} \]

       2. associate-/r/ 81.9%

          \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{\frac{A}{-0.5}}\right)}}{\pi \cdot -0.005555555555555556} \]

   11. Simplified 81.9%

       \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{\frac{A}{-0.5}}\right)}}{\pi \cdot -0.005555555555555556} \]

   if -2.3999999999999999e77 < A < -1.49999999999999989e-274

   1. Initial program 46.4%

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

   3. Simplified 46.1%

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

   4. Taylor expanded in A around 0 46.5%

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

      1. unpow2 46.5%

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

      2. unpow2 46.5%

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

      3. hypot-def 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in C around 0 49.3%

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

      1. mul-1-neg 49.3%

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

      2. unsub-neg 49.3%

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

   9. Simplified 49.3%

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

   if -1.49999999999999989e-274 < A < 0.160000000000000003

   1. Initial program 59.8%

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

   3. Simplified 59.8%

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

   4. Taylor expanded in A around 0 57.1%

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

      1. unpow2 57.1%

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

      2. unpow2 57.1%

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

      3. hypot-def 82.7%

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

   6. Simplified 82.7%

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

   7. Taylor expanded in B around -inf 59.7%

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

   if 0.160000000000000003 < A

   1. Initial program 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in C around 0 71.6%

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

      1. associate-*r/ 71.6%

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

      2. mul-1-neg 71.6%

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

      3. +-commutative 71.6%

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

      4. unpow2 71.6%

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

      5. unpow2 71.6%

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

      6. hypot-def 83.8%

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

   6. Simplified 83.8%

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

   7. Taylor expanded in B around -inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. unsub-neg 70.2%

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

   9. Simplified 70.2%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.4 \cdot 10^{+77}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{A}{-0.5}}\right)}{\pi \cdot -0.005555555555555556}\\ \mathbf{elif}\;A \leq -1.5 \cdot 10^{-274}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 0.16:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10: 59.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{+79}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{A}{-0.5}}\right)}{\pi \cdot -0.005555555555555556}\\ \mathbf{elif}\;A \leq -1.3 \cdot 10^{-275}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.15 \cdot 10^{-11}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.9e+79)
   (/ (atan (/ B (/ A -0.5))) (* PI -0.005555555555555556))
   (if (<= A -1.3e-275)
     (* 180.0 (/ (atan (/ (- C B) B)) PI))
     (if (<= A 1.15e-11)
       (* 180.0 (/ (atan (/ (+ B C) B)) PI))
       (/ (* -180.0 (atan (/ (+ B A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e+79) {
		tmp = atan((B / (A / -0.5))) / (((double) M_PI) * -0.005555555555555556);
	} else if (A <= -1.3e-275) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (A <= 1.15e-11) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else {
		tmp = (-180.0 * atan(((B + A) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e+79) {
		tmp = Math.atan((B / (A / -0.5))) / (Math.PI * -0.005555555555555556);
	} else if (A <= -1.3e-275) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (A <= 1.15e-11) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else {
		tmp = (-180.0 * Math.atan(((B + A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.9e+79:
		tmp = math.atan((B / (A / -0.5))) / (math.pi * -0.005555555555555556)
	elif A <= -1.3e-275:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif A <= 1.15e-11:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	else:
		tmp = (-180.0 * math.atan(((B + A) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.9e+79)
		tmp = Float64(atan(Float64(B / Float64(A / -0.5))) / Float64(pi * -0.005555555555555556));
	elseif (A <= -1.3e-275)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (A <= 1.15e-11)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(B + A) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.9e+79)
		tmp = atan((B / (A / -0.5))) / (pi * -0.005555555555555556);
	elseif (A <= -1.3e-275)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (A <= 1.15e-11)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	else
		tmp = (-180.0 * atan(((B + A) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.9e+79], N[(N[ArcTan[N[(B / N[(A / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * -0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.3e-275], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.15e-11], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(-180.0 * N[ArcTan[N[(N[(B + A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -2.89999999999999992e79

   1. Initial program 17.6%

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

   3. Simplified 12.2%

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

   4. Taylor expanded in C around 0 17.6%

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

      1. associate-*r/ 17.6%

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

      2. mul-1-neg 17.6%

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

      3. +-commutative 17.6%

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

      4. unpow2 17.6%

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

      5. unpow2 17.6%

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

      6. hypot-def 52.6%

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

   6. Simplified 52.6%

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

      1. *-commutative 52.6%

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

      2. frac-2neg 52.6%

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

      3. associate-*l/ 52.6%

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

      4. associate-/l* 52.6%

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

      5. distribute-frac-neg 52.6%

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

      6. atan-neg 52.6%

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

      7. remove-double-neg 52.6%

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

      8. hypot-udef 17.6%

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

      9. +-commutative 17.6%

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

      10. hypot-def 52.6%

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

      11. distribute-neg-frac 52.6%

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

      12. div-inv 52.6%

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

      13. distribute-rgt-neg-in 52.6%

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

      14. metadata-eval 52.6%

          \[\leadsto \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot \left(-\color{blue}{0.005555555555555556}\right)} \]

      15. metadata-eval 52.6%

          \[\leadsto \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot \color{blue}{-0.005555555555555556}} \]

   8. Applied egg-rr 52.6%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot -0.005555555555555556}} \]

   9. Taylor expanded in A around -inf 81.9%

      \[\leadsto \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{A}\right)}}{\pi \cdot -0.005555555555555556} \]
   10. Step-by-step derivation

       1. *-commutative 81.9%

          \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{A} \cdot -0.5\right)}}{\pi \cdot -0.005555555555555556} \]

       2. associate-/r/ 81.9%

          \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{\frac{A}{-0.5}}\right)}}{\pi \cdot -0.005555555555555556} \]

   11. Simplified 81.9%

       \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{\frac{A}{-0.5}}\right)}}{\pi \cdot -0.005555555555555556} \]

   if -2.89999999999999992e79 < A < -1.29999999999999996e-275

   1. Initial program 46.4%

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

   3. Simplified 46.1%

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

   4. Taylor expanded in A around 0 46.5%

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

      1. unpow2 46.5%

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

      2. unpow2 46.5%

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

      3. hypot-def 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in C around 0 49.3%

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

      1. mul-1-neg 49.3%

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

      2. unsub-neg 49.3%

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

   9. Simplified 49.3%

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

   if -1.29999999999999996e-275 < A < 1.15000000000000007e-11

   1. Initial program 59.4%

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

   3. Simplified 59.4%

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

   4. Taylor expanded in A around 0 57.9%

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

      1. unpow2 57.9%

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

      2. unpow2 57.9%

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

      3. hypot-def 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in B around -inf 60.8%

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

   if 1.15000000000000007e-11 < A

   1. Initial program 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in C around 0 70.3%

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

      1. associate-*r/ 70.3%

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

      2. mul-1-neg 70.3%

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

      3. +-commutative 70.3%

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

      4. unpow2 70.3%

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

      5. unpow2 70.3%

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

      6. hypot-def 82.0%

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

   6. Simplified 82.0%

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

   7. Taylor expanded in A around 0 70.5%

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

      1. +-commutative 70.5%

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

   9. Simplified 70.5%

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

       1. *-commutative 70.5%

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

       2. frac-2neg 70.5%

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

       3. associate-*l/ 70.5%

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

       4. clear-num 70.5%

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

       5. *-commutative 70.5%

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

       6. distribute-frac-neg 70.5%

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

       7. atan-neg 70.5%

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

       8. remove-double-neg 70.5%

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

       9. +-commutative 70.5%

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

   11. Applied egg-rr 70.5%

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

       1. associate-/r* 70.5%

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

       2. associate-/l* 70.5%

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

       3. *-lft-identity 70.5%

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

       4. associate-/l* 70.5%

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

       5. *-commutative 70.5%

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

       6. neg-mul-1 70.5%

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

       7. associate-/r* 70.5%

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

       8. associate-/l* 70.5%

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

       9. associate-/r/ 70.5%

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

       10. metadata-eval 70.5%

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

       11. +-commutative 70.5%

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

   13. Simplified 70.5%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{+79}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{A}{-0.5}}\right)}{\pi \cdot -0.005555555555555556}\\ \mathbf{elif}\;A \leq -1.3 \cdot 10^{-275}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.15 \cdot 10^{-11}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 11: 59.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.1 \cdot 10^{+82}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{A}{-0.5}}\right)}{\pi \cdot -0.005555555555555556}\\ \mathbf{elif}\;A \leq -2.7 \cdot 10^{-275}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-12}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.1e+82)
   (/ (atan (/ B (/ A -0.5))) (* PI -0.005555555555555556))
   (if (<= A -2.7e-275)
     (/ (* 180.0 (atan (+ -1.0 (/ C B)))) PI)
     (if (<= A 5.2e-12)
       (* 180.0 (/ (atan (/ (+ B C) B)) PI))
       (/ (* -180.0 (atan (/ (+ B A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.1e+82) {
		tmp = atan((B / (A / -0.5))) / (((double) M_PI) * -0.005555555555555556);
	} else if (A <= -2.7e-275) {
		tmp = (180.0 * atan((-1.0 + (C / B)))) / ((double) M_PI);
	} else if (A <= 5.2e-12) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else {
		tmp = (-180.0 * atan(((B + A) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.1e+82) {
		tmp = Math.atan((B / (A / -0.5))) / (Math.PI * -0.005555555555555556);
	} else if (A <= -2.7e-275) {
		tmp = (180.0 * Math.atan((-1.0 + (C / B)))) / Math.PI;
	} else if (A <= 5.2e-12) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else {
		tmp = (-180.0 * Math.atan(((B + A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.1e+82:
		tmp = math.atan((B / (A / -0.5))) / (math.pi * -0.005555555555555556)
	elif A <= -2.7e-275:
		tmp = (180.0 * math.atan((-1.0 + (C / B)))) / math.pi
	elif A <= 5.2e-12:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	else:
		tmp = (-180.0 * math.atan(((B + A) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.1e+82)
		tmp = Float64(atan(Float64(B / Float64(A / -0.5))) / Float64(pi * -0.005555555555555556));
	elseif (A <= -2.7e-275)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 + Float64(C / B)))) / pi);
	elseif (A <= 5.2e-12)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(B + A) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.1e+82)
		tmp = atan((B / (A / -0.5))) / (pi * -0.005555555555555556);
	elseif (A <= -2.7e-275)
		tmp = (180.0 * atan((-1.0 + (C / B)))) / pi;
	elseif (A <= 5.2e-12)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	else
		tmp = (-180.0 * atan(((B + A) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.1e+82], N[(N[ArcTan[N[(B / N[(A / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * -0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.7e-275], N[(N[(180.0 * N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 5.2e-12], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(-180.0 * N[ArcTan[N[(N[(B + A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.1000000000000001e82

   1. Initial program 17.6%

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

   3. Simplified 12.2%

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

   4. Taylor expanded in C around 0 17.6%

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

      1. associate-*r/ 17.6%

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

      2. mul-1-neg 17.6%

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

      3. +-commutative 17.6%

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

      4. unpow2 17.6%

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

      5. unpow2 17.6%

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

      6. hypot-def 52.6%

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

   6. Simplified 52.6%

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

      1. *-commutative 52.6%

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

      2. frac-2neg 52.6%

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

      3. associate-*l/ 52.6%

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

      4. associate-/l* 52.6%

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

      5. distribute-frac-neg 52.6%

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

      6. atan-neg 52.6%

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

      7. remove-double-neg 52.6%

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

      8. hypot-udef 17.6%

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

      9. +-commutative 17.6%

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

      10. hypot-def 52.6%

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

      11. distribute-neg-frac 52.6%

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

      12. div-inv 52.6%

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

      13. distribute-rgt-neg-in 52.6%

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

      14. metadata-eval 52.6%

          \[\leadsto \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot \left(-\color{blue}{0.005555555555555556}\right)} \]

      15. metadata-eval 52.6%

          \[\leadsto \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot \color{blue}{-0.005555555555555556}} \]

   8. Applied egg-rr 52.6%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot -0.005555555555555556}} \]

   9. Taylor expanded in A around -inf 81.9%

      \[\leadsto \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{A}\right)}}{\pi \cdot -0.005555555555555556} \]
   10. Step-by-step derivation

       1. *-commutative 81.9%

          \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{A} \cdot -0.5\right)}}{\pi \cdot -0.005555555555555556} \]

       2. associate-/r/ 81.9%

          \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{\frac{A}{-0.5}}\right)}}{\pi \cdot -0.005555555555555556} \]

   11. Simplified 81.9%

       \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{\frac{A}{-0.5}}\right)}}{\pi \cdot -0.005555555555555556} \]

   if -1.1000000000000001e82 < A < -2.69999999999999993e-275

   1. Initial program 46.4%

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

   3. Simplified 46.1%

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

   4. Taylor expanded in A around 0 46.5%

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

      1. unpow2 46.5%

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

      2. unpow2 46.5%

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

      3. hypot-def 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in C around 0 49.3%

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

      1. mul-1-neg 49.3%

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

      2. unsub-neg 49.3%

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

   9. Simplified 49.3%

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

       1. associate-*r/ 49.3%

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

       2. div-sub 49.3%

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

       3. *-inverses 49.3%

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

       4. sub-neg 49.3%

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

       5. metadata-eval 49.3%

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

       6. +-commutative 49.3%

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

   11. Applied egg-rr 49.3%

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

   if -2.69999999999999993e-275 < A < 5.19999999999999965e-12

   1. Initial program 59.4%

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

   3. Simplified 59.4%

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

   4. Taylor expanded in A around 0 57.9%

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

      1. unpow2 57.9%

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

      2. unpow2 57.9%

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

      3. hypot-def 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in B around -inf 60.8%

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

   if 5.19999999999999965e-12 < A

   1. Initial program 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in C around 0 70.3%

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

      1. associate-*r/ 70.3%

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

      2. mul-1-neg 70.3%

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

      3. +-commutative 70.3%

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

      4. unpow2 70.3%

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

      5. unpow2 70.3%

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

      6. hypot-def 82.0%

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

   6. Simplified 82.0%

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

   7. Taylor expanded in A around 0 70.5%

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

      1. +-commutative 70.5%

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

   9. Simplified 70.5%

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

       1. *-commutative 70.5%

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

       2. frac-2neg 70.5%

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

       3. associate-*l/ 70.5%

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

       4. clear-num 70.5%

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

       5. *-commutative 70.5%

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

       6. distribute-frac-neg 70.5%

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

       7. atan-neg 70.5%

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

       8. remove-double-neg 70.5%

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

       9. +-commutative 70.5%

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

   11. Applied egg-rr 70.5%

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

       1. associate-/r* 70.5%

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

       2. associate-/l* 70.5%

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

       3. *-lft-identity 70.5%

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

       4. associate-/l* 70.5%

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

       5. *-commutative 70.5%

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

       6. neg-mul-1 70.5%

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

       7. associate-/r* 70.5%

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

       8. associate-/l* 70.5%

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

       9. associate-/r/ 70.5%

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

       10. metadata-eval 70.5%

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

       11. +-commutative 70.5%

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

   13. Simplified 70.5%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.1 \cdot 10^{+82}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{A}{-0.5}}\right)}{\pi \cdot -0.005555555555555556}\\ \mathbf{elif}\;A \leq -2.7 \cdot 10^{-275}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-12}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{B + A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 12: 60.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{+81}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{A}{-0.5}}\right)}{\pi \cdot -0.005555555555555556}\\ \mathbf{elif}\;A \leq -1.55 \cdot 10^{-274}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.9e+81)
   (/ (atan (/ B (/ A -0.5))) (* PI -0.005555555555555556))
   (if (<= A -1.55e-274)
     (/ (* 180.0 (atan (+ -1.0 (/ C B)))) PI)
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e+81) {
		tmp = atan((B / (A / -0.5))) / (((double) M_PI) * -0.005555555555555556);
	} else if (A <= -1.55e-274) {
		tmp = (180.0 * atan((-1.0 + (C / B)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e+81) {
		tmp = Math.atan((B / (A / -0.5))) / (Math.PI * -0.005555555555555556);
	} else if (A <= -1.55e-274) {
		tmp = (180.0 * Math.atan((-1.0 + (C / B)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.9e+81:
		tmp = math.atan((B / (A / -0.5))) / (math.pi * -0.005555555555555556)
	elif A <= -1.55e-274:
		tmp = (180.0 * math.atan((-1.0 + (C / B)))) / math.pi
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.9e+81)
		tmp = Float64(atan(Float64(B / Float64(A / -0.5))) / Float64(pi * -0.005555555555555556));
	elseif (A <= -1.55e-274)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 + Float64(C / B)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.9e+81)
		tmp = atan((B / (A / -0.5))) / (pi * -0.005555555555555556);
	elseif (A <= -1.55e-274)
		tmp = (180.0 * atan((-1.0 + (C / B)))) / pi;
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.9e+81], N[(N[ArcTan[N[(B / N[(A / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * -0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.55e-274], N[(N[(180.0 * N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.9e81

   1. Initial program 17.6%

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

   3. Simplified 12.2%

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

   4. Taylor expanded in C around 0 17.6%

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

      1. associate-*r/ 17.6%

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

      2. mul-1-neg 17.6%

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

      3. +-commutative 17.6%

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

      4. unpow2 17.6%

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

      5. unpow2 17.6%

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

      6. hypot-def 52.6%

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

   6. Simplified 52.6%

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

      1. *-commutative 52.6%

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

      2. frac-2neg 52.6%

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

      3. associate-*l/ 52.6%

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

      4. associate-/l* 52.6%

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

      5. distribute-frac-neg 52.6%

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

      6. atan-neg 52.6%

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

      7. remove-double-neg 52.6%

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

      8. hypot-udef 17.6%

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

      9. +-commutative 17.6%

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

      10. hypot-def 52.6%

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

      11. distribute-neg-frac 52.6%

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

      12. div-inv 52.6%

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

      13. distribute-rgt-neg-in 52.6%

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

      14. metadata-eval 52.6%

          \[\leadsto \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot \left(-\color{blue}{0.005555555555555556}\right)} \]

      15. metadata-eval 52.6%

          \[\leadsto \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot \color{blue}{-0.005555555555555556}} \]

   8. Applied egg-rr 52.6%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi \cdot -0.005555555555555556}} \]

   9. Taylor expanded in A around -inf 81.9%

      \[\leadsto \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{A}\right)}}{\pi \cdot -0.005555555555555556} \]
   10. Step-by-step derivation

       1. *-commutative 81.9%

          \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{A} \cdot -0.5\right)}}{\pi \cdot -0.005555555555555556} \]

       2. associate-/r/ 81.9%

          \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{\frac{A}{-0.5}}\right)}}{\pi \cdot -0.005555555555555556} \]

   11. Simplified 81.9%

       \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{\frac{A}{-0.5}}\right)}}{\pi \cdot -0.005555555555555556} \]

   if -1.9e81 < A < -1.54999999999999989e-274

   1. Initial program 46.4%

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

   3. Simplified 46.1%

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

   4. Taylor expanded in A around 0 46.5%

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

      1. unpow2 46.5%

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

      2. unpow2 46.5%

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

      3. hypot-def 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in C around 0 49.3%

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

      1. mul-1-neg 49.3%

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

      2. unsub-neg 49.3%

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

   9. Simplified 49.3%

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

       1. associate-*r/ 49.3%

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

       2. div-sub 49.3%

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

       3. *-inverses 49.3%

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

       4. sub-neg 49.3%

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

       5. metadata-eval 49.3%

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

       6. +-commutative 49.3%

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

   11. Applied egg-rr 49.3%

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

   if -1.54999999999999989e-274 < A

   1. Initial program 65.6%

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

   3. Simplified 65.6%

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

   4. Taylor expanded in B around -inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. div-sub 66.4%

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

   6. Simplified 66.4%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{+81}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{A}{-0.5}}\right)}{\pi \cdot -0.005555555555555556}\\ \mathbf{elif}\;A \leq -1.55 \cdot 10^{-274}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 13: 63.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-274}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.4e-42)
   (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
   (if (<= A -2.8e-274)
     (/ (* 180.0 (atan (+ -1.0 (/ C B)))) PI)
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.4e-42) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else if (A <= -2.8e-274) {
		tmp = (180.0 * atan((-1.0 + (C / B)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.4e-42) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else if (A <= -2.8e-274) {
		tmp = (180.0 * Math.atan((-1.0 + (C / B)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.4e-42:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	elif A <= -2.8e-274:
		tmp = (180.0 * math.atan((-1.0 + (C / B)))) / math.pi
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.4e-42)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	elseif (A <= -2.8e-274)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 + Float64(C / B)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.4e-42)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	elseif (A <= -2.8e-274)
		tmp = (180.0 * atan((-1.0 + (C / B)))) / pi;
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.4e-42], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.8e-274], N[(N[(180.0 * N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -4.4000000000000001e-42

   1. Initial program 24.1%

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

   3. Simplified 60.4%

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

   4. Taylor expanded in B around 0 75.9%

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

      1. associate-*r/ 75.9%

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

   6. Simplified 75.9%

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

   if -4.4000000000000001e-42 < A < -2.79999999999999975e-274

   1. Initial program 48.3%

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

   3. Simplified 48.3%

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

   4. Taylor expanded in A around 0 48.7%

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

      1. unpow2 48.7%

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

      2. unpow2 48.7%

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

      3. hypot-def 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in C around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. unsub-neg 54.8%

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

   9. Simplified 54.8%

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

       1. associate-*r/ 54.8%

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

       2. div-sub 54.8%

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

       3. *-inverses 54.8%

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

       4. sub-neg 54.8%

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

       5. metadata-eval 54.8%

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

       6. +-commutative 54.8%

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

   11. Applied egg-rr 54.8%

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

   if -2.79999999999999975e-274 < A

   1. Initial program 65.6%

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

   3. Simplified 65.6%

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

   4. Taylor expanded in B around -inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. div-sub 66.4%

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

   6. Simplified 66.4%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.4 \cdot 10^{-42}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-274}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 14: 63.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{-42}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-274}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.1e-42)
   (/ (atan (/ B (/ (- C A) -0.5))) (* PI 0.005555555555555556))
   (if (<= A -2e-274)
     (/ (* 180.0 (atan (+ -1.0 (/ C B)))) PI)
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e-42) {
		tmp = atan((B / ((C - A) / -0.5))) / (((double) M_PI) * 0.005555555555555556);
	} else if (A <= -2e-274) {
		tmp = (180.0 * atan((-1.0 + (C / B)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e-42) {
		tmp = Math.atan((B / ((C - A) / -0.5))) / (Math.PI * 0.005555555555555556);
	} else if (A <= -2e-274) {
		tmp = (180.0 * Math.atan((-1.0 + (C / B)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.1e-42:
		tmp = math.atan((B / ((C - A) / -0.5))) / (math.pi * 0.005555555555555556)
	elif A <= -2e-274:
		tmp = (180.0 * math.atan((-1.0 + (C / B)))) / math.pi
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.1e-42)
		tmp = Float64(atan(Float64(B / Float64(Float64(C - A) / -0.5))) / Float64(pi * 0.005555555555555556));
	elseif (A <= -2e-274)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 + Float64(C / B)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.1e-42)
		tmp = atan((B / ((C - A) / -0.5))) / (pi * 0.005555555555555556);
	elseif (A <= -2e-274)
		tmp = (180.0 * atan((-1.0 + (C / B)))) / pi;
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.1e-42], N[(N[ArcTan[N[(B / N[(N[(C - A), $MachinePrecision] / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2e-274], N[(N[(180.0 * N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.1000000000000003e-42

   1. Initial program 24.1%

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

   3. Simplified 60.4%

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

   4. Taylor expanded in B around 0 75.9%

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

      1. associate-*r/ 75.9%

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

   6. Simplified 75.9%

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

      1. *-commutative 75.9%

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

      2. clear-num 75.9%

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

      3. un-div-inv 76.0%

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

      4. div-inv 76.0%

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

      5. associate-/r* 76.0%

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

   8. Applied egg-rr 75.9%

      \[\leadsto \color{blue}{\frac{\frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}}{0.005555555555555556}} \]

   9. Taylor expanded in A around -inf 75.9%

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

       1. associate-*r/ 75.9%

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

       2. *-commutative 75.9%

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

       3. mul-1-neg 75.9%

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

       4. sub-neg 75.9%

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

       5. associate-*r/ 75.8%

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

       6. /-rgt-identity 75.8%

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

       7. associate-*r/ 75.8%

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

       8. *-commutative 75.8%

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

       9. associate-*r/ 75.9%

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

       10. associate-/l* 75.9%

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

       11. associate-*r/ 76.0%

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

       12. associate-/l* 76.0%

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

       13. associate-/r/ 76.0%

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

       14. metadata-eval 76.0%

           \[\leadsto \frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\color{blue}{0.005555555555555556} \cdot \pi} \]

       15. *-commutative 76.0%

           \[\leadsto \frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\color{blue}{\pi \cdot 0.005555555555555556}} \]

   11. Simplified 76.0%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}} \]

   if -3.1000000000000003e-42 < A < -1.99999999999999993e-274

   1. Initial program 48.3%

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

   3. Simplified 48.3%

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

   4. Taylor expanded in A around 0 48.7%

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

      1. unpow2 48.7%

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

      2. unpow2 48.7%

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

      3. hypot-def 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in C around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. unsub-neg 54.8%

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

   9. Simplified 54.8%

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

       1. associate-*r/ 54.8%

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

       2. div-sub 54.8%

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

       3. *-inverses 54.8%

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

       4. sub-neg 54.8%

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

       5. metadata-eval 54.8%

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

       6. +-commutative 54.8%

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

   11. Applied egg-rr 54.8%

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

   if -1.99999999999999993e-274 < A

   1. Initial program 65.6%

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

   3. Simplified 65.6%

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

   4. Taylor expanded in B around -inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. div-sub 66.4%

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

   6. Simplified 66.4%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{-42}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-274}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 15: 44.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.8 \cdot 10^{-57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.8e-57)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -9.5e-289)
     (* 180.0 (/ (atan (/ C B)) PI))
     (if (<= B 1.85e-55)
       (* 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 <= -4.8e-57) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -9.5e-289) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= 1.85e-55) {
		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 <= -4.8e-57) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -9.5e-289) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= 1.85e-55) {
		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 <= -4.8e-57:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -9.5e-289:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= 1.85e-55:
		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 <= -4.8e-57)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -9.5e-289)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= 1.85e-55)
		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 <= -4.8e-57)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -9.5e-289)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= 1.85e-55)
		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, -4.8e-57], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -9.5e-289], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.85e-55], 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 < -4.80000000000000012e-57

   1. Initial program 53.5%

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

   3. Simplified 53.5%

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

   4. Taylor expanded in B around -inf 54.0%

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

   if -4.80000000000000012e-57 < B < -9.4999999999999995e-289

   1. Initial program 53.9%

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

   3. Simplified 51.8%

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

   4. Taylor expanded in A around 0 42.3%

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

      1. unpow2 42.3%

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

      2. unpow2 42.3%

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

      3. hypot-def 55.1%

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

   6. Simplified 55.1%

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

   7. Taylor expanded in B around -inf 39.9%

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

   8. Taylor expanded in B around 0 37.0%

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

   if -9.4999999999999995e-289 < B < 1.84999999999999993e-55

   1. Initial program 44.6%

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

   3. Simplified 41.2%

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

   4. Taylor expanded in C around inf 43.9%

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

      1. associate-*r/ 43.9%

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

      2. distribute-rgt1-in 43.9%

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

      3. metadata-eval 43.9%

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

      4. mul0-lft 43.9%

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

      5. metadata-eval 43.9%

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

   6. Simplified 43.9%

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

   if 1.84999999999999993e-55 < B

   1. Initial program 50.3%

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

   3. Simplified 50.2%

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

   4. Taylor expanded in B around inf 53.1%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.8 \cdot 10^{-57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 16: 59.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.45 \cdot 10^{-14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 50:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.45e-14)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 50.0)
     (* 180.0 (/ (atan (/ (+ B C) B)) PI))
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.45e-14) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 50.0) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.45e-14) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 50.0) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.45e-14:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 50.0:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.45e-14)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 50.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.45e-14)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 50.0)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.45e-14], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 50.0], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.4500000000000001e-14

   1. Initial program 22.6%

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

   3. Simplified 18.2%

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

   4. Taylor expanded in A around -inf 72.8%

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

      1. associate-*r/ 72.8%

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

   6. Simplified 72.8%

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

   if -1.4500000000000001e-14 < A < 50

   1. Initial program 54.5%

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

   3. Simplified 54.4%

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

   4. Taylor expanded in A around 0 53.1%

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

      1. unpow2 53.1%

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

      2. unpow2 53.1%

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

      3. hypot-def 77.5%

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

   6. Simplified 77.5%

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

   7. Taylor expanded in B around -inf 50.0%

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

   if 50 < A

   1. Initial program 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in C around 0 71.6%

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

      1. associate-*r/ 71.6%

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

      2. mul-1-neg 71.6%

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

      3. +-commutative 71.6%

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

      4. unpow2 71.6%

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

      5. unpow2 71.6%

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

      6. hypot-def 83.8%

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

   6. Simplified 83.8%

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

   7. Taylor expanded in B around -inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. unsub-neg 70.2%

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

   9. Simplified 70.2%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.45 \cdot 10^{-14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 50:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 17: 43.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.1 \cdot 10^{-156}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.1e-156)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.85e-55)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.1e-156) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.85e-55) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.1e-156) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.85e-55) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.1e-156:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.85e-55:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.1e-156)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.85e-55)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.1e-156)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.85e-55)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.1e-156], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.85e-55], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.1e-156

   1. Initial program 54.8%

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

   3. Simplified 54.8%

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

   4. Taylor expanded in B around -inf 47.2%

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

   if -1.1e-156 < B < 1.84999999999999993e-55

   1. Initial program 46.3%

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

   3. Simplified 43.0%

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

   4. Taylor expanded in C around inf 40.5%

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

      1. associate-*r/ 40.5%

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

      2. distribute-rgt1-in 40.5%

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

      3. metadata-eval 40.5%

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

      4. mul0-lft 40.5%

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

      5. metadata-eval 40.5%

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

   6. Simplified 40.5%

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

   if 1.84999999999999993e-55 < B

   1. Initial program 50.3%

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

   3. Simplified 50.2%

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

   4. Taylor expanded in B around inf 53.1%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.1 \cdot 10^{-156}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 18: 53.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.35e-281)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e-281) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e-281) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.35e-281:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.35e-281)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.35e-281)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.35e-281], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.34999999999999995e-281

   1. Initial program 35.0%

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

   3. Simplified 32.6%

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

   4. Taylor expanded in A around -inf 56.3%

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

      1. associate-*r/ 56.3%

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

   6. Simplified 56.3%

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

   if -1.34999999999999995e-281 < A

   1. Initial program 64.9%

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

   3. Simplified 64.9%

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

   4. Taylor expanded in C around 0 59.3%

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

      1. associate-*r/ 59.3%

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

      2. mul-1-neg 59.3%

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

      3. +-commutative 59.3%

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

      4. unpow2 59.3%

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

      5. unpow2 59.3%

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

      6. hypot-def 73.5%

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

   6. Simplified 73.5%

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

   7. Taylor expanded in B around -inf 58.2%

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

      1. mul-1-neg 58.2%

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

      2. unsub-neg 58.2%

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

   9. Simplified 58.2%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 19: 39.2% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -4.999999999999985e-310

   1. Initial program 53.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 52.4%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 38.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -4.999999999999985e-310 < B

   1. Initial program 48.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   3. Simplified 46.5%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

   4. Taylor expanded in B around inf 34.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 20: 20.3% 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 50.5%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

3. Simplified 49.3%

   \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(A + \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)}{\pi}} \]

4. Taylor expanded in B around inf 19.0%

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

5. Final simplification 19.0%

   \[\leadsto 180 \cdot \frac{\tan^{-1} -1}{\pi} \]

Reproduce

herbie shell --seed 2023297 
(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)))