ABCF->ab-angle angle

Percentage Accurate: 53.4% → 80.5%

Time: 23.8s

Alternatives: 25

Speedup: 3.4×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.4% 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: 80.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 2.35 \cdot 10^{+92}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}}{0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}}{0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 2.35e+92)
   (/ (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI) 0.005555555555555556)
   (/ (/ (atan (* -0.5 (/ B C))) PI) 0.005555555555555556)))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.35e+92) {
		tmp = (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI)) / 0.005555555555555556;
	} else {
		tmp = (atan((-0.5 * (B / C))) / ((double) M_PI)) / 0.005555555555555556;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.35e+92) {
		tmp = (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI) / 0.005555555555555556;
	} else {
		tmp = (Math.atan((-0.5 * (B / C))) / Math.PI) / 0.005555555555555556;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 2.35e+92:
		tmp = (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi) / 0.005555555555555556
	else:
		tmp = (math.atan((-0.5 * (B / C))) / math.pi) / 0.005555555555555556
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 2.35e+92)
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi) / 0.005555555555555556);
	else
		tmp = Float64(Float64(atan(Float64(-0.5 * Float64(B / C))) / pi) / 0.005555555555555556);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 2.35e+92)
		tmp = (atan((((C - A) - hypot(B, (A - C))) / B)) / pi) / 0.005555555555555556;
	else
		tmp = (atan((-0.5 * (B / C))) / pi) / 0.005555555555555556;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 2.35e+92], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] / 0.005555555555555556), $MachinePrecision], N[(N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] / 0.005555555555555556), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 2.35e92

   1. Initial program 60.6%

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

   4. Applied egg-rr 82.7%

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

      1. clear-num 82.7%

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

      2. inv-pow 82.7%

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

      3. div-inv 82.7%

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

      4. associate--l- 76.7%

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

      5. metadata-eval 76.7%

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

   6. Applied egg-rr 76.7%

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

   8. Simplified 82.7%

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

   if 2.35e92 < C

   1. Initial program 21.9%

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

   4. Applied egg-rr 51.2%

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

      1. clear-num 51.2%

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

      2. inv-pow 51.2%

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

      3. div-inv 51.2%

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

      4. associate--l- 48.9%

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

      5. metadata-eval 48.9%

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

   6. Applied egg-rr 48.9%

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

   8. Simplified 51.2%

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

   9. Taylor expanded in A around 0 19.9%

      \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{\color{blue}{C - \sqrt{{B}^{2} + {C}^{2}}}}{B}\right)}{\pi}}{0.005555555555555556} \]
   10. Step-by-step derivation

       1. unpow2 19.9%

          \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi}}{0.005555555555555556} \]

       2. unpow2 19.9%

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

       3. hypot-undefine 44.5%

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

   11. Simplified 44.5%

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

   12. Taylor expanded in C around inf 75.7%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 2.35 \cdot 10^{+92}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}}{0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}}{0.005555555555555556}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -3.2 \cdot 10^{+77}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{elif}\;C \leq 2.8 \cdot 10^{+92}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}}{0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -3.2e+77)
   (/ 180.0 (/ PI (atan (/ (- C (hypot B C)) B))))
   (if (<= C 2.8e+92)
     (* 180.0 (/ (atan (/ (+ A (hypot B A)) (- B))) PI))
     (/ (/ (atan (* -0.5 (/ B C))) PI) 0.005555555555555556))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.2e+77) {
		tmp = 180.0 / (((double) M_PI) / atan(((C - hypot(B, C)) / B)));
	} else if (C <= 2.8e+92) {
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / ((double) M_PI));
	} else {
		tmp = (atan((-0.5 * (B / C))) / ((double) M_PI)) / 0.005555555555555556;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.2e+77) {
		tmp = 180.0 / (Math.PI / Math.atan(((C - Math.hypot(B, C)) / B)));
	} else if (C <= 2.8e+92) {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(B, A)) / -B)) / Math.PI);
	} else {
		tmp = (Math.atan((-0.5 * (B / C))) / Math.PI) / 0.005555555555555556;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -3.2e+77:
		tmp = 180.0 / (math.pi / math.atan(((C - math.hypot(B, C)) / B)))
	elif C <= 2.8e+92:
		tmp = 180.0 * (math.atan(((A + math.hypot(B, A)) / -B)) / math.pi)
	else:
		tmp = (math.atan((-0.5 * (B / C))) / math.pi) / 0.005555555555555556
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -3.2e+77)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - hypot(B, C)) / B))));
	elseif (C <= 2.8e+92)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / Float64(-B))) / pi));
	else
		tmp = Float64(Float64(atan(Float64(-0.5 * Float64(B / C))) / pi) / 0.005555555555555556);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -3.2e+77)
		tmp = 180.0 / (pi / atan(((C - hypot(B, C)) / B)));
	elseif (C <= 2.8e+92)
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / pi);
	else
		tmp = (atan((-0.5 * (B / C))) / pi) / 0.005555555555555556;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -3.2e+77], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.8e+92], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] / 0.005555555555555556), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -3.2000000000000002e77

   1. Initial program 79.5%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in A around 0 79.5%

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

      1. unpow2 79.5%

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

      2. unpow2 79.5%

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

      3. hypot-define 96.2%

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

   7. Simplified 96.2%

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

   if -3.2000000000000002e77 < C < 2.80000000000000001e92

   1. Initial program 54.2%

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

   3. Taylor expanded in C around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. distribute-neg-frac2 51.5%

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

      3. +-commutative 51.5%

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

      4. unpow2 51.5%

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

      5. unpow2 51.5%

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

      6. hypot-define 74.2%

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

   5. Simplified 74.2%

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

   if 2.80000000000000001e92 < C

   1. Initial program 21.9%

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

   4. Applied egg-rr 51.2%

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

      1. clear-num 51.2%

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

      2. inv-pow 51.2%

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

      3. div-inv 51.2%

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

      4. associate--l- 48.9%

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

      5. metadata-eval 48.9%

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

   6. Applied egg-rr 48.9%

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

   8. Simplified 51.2%

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

   9. Taylor expanded in A around 0 19.9%

      \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{\color{blue}{C - \sqrt{{B}^{2} + {C}^{2}}}}{B}\right)}{\pi}}{0.005555555555555556} \]
   10. Step-by-step derivation

       1. unpow2 19.9%

          \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi}}{0.005555555555555556} \]

       2. unpow2 19.9%

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

       3. hypot-undefine 44.5%

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

   11. Simplified 44.5%

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

   12. Taylor expanded in C around inf 75.7%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -3.2 \cdot 10^{+77}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{elif}\;C \leq 2.8 \cdot 10^{+92}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}}{0.005555555555555556}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -3.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{elif}\;C \leq 2 \cdot 10^{+92}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}}{0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}}{0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -3.6e+77)
   (/ 180.0 (/ PI (atan (/ (- C (hypot B C)) B))))
   (if (<= C 2e+92)
     (/ (/ (atan (/ (+ A (hypot A B)) (- B))) PI) 0.005555555555555556)
     (/ (/ (atan (* -0.5 (/ B C))) PI) 0.005555555555555556))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.6e+77) {
		tmp = 180.0 / (((double) M_PI) / atan(((C - hypot(B, C)) / B)));
	} else if (C <= 2e+92) {
		tmp = (atan(((A + hypot(A, B)) / -B)) / ((double) M_PI)) / 0.005555555555555556;
	} else {
		tmp = (atan((-0.5 * (B / C))) / ((double) M_PI)) / 0.005555555555555556;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.6e+77) {
		tmp = 180.0 / (Math.PI / Math.atan(((C - Math.hypot(B, C)) / B)));
	} else if (C <= 2e+92) {
		tmp = (Math.atan(((A + Math.hypot(A, B)) / -B)) / Math.PI) / 0.005555555555555556;
	} else {
		tmp = (Math.atan((-0.5 * (B / C))) / Math.PI) / 0.005555555555555556;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -3.6e+77:
		tmp = 180.0 / (math.pi / math.atan(((C - math.hypot(B, C)) / B)))
	elif C <= 2e+92:
		tmp = (math.atan(((A + math.hypot(A, B)) / -B)) / math.pi) / 0.005555555555555556
	else:
		tmp = (math.atan((-0.5 * (B / C))) / math.pi) / 0.005555555555555556
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -3.6e+77)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - hypot(B, C)) / B))));
	elseif (C <= 2e+92)
		tmp = Float64(Float64(atan(Float64(Float64(A + hypot(A, B)) / Float64(-B))) / pi) / 0.005555555555555556);
	else
		tmp = Float64(Float64(atan(Float64(-0.5 * Float64(B / C))) / pi) / 0.005555555555555556);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -3.6e+77)
		tmp = 180.0 / (pi / atan(((C - hypot(B, C)) / B)));
	elseif (C <= 2e+92)
		tmp = (atan(((A + hypot(A, B)) / -B)) / pi) / 0.005555555555555556;
	else
		tmp = (atan((-0.5 * (B / C))) / pi) / 0.005555555555555556;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -3.6e+77], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2e+92], N[(N[(N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] / 0.005555555555555556), $MachinePrecision], N[(N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] / 0.005555555555555556), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -3.5999999999999998e77

   1. Initial program 79.5%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in A around 0 79.5%

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

      1. unpow2 79.5%

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

      2. unpow2 79.5%

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

      3. hypot-define 96.2%

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

   7. Simplified 96.2%

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

   if -3.5999999999999998e77 < C < 2.0000000000000001e92

   1. Initial program 54.2%

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

   4. Applied egg-rr 76.9%

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

      1. clear-num 76.9%

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

      2. inv-pow 76.9%

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

      3. div-inv 76.9%

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

      4. associate--l- 70.1%

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

      5. metadata-eval 70.1%

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

   6. Applied egg-rr 70.1%

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

   8. Simplified 76.9%

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

   9. Taylor expanded in C around 0 51.5%

      \[\leadsto \frac{\frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + \sqrt{{A}^{2} + {B}^{2}}}{B}\right)}}{\pi}}{0.005555555555555556} \]
   10. Step-by-step derivation

       1. mul-1-neg 51.5%

          \[\leadsto \frac{\frac{\tan^{-1} \color{blue}{\left(-\frac{A + \sqrt{{A}^{2} + {B}^{2}}}{B}\right)}}{\pi}}{0.005555555555555556} \]

       2. distribute-neg-frac2 51.5%

          \[\leadsto \frac{\frac{\tan^{-1} \color{blue}{\left(\frac{A + \sqrt{{A}^{2} + {B}^{2}}}{-B}\right)}}{\pi}}{0.005555555555555556} \]

       3. unpow2 51.5%

          \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{A + \sqrt{\color{blue}{A \cdot A} + {B}^{2}}}{-B}\right)}{\pi}}{0.005555555555555556} \]

       4. unpow2 51.5%

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

       5. hypot-define 74.2%

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

   11. Simplified 74.2%

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

   if 2.0000000000000001e92 < C

   1. Initial program 21.9%

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

   4. Applied egg-rr 51.2%

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

      1. clear-num 51.2%

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

      2. inv-pow 51.2%

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

      3. div-inv 51.2%

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

      4. associate--l- 48.9%

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

      5. metadata-eval 48.9%

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

   6. Applied egg-rr 48.9%

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

   8. Simplified 51.2%

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

   9. Taylor expanded in A around 0 19.9%

      \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{\color{blue}{C - \sqrt{{B}^{2} + {C}^{2}}}}{B}\right)}{\pi}}{0.005555555555555556} \]
   10. Step-by-step derivation

       1. unpow2 19.9%

          \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi}}{0.005555555555555556} \]

       2. unpow2 19.9%

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

       3. hypot-undefine 44.5%

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

   11. Simplified 44.5%

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

   12. Taylor expanded in C around inf 75.7%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -3.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{elif}\;C \leq 2 \cdot 10^{+92}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}}{0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}}{0.005555555555555556}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4 \cdot 10^{+132}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{+129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4e+132)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (if (<= A 1.1e+129)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4e+132) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= 1.1e+129) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4e+132) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= 1.1e+129) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4e+132:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= 1.1e+129:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4e+132)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= 1.1e+129)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4e+132)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= 1.1e+129)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4e+132], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.1e+129], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.99999999999999996e132

   1. Initial program 23.6%

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

   3. Taylor expanded in A around -inf 64.6%

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

   4. Taylor expanded in B around 0 78.0%

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

      1. associate-*r/ 78.3%

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

   6. Simplified 78.3%

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

   if -3.99999999999999996e132 < A < 1.1e129

   1. Initial program 57.2%

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

   3. Taylor expanded in A around 0 52.9%

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

      1. unpow2 52.9%

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

      2. unpow2 52.9%

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

      3. hypot-define 75.7%

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

   5. Simplified 75.7%

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

   if 1.1e129 < A

   1. Initial program 75.6%

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

   3. Taylor expanded in B around -inf 76.1%

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

      1. associate--l+ 76.1%

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

      2. div-sub 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in C around 0 82.5%

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

      1. associate-*r/ 82.5%

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

      2. neg-mul-1 82.5%

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

   8. Simplified 82.5%

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

   9. Taylor expanded in A around 0 82.5%

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

       1. mul-1-neg 82.5%

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

       2. distribute-frac-neg 82.5%

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

       3. distribute-frac-neg 82.5%

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

       4. sub-neg 82.5%

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

   11. Simplified 82.5%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4 \cdot 10^{+132}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{+129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.4 \cdot 10^{+130}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{+131}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.4e+130)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (if (<= A 1.45e+131)
     (/ 180.0 (/ PI (atan (/ (- C (hypot B C)) B))))
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.4e+130) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= 1.45e+131) {
		tmp = 180.0 / (((double) M_PI) / atan(((C - hypot(B, C)) / B)));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.4e+130) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= 1.45e+131) {
		tmp = 180.0 / (Math.PI / Math.atan(((C - Math.hypot(B, C)) / B)));
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.4e+130:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= 1.45e+131:
		tmp = 180.0 / (math.pi / math.atan(((C - math.hypot(B, C)) / B)))
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.4e+130)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= 1.45e+131)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - hypot(B, C)) / B))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.4e+130)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= 1.45e+131)
		tmp = 180.0 / (pi / atan(((C - hypot(B, C)) / B)));
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.4e+130], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.45e+131], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.39999999999999962e130

   1. Initial program 23.6%

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

   3. Taylor expanded in A around -inf 64.6%

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

   4. Taylor expanded in B around 0 78.0%

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

      1. associate-*r/ 78.3%

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

   6. Simplified 78.3%

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

   if -8.39999999999999962e130 < A < 1.45000000000000005e131

   1. Initial program 57.2%

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

   4. Applied egg-rr 80.0%

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

   5. Taylor expanded in A around 0 52.9%

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

      1. unpow2 52.9%

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

      2. unpow2 52.9%

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

      3. hypot-define 75.7%

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

   7. Simplified 75.7%

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

   if 1.45000000000000005e131 < A

   1. Initial program 75.6%

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

   3. Taylor expanded in B around -inf 76.1%

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

      1. associate--l+ 76.1%

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

      2. div-sub 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in C around 0 82.5%

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

      1. associate-*r/ 82.5%

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

      2. neg-mul-1 82.5%

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

   8. Simplified 82.5%

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

   9. Taylor expanded in A around 0 82.5%

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

       1. mul-1-neg 82.5%

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

       2. distribute-frac-neg 82.5%

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

       3. distribute-frac-neg 82.5%

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

       4. sub-neg 82.5%

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

   11. Simplified 82.5%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.4 \cdot 10^{+130}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{+131}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{+133}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.9e+133)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e+133) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e+133) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.9e+133:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.9e+133)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.9e+133)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.9e+133], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -2.9000000000000001e133

   1. Initial program 23.6%

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

   3. Taylor expanded in A around -inf 64.6%

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

   4. Taylor expanded in B around 0 78.0%

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

      1. associate-*r/ 78.3%

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

   6. Simplified 78.3%

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

   if -2.9000000000000001e133 < A

   1. Initial program 60.2%

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

   3. Simplified 81.3%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{+133}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 2 \cdot 10^{+92}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}}{0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 2e+92)
   (* (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI) 180.0)
   (/ (/ (atan (* -0.5 (/ B C))) PI) 0.005555555555555556)))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 2e+92) {
		tmp = (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI)) * 180.0;
	} else {
		tmp = (atan((-0.5 * (B / C))) / ((double) M_PI)) / 0.005555555555555556;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 2e+92) {
		tmp = (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI) * 180.0;
	} else {
		tmp = (Math.atan((-0.5 * (B / C))) / Math.PI) / 0.005555555555555556;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 2e+92:
		tmp = (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi) * 180.0
	else:
		tmp = (math.atan((-0.5 * (B / C))) / math.pi) / 0.005555555555555556
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 2e+92)
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi) * 180.0);
	else
		tmp = Float64(Float64(atan(Float64(-0.5 * Float64(B / C))) / pi) / 0.005555555555555556);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 2e+92)
		tmp = (atan((((C - A) - hypot(B, (A - C))) / B)) / pi) * 180.0;
	else
		tmp = (atan((-0.5 * (B / C))) / pi) / 0.005555555555555556;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 2e+92], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] / 0.005555555555555556), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 2.0000000000000001e92

   1. Initial program 60.6%

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

      1. associate-*l/ 60.6%

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

      2. *-lft-identity 60.6%

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

      3. +-commutative 60.6%

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

      4. unpow2 60.6%

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

      5. unpow2 60.6%

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

      6. hypot-define 82.7%

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

   3. Simplified 82.7%

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

   if 2.0000000000000001e92 < C

   1. Initial program 21.9%

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

   4. Applied egg-rr 51.2%

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

      1. clear-num 51.2%

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

      2. inv-pow 51.2%

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

      3. div-inv 51.2%

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

      4. associate--l- 48.9%

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

      5. metadata-eval 48.9%

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

   6. Applied egg-rr 48.9%

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

   8. Simplified 51.2%

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

   9. Taylor expanded in A around 0 19.9%

      \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{\color{blue}{C - \sqrt{{B}^{2} + {C}^{2}}}}{B}\right)}{\pi}}{0.005555555555555556} \]
   10. Step-by-step derivation

       1. unpow2 19.9%

          \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi}}{0.005555555555555556} \]

       2. unpow2 19.9%

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

       3. hypot-undefine 44.5%

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

   11. Simplified 44.5%

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

   12. Taylor expanded in C around inf 75.7%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 2 \cdot 10^{+92}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}}{0.005555555555555556}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 2.7 \cdot 10^{+92}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}}{0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 2.7e+92)
   (/ 180.0 (/ PI (atan (/ (- (- C A) (hypot (- A C) B)) B))))
   (/ (/ (atan (* -0.5 (/ B C))) PI) 0.005555555555555556)))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.7e+92) {
		tmp = 180.0 / (((double) M_PI) / atan((((C - A) - hypot((A - C), B)) / B)));
	} else {
		tmp = (atan((-0.5 * (B / C))) / ((double) M_PI)) / 0.005555555555555556;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.7e+92) {
		tmp = 180.0 / (Math.PI / Math.atan((((C - A) - Math.hypot((A - C), B)) / B)));
	} else {
		tmp = (Math.atan((-0.5 * (B / C))) / Math.PI) / 0.005555555555555556;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 2.7e+92:
		tmp = 180.0 / (math.pi / math.atan((((C - A) - math.hypot((A - C), B)) / B)))
	else:
		tmp = (math.atan((-0.5 * (B / C))) / math.pi) / 0.005555555555555556
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 2.7e+92)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B))));
	else
		tmp = Float64(Float64(atan(Float64(-0.5 * Float64(B / C))) / pi) / 0.005555555555555556);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 2.7e+92)
		tmp = 180.0 / (pi / atan((((C - A) - hypot((A - C), B)) / B)));
	else
		tmp = (atan((-0.5 * (B / C))) / pi) / 0.005555555555555556;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 2.7e+92], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] / 0.005555555555555556), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 2.6999999999999999e92

   1. Initial program 60.6%

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

   4. Applied egg-rr 82.7%

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

   if 2.6999999999999999e92 < C

   1. Initial program 21.9%

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

   4. Applied egg-rr 51.2%

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

      1. clear-num 51.2%

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

      2. inv-pow 51.2%

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

      3. div-inv 51.2%

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

      4. associate--l- 48.9%

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

      5. metadata-eval 48.9%

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

   6. Applied egg-rr 48.9%

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

   8. Simplified 51.2%

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

   9. Taylor expanded in A around 0 19.9%

      \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{\color{blue}{C - \sqrt{{B}^{2} + {C}^{2}}}}{B}\right)}{\pi}}{0.005555555555555556} \]
   10. Step-by-step derivation

       1. unpow2 19.9%

          \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi}}{0.005555555555555556} \]

       2. unpow2 19.9%

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

       3. hypot-undefine 44.5%

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

   11. Simplified 44.5%

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

   12. Taylor expanded in C around inf 75.7%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 2.7 \cdot 10^{+92}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}}{0.005555555555555556}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -8 \cdot 10^{+167}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{+96}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -8.6 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-307}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-210}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-107}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* (/ C B) 2.0)) PI)))
        (t_1 (* 180.0 (/ (atan 1.0) PI)))
        (t_2 (* 180.0 (/ (atan (/ 0.0 B)) PI))))
   (if (<= B -8e+167)
     t_1
     (if (<= B -1.4e+96)
       t_0
       (if (<= B -8.6e-61)
         t_1
         (if (<= B -1.5e-223)
           (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
           (if (<= B 2.7e-307)
             t_2
             (if (<= B 5.2e-210)
               t_0
               (if (<= B 4.8e-107) t_2 (* 180.0 (/ (atan -1.0) PI)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	double t_1 = 180.0 * (atan(1.0) / ((double) M_PI));
	double t_2 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double tmp;
	if (B <= -8e+167) {
		tmp = t_1;
	} else if (B <= -1.4e+96) {
		tmp = t_0;
	} else if (B <= -8.6e-61) {
		tmp = t_1;
	} else if (B <= -1.5e-223) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 2.7e-307) {
		tmp = t_2;
	} else if (B <= 5.2e-210) {
		tmp = t_0;
	} else if (B <= 4.8e-107) {
		tmp = t_2;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	double t_1 = 180.0 * (Math.atan(1.0) / Math.PI);
	double t_2 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double tmp;
	if (B <= -8e+167) {
		tmp = t_1;
	} else if (B <= -1.4e+96) {
		tmp = t_0;
	} else if (B <= -8.6e-61) {
		tmp = t_1;
	} else if (B <= -1.5e-223) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 2.7e-307) {
		tmp = t_2;
	} else if (B <= 5.2e-210) {
		tmp = t_0;
	} else if (B <= 4.8e-107) {
		tmp = t_2;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	t_1 = 180.0 * (math.atan(1.0) / math.pi)
	t_2 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	tmp = 0
	if B <= -8e+167:
		tmp = t_1
	elif B <= -1.4e+96:
		tmp = t_0
	elif B <= -8.6e-61:
		tmp = t_1
	elif B <= -1.5e-223:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 2.7e-307:
		tmp = t_2
	elif B <= 5.2e-210:
		tmp = t_0
	elif B <= 4.8e-107:
		tmp = t_2
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi))
	t_1 = Float64(180.0 * Float64(atan(1.0) / pi))
	t_2 = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi))
	tmp = 0.0
	if (B <= -8e+167)
		tmp = t_1;
	elseif (B <= -1.4e+96)
		tmp = t_0;
	elseif (B <= -8.6e-61)
		tmp = t_1;
	elseif (B <= -1.5e-223)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 2.7e-307)
		tmp = t_2;
	elseif (B <= 5.2e-210)
		tmp = t_0;
	elseif (B <= 4.8e-107)
		tmp = t_2;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C / B) * 2.0)) / pi);
	t_1 = 180.0 * (atan(1.0) / pi);
	t_2 = 180.0 * (atan((0.0 / B)) / pi);
	tmp = 0.0;
	if (B <= -8e+167)
		tmp = t_1;
	elseif (B <= -1.4e+96)
		tmp = t_0;
	elseif (B <= -8.6e-61)
		tmp = t_1;
	elseif (B <= -1.5e-223)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 2.7e-307)
		tmp = t_2;
	elseif (B <= 5.2e-210)
		tmp = t_0;
	elseif (B <= 4.8e-107)
		tmp = t_2;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -8e+167], t$95$1, If[LessEqual[B, -1.4e+96], t$95$0, If[LessEqual[B, -8.6e-61], t$95$1, If[LessEqual[B, -1.5e-223], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.7e-307], t$95$2, If[LessEqual[B, 5.2e-210], t$95$0, If[LessEqual[B, 4.8e-107], t$95$2, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -8.0000000000000003e167 or -1.4e96 < B < -8.6000000000000007e-61

   1. Initial program 43.4%

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

   3. Taylor expanded in B around -inf 56.2%

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

   if -8.0000000000000003e167 < B < -1.4e96 or 2.69999999999999985e-307 < B < 5.1999999999999997e-210

   1. Initial program 63.0%

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

   3. Taylor expanded in C around -inf 47.7%

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

   if -8.6000000000000007e-61 < B < -1.49999999999999996e-223

   1. Initial program 75.5%

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

   3. Taylor expanded in A around inf 56.6%

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

   if -1.49999999999999996e-223 < B < 2.69999999999999985e-307 or 5.1999999999999997e-210 < B < 4.79999999999999989e-107

   1. Initial program 41.1%

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

   3. Taylor expanded in C around inf 53.6%

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

      1. associate-*r/ 53.6%

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

      2. distribute-rgt1-in 53.6%

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

      3. metadata-eval 53.6%

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

      4. mul0-lft 53.6%

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

      5. metadata-eval 53.6%

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

   5. Simplified 53.6%

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

   if 4.79999999999999989e-107 < B

   1. Initial program 53.1%

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

   3. Taylor expanded in B around inf 55.5%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8 \cdot 10^{+167}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{+96}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.6 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-307}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{-210}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-107}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.4 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq -9.6 \cdot 10^{-206}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-305}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.86 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 1.18 \cdot 10^{-107}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ 0.0 B)) PI)))
        (t_1 (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))))
   (if (<= B -2.4e-101)
     t_1
     (if (<= B -9.6e-206)
       (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
       (if (<= B -8.5e-223)
         t_1
         (if (<= B 1.1e-305)
           t_0
           (if (<= B 1.86e-208)
             t_1
             (if (<= B 1.18e-107) 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 t_1 = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	double tmp;
	if (B <= -2.4e-101) {
		tmp = t_1;
	} else if (B <= -9.6e-206) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= -8.5e-223) {
		tmp = t_1;
	} else if (B <= 1.1e-305) {
		tmp = t_0;
	} else if (B <= 1.86e-208) {
		tmp = t_1;
	} else if (B <= 1.18e-107) {
		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 t_1 = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	double tmp;
	if (B <= -2.4e-101) {
		tmp = t_1;
	} else if (B <= -9.6e-206) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= -8.5e-223) {
		tmp = t_1;
	} else if (B <= 1.1e-305) {
		tmp = t_0;
	} else if (B <= 1.86e-208) {
		tmp = t_1;
	} else if (B <= 1.18e-107) {
		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)
	t_1 = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	tmp = 0
	if B <= -2.4e-101:
		tmp = t_1
	elif B <= -9.6e-206:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= -8.5e-223:
		tmp = t_1
	elif B <= 1.1e-305:
		tmp = t_0
	elif B <= 1.86e-208:
		tmp = t_1
	elif B <= 1.18e-107:
		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))
	t_1 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi))
	tmp = 0.0
	if (B <= -2.4e-101)
		tmp = t_1;
	elseif (B <= -9.6e-206)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= -8.5e-223)
		tmp = t_1;
	elseif (B <= 1.1e-305)
		tmp = t_0;
	elseif (B <= 1.86e-208)
		tmp = t_1;
	elseif (B <= 1.18e-107)
		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);
	t_1 = 180.0 * (atan((1.0 + (C / B))) / pi);
	tmp = 0.0;
	if (B <= -2.4e-101)
		tmp = t_1;
	elseif (B <= -9.6e-206)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= -8.5e-223)
		tmp = t_1;
	elseif (B <= 1.1e-305)
		tmp = t_0;
	elseif (B <= 1.86e-208)
		tmp = t_1;
	elseif (B <= 1.18e-107)
		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]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.4e-101], t$95$1, If[LessEqual[B, -9.6e-206], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.5e-223], t$95$1, If[LessEqual[B, 1.1e-305], t$95$0, If[LessEqual[B, 1.86e-208], t$95$1, If[LessEqual[B, 1.18e-107], 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 < -2.4e-101 or -9.5999999999999998e-206 < B < -8.5000000000000003e-223 or 1.09999999999999998e-305 < B < 1.86e-208

   1. Initial program 50.6%

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

   3. Taylor expanded in B around -inf 66.7%

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

      1. associate--l+ 66.7%

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

      2. div-sub 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in C around inf 60.5%

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

   if -2.4e-101 < B < -9.5999999999999998e-206

   1. Initial program 79.3%

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

   3. Taylor expanded in A around inf 66.2%

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

   if -8.5000000000000003e-223 < B < 1.09999999999999998e-305 or 1.86e-208 < B < 1.17999999999999993e-107

   1. Initial program 42.9%

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

   3. Taylor expanded in C around inf 52.0%

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

      1. associate-*r/ 52.0%

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

      2. distribute-rgt1-in 52.0%

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

      3. metadata-eval 52.0%

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

      4. mul0-lft 52.0%

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

      5. metadata-eval 52.0%

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

   5. Simplified 52.0%

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

   if 1.17999999999999993e-107 < B

   1. Initial program 53.1%

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

   3. Taylor expanded in B around inf 55.5%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.4 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -9.6 \cdot 10^{-206}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-305}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.86 \cdot 10^{-208}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.18 \cdot 10^{-107}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -9.5 \cdot 10^{-100}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-212}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-107}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI)))
        (t_1 (* 180.0 (/ (atan (/ 0.0 B)) PI))))
   (if (<= B -9.5e-100)
     t_0
     (if (<= B -6.2e-223)
       (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
       (if (<= B 1.8e-304)
         t_1
         (if (<= B 4.8e-212)
           t_0
           (if (<= B 9.5e-107) t_1 (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	double t_1 = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	double tmp;
	if (B <= -9.5e-100) {
		tmp = t_0;
	} else if (B <= -6.2e-223) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= 1.8e-304) {
		tmp = t_1;
	} else if (B <= 4.8e-212) {
		tmp = t_0;
	} else if (B <= 9.5e-107) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	double tmp;
	if (B <= -9.5e-100) {
		tmp = t_0;
	} else if (B <= -6.2e-223) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= 1.8e-304) {
		tmp = t_1;
	} else if (B <= 4.8e-212) {
		tmp = t_0;
	} else if (B <= 9.5e-107) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	t_1 = 180.0 * (math.atan((0.0 / B)) / math.pi)
	tmp = 0
	if B <= -9.5e-100:
		tmp = t_0
	elif B <= -6.2e-223:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= 1.8e-304:
		tmp = t_1
	elif B <= 4.8e-212:
		tmp = t_0
	elif B <= 9.5e-107:
		tmp = t_1
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi))
	tmp = 0.0
	if (B <= -9.5e-100)
		tmp = t_0;
	elseif (B <= -6.2e-223)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= 1.8e-304)
		tmp = t_1;
	elseif (B <= 4.8e-212)
		tmp = t_0;
	elseif (B <= 9.5e-107)
		tmp = t_1;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 + (C / B))) / pi);
	t_1 = 180.0 * (atan((0.0 / B)) / pi);
	tmp = 0.0;
	if (B <= -9.5e-100)
		tmp = t_0;
	elseif (B <= -6.2e-223)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= 1.8e-304)
		tmp = t_1;
	elseif (B <= 4.8e-212)
		tmp = t_0;
	elseif (B <= 9.5e-107)
		tmp = t_1;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -9.5e-100], t$95$0, If[LessEqual[B, -6.2e-223], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.8e-304], t$95$1, If[LessEqual[B, 4.8e-212], t$95$0, If[LessEqual[B, 9.5e-107], t$95$1, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -9.4999999999999992e-100 or 1.8000000000000001e-304 < B < 4.79999999999999978e-212

   1. Initial program 51.0%

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

   3. Taylor expanded in B around -inf 66.7%

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

      1. associate--l+ 66.7%

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

      2. div-sub 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in C around inf 60.2%

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

   if -9.4999999999999992e-100 < B < -6.20000000000000036e-223

   1. Initial program 75.4%

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

   3. Taylor expanded in B around -inf 67.6%

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

      1. associate--l+ 67.6%

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

      2. div-sub 71.3%

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

   5. Simplified 71.3%

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

   6. Taylor expanded in C around 0 64.1%

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

      1. associate-*r/ 64.1%

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

      2. neg-mul-1 64.1%

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

   8. Simplified 64.1%

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

   9. Taylor expanded in A around 0 64.1%

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

       1. mul-1-neg 64.1%

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

       2. distribute-frac-neg 64.1%

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

       3. distribute-frac-neg 64.1%

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

       4. sub-neg 64.1%

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

   11. Simplified 64.1%

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

   if -6.20000000000000036e-223 < B < 1.8000000000000001e-304 or 4.79999999999999978e-212 < B < 9.4999999999999999e-107

   1. Initial program 41.1%

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

   3. Taylor expanded in C around inf 53.6%

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

      1. associate-*r/ 53.6%

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

      2. distribute-rgt1-in 53.6%

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

      3. metadata-eval 53.6%

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

      4. mul0-lft 53.6%

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

      5. metadata-eval 53.6%

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

   5. Simplified 53.6%

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

   if 9.4999999999999999e-107 < B

   1. Initial program 53.1%

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

   3. Taylor expanded in B around inf 55.5%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9.5 \cdot 10^{-100}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -6.2 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-304}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-212}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-107}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{-223}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{-308}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-207}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C \cdot \left(1 + -0.5 \cdot \frac{C}{B}\right) - B}{B}\right)}}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-109}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(t\_0 + -1\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -1.55e-223)
     (/ (* 180.0 (atan (+ 1.0 t_0))) PI)
     (if (<= B 5.4e-308)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 3.8e-207)
         (/ 180.0 (/ PI (atan (/ (- (* C (+ 1.0 (* -0.5 (/ C B)))) B) B))))
         (if (<= B 1.6e-109)
           (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
           (/ 180.0 (/ PI (atan (+ t_0 -1.0))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.55e-223) {
		tmp = (180.0 * atan((1.0 + t_0))) / ((double) M_PI);
	} else if (B <= 5.4e-308) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 3.8e-207) {
		tmp = 180.0 / (((double) M_PI) / atan((((C * (1.0 + (-0.5 * (C / B)))) - B) / B)));
	} else if (B <= 1.6e-109) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((t_0 + -1.0)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.55e-223) {
		tmp = (180.0 * Math.atan((1.0 + t_0))) / Math.PI;
	} else if (B <= 5.4e-308) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 3.8e-207) {
		tmp = 180.0 / (Math.PI / Math.atan((((C * (1.0 + (-0.5 * (C / B)))) - B) / B)));
	} else if (B <= 1.6e-109) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((t_0 + -1.0)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -1.55e-223:
		tmp = (180.0 * math.atan((1.0 + t_0))) / math.pi
	elif B <= 5.4e-308:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 3.8e-207:
		tmp = 180.0 / (math.pi / math.atan((((C * (1.0 + (-0.5 * (C / B)))) - B) / B)))
	elif B <= 1.6e-109:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	else:
		tmp = 180.0 / (math.pi / math.atan((t_0 + -1.0)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -1.55e-223)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + t_0))) / pi);
	elseif (B <= 5.4e-308)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 3.8e-207)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C * Float64(1.0 + Float64(-0.5 * Float64(C / B)))) - B) / B))));
	elseif (B <= 1.6e-109)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(t_0 + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -1.55e-223)
		tmp = (180.0 * atan((1.0 + t_0))) / pi;
	elseif (B <= 5.4e-308)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 3.8e-207)
		tmp = 180.0 / (pi / atan((((C * (1.0 + (-0.5 * (C / B)))) - B) / B)));
	elseif (B <= 1.6e-109)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	else
		tmp = 180.0 / (pi / atan((t_0 + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -1.55e-223], N[(N[(180.0 * N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 5.4e-308], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.8e-207], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C * N[(1.0 + N[(-0.5 * N[(C / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.6e-109], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.55000000000000009e-223

   1. Initial program 54.9%

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

   3. Taylor expanded in B around -inf 67.9%

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

      1. associate--l+ 67.9%

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

      2. div-sub 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in C around 0 67.9%

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

      1. associate-*r/ 67.9%

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

      2. associate--l+ 67.9%

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

      3. div-sub 68.8%

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

   8. Simplified 68.8%

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

   if -1.55000000000000009e-223 < B < 5.4000000000000003e-308

   1. Initial program 55.4%

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

   3. Taylor expanded in C around inf 70.3%

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

      1. associate-*r/ 70.3%

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

      2. distribute-rgt1-in 70.3%

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

      3. metadata-eval 70.3%

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

      4. mul0-lft 70.3%

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

      5. metadata-eval 70.3%

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

   5. Simplified 70.3%

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

   if 5.4000000000000003e-308 < B < 3.8e-207

   1. Initial program 65.9%

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

   4. Applied egg-rr 86.7%

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

   5. Taylor expanded in A around 0 58.4%

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

      1. unpow2 58.4%

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

      2. unpow2 58.4%

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

      3. hypot-define 65.5%

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

   7. Simplified 65.5%

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

   8. Taylor expanded in C around 0 65.6%

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

   if 3.8e-207 < B < 1.6000000000000001e-109

   1. Initial program 30.7%

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

   3. Taylor expanded in A around -inf 54.3%

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

   4. Taylor expanded in B around 0 62.3%

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

      1. associate-*r/ 62.4%

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

   6. Simplified 62.4%

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

   if 1.6000000000000001e-109 < B

   1. Initial program 53.1%

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

   4. Applied egg-rr 75.7%

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

   5. Taylor expanded in B around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. associate--r+ 72.2%

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

      3. div-sub 72.2%

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

      4. sub-neg 72.2%

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

      5. metadata-eval 72.2%

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

   7. Simplified 72.2%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.55 \cdot 10^{-223}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{-308}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-207}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C \cdot \left(1 + -0.5 \cdot \frac{C}{B}\right) - B}{B}\right)}}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-109}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{if}\;B \leq -4.2 \cdot 10^{-224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 3 \cdot 10^{-308}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-110}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(t\_0 + -1\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)) (t_1 (* 180.0 (/ (atan (+ 1.0 t_0)) PI))))
   (if (<= B -4.2e-224)
     t_1
     (if (<= B 3e-308)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 9e-208)
         t_1
         (if (<= B 1.15e-110)
           (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
           (/ 180.0 (/ PI (atan (+ t_0 -1.0))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double t_1 = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	double tmp;
	if (B <= -4.2e-224) {
		tmp = t_1;
	} else if (B <= 3e-308) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 9e-208) {
		tmp = t_1;
	} else if (B <= 1.15e-110) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((t_0 + -1.0)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double t_1 = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	double tmp;
	if (B <= -4.2e-224) {
		tmp = t_1;
	} else if (B <= 3e-308) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 9e-208) {
		tmp = t_1;
	} else if (B <= 1.15e-110) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((t_0 + -1.0)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	t_1 = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	tmp = 0
	if B <= -4.2e-224:
		tmp = t_1
	elif B <= 3e-308:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 9e-208:
		tmp = t_1
	elif B <= 1.15e-110:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	else:
		tmp = 180.0 / (math.pi / math.atan((t_0 + -1.0)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	t_1 = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi))
	tmp = 0.0
	if (B <= -4.2e-224)
		tmp = t_1;
	elseif (B <= 3e-308)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 9e-208)
		tmp = t_1;
	elseif (B <= 1.15e-110)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(t_0 + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	t_1 = 180.0 * (atan((1.0 + t_0)) / pi);
	tmp = 0.0;
	if (B <= -4.2e-224)
		tmp = t_1;
	elseif (B <= 3e-308)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 9e-208)
		tmp = t_1;
	elseif (B <= 1.15e-110)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	else
		tmp = 180.0 / (pi / atan((t_0 + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -4.2e-224], t$95$1, If[LessEqual[B, 3e-308], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9e-208], t$95$1, If[LessEqual[B, 1.15e-110], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -4.20000000000000013e-224 or 3.00000000000000022e-308 < B < 8.9999999999999992e-208

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf 66.9%

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

      1. associate--l+ 66.9%

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

      2. div-sub 68.4%

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

   5. Simplified 68.4%

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

   if -4.20000000000000013e-224 < B < 3.00000000000000022e-308

   1. Initial program 55.4%

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

   3. Taylor expanded in C around inf 70.3%

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

      1. associate-*r/ 70.3%

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

      2. distribute-rgt1-in 70.3%

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

      3. metadata-eval 70.3%

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

      4. mul0-lft 70.3%

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

      5. metadata-eval 70.3%

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

   5. Simplified 70.3%

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

   if 8.9999999999999992e-208 < B < 1.1500000000000001e-110

   1. Initial program 30.7%

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

   3. Taylor expanded in A around -inf 54.3%

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

   4. Taylor expanded in B around 0 62.3%

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

      1. associate-*r/ 62.4%

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

   6. Simplified 62.4%

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

   if 1.1500000000000001e-110 < B

   1. Initial program 53.1%

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

   4. Applied egg-rr 75.7%

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

   5. Taylor expanded in B around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. associate--r+ 72.2%

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

      3. div-sub 72.2%

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

      4. sub-neg 72.2%

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

      5. metadata-eval 72.2%

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

   7. Simplified 72.2%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.2 \cdot 10^{-224}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3 \cdot 10^{-308}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-208}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-110}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ t_1 := \tan^{-1} \left(1 + t\_0\right)\\ \mathbf{if}\;B \leq -3.3 \cdot 10^{-224}:\\ \;\;\;\;\frac{180 \cdot t\_1}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-307}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-208}:\\ \;\;\;\;180 \cdot \frac{t\_1}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-112}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(t\_0 + -1\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)) (t_1 (atan (+ 1.0 t_0))))
   (if (<= B -3.3e-224)
     (/ (* 180.0 t_1) PI)
     (if (<= B 5e-307)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 7e-208)
         (* 180.0 (/ t_1 PI))
         (if (<= B 2.7e-112)
           (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
           (/ 180.0 (/ PI (atan (+ t_0 -1.0))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double t_1 = atan((1.0 + t_0));
	double tmp;
	if (B <= -3.3e-224) {
		tmp = (180.0 * t_1) / ((double) M_PI);
	} else if (B <= 5e-307) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 7e-208) {
		tmp = 180.0 * (t_1 / ((double) M_PI));
	} else if (B <= 2.7e-112) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((t_0 + -1.0)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double t_1 = Math.atan((1.0 + t_0));
	double tmp;
	if (B <= -3.3e-224) {
		tmp = (180.0 * t_1) / Math.PI;
	} else if (B <= 5e-307) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 7e-208) {
		tmp = 180.0 * (t_1 / Math.PI);
	} else if (B <= 2.7e-112) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((t_0 + -1.0)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	t_1 = math.atan((1.0 + t_0))
	tmp = 0
	if B <= -3.3e-224:
		tmp = (180.0 * t_1) / math.pi
	elif B <= 5e-307:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 7e-208:
		tmp = 180.0 * (t_1 / math.pi)
	elif B <= 2.7e-112:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	else:
		tmp = 180.0 / (math.pi / math.atan((t_0 + -1.0)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	t_1 = atan(Float64(1.0 + t_0))
	tmp = 0.0
	if (B <= -3.3e-224)
		tmp = Float64(Float64(180.0 * t_1) / pi);
	elseif (B <= 5e-307)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 7e-208)
		tmp = Float64(180.0 * Float64(t_1 / pi));
	elseif (B <= 2.7e-112)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(t_0 + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	t_1 = atan((1.0 + t_0));
	tmp = 0.0;
	if (B <= -3.3e-224)
		tmp = (180.0 * t_1) / pi;
	elseif (B <= 5e-307)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 7e-208)
		tmp = 180.0 * (t_1 / pi);
	elseif (B <= 2.7e-112)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	else
		tmp = 180.0 / (pi / atan((t_0 + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[B, -3.3e-224], N[(N[(180.0 * t$95$1), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 5e-307], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7e-208], N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.7e-112], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -3.3000000000000001e-224

   1. Initial program 54.9%

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

   3. Taylor expanded in B around -inf 67.9%

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

      1. associate--l+ 67.9%

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

      2. div-sub 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in C around 0 67.9%

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

      1. associate-*r/ 67.9%

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

      2. associate--l+ 67.9%

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

      3. div-sub 68.8%

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

   8. Simplified 68.8%

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

   if -3.3000000000000001e-224 < B < 5.00000000000000014e-307

   1. Initial program 55.4%

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

   3. Taylor expanded in C around inf 70.3%

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

      1. associate-*r/ 70.3%

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

      2. distribute-rgt1-in 70.3%

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

      3. metadata-eval 70.3%

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

      4. mul0-lft 70.3%

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

      5. metadata-eval 70.3%

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

   5. Simplified 70.3%

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

   if 5.00000000000000014e-307 < B < 6.99999999999999982e-208

   1. Initial program 65.9%

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

   3. Taylor expanded in B around -inf 58.2%

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

      1. associate--l+ 58.2%

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

      2. div-sub 65.3%

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

   5. Simplified 65.3%

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

   if 6.99999999999999982e-208 < B < 2.7000000000000001e-112

   1. Initial program 30.7%

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

   3. Taylor expanded in A around -inf 54.3%

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

   4. Taylor expanded in B around 0 62.3%

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

      1. associate-*r/ 62.4%

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

   6. Simplified 62.4%

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

   if 2.7000000000000001e-112 < B

   1. Initial program 53.1%

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

   4. Applied egg-rr 75.7%

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

   5. Taylor expanded in B around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. associate--r+ 72.2%

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

      3. div-sub 72.2%

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

      4. sub-neg 72.2%

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

      5. metadata-eval 72.2%

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

   7. Simplified 72.2%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.3 \cdot 10^{-224}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-307}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-208}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-112}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - B}{B}\right)}}\\ \mathbf{if}\;A \leq -7.2 \cdot 10^{+96}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{-283}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq 3.25 \cdot 10^{-251}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-37}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ 180.0 (/ PI (atan (/ (- C B) B))))))
   (if (<= A -7.2e+96)
     (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
     (if (<= A 1.4e-283)
       t_0
       (if (<= A 3.25e-251)
         (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
         (if (<= A 5e-37) t_0 (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 / (((double) M_PI) / atan(((C - B) / B)));
	double tmp;
	if (A <= -7.2e+96) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 1.4e-283) {
		tmp = t_0;
	} else if (A <= 3.25e-251) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (A <= 5e-37) {
		tmp = t_0;
	} 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 t_0 = 180.0 / (Math.PI / Math.atan(((C - B) / B)));
	double tmp;
	if (A <= -7.2e+96) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 1.4e-283) {
		tmp = t_0;
	} else if (A <= 3.25e-251) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (A <= 5e-37) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 / (math.pi / math.atan(((C - B) / B)))
	tmp = 0
	if A <= -7.2e+96:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 1.4e-283:
		tmp = t_0
	elif A <= 3.25e-251:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif A <= 5e-37:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - B) / B))))
	tmp = 0.0
	if (A <= -7.2e+96)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 1.4e-283)
		tmp = t_0;
	elseif (A <= 3.25e-251)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (A <= 5e-37)
		tmp = t_0;
	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)
	t_0 = 180.0 / (pi / atan(((C - B) / B)));
	tmp = 0.0;
	if (A <= -7.2e+96)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 1.4e-283)
		tmp = t_0;
	elseif (A <= 3.25e-251)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (A <= 5e-37)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -7.2e+96], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.4e-283], t$95$0, If[LessEqual[A, 3.25e-251], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5e-37], t$95$0, 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 < -7.20000000000000026e96

   1. Initial program 27.2%

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

   3. Taylor expanded in A around -inf 74.1%

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

      1. associate-*r/ 74.1%

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

   5. Simplified 74.1%

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

   if -7.20000000000000026e96 < A < 1.3999999999999999e-283 or 3.2500000000000001e-251 < A < 4.9999999999999997e-37

   1. Initial program 56.5%

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

   4. Applied egg-rr 76.2%

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

   5. Taylor expanded in A around 0 55.2%

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

      1. unpow2 55.2%

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

      2. unpow2 55.2%

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

      3. hypot-define 75.0%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in C around 0 55.6%

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

   if 1.3999999999999999e-283 < A < 3.2500000000000001e-251

   1. Initial program 60.9%

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

   3. Taylor expanded in B around -inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. div-sub 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in C around inf 78.2%

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

   if 4.9999999999999997e-37 < A

   1. Initial program 69.1%

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

   3. Taylor expanded in B around -inf 71.8%

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

      1. associate--l+ 71.8%

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

      2. div-sub 74.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in C around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

   8. Simplified 72.3%

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

   9. Taylor expanded in A around 0 72.3%

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

       1. mul-1-neg 72.3%

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

       2. distribute-frac-neg 72.3%

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

       3. distribute-frac-neg 72.3%

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

       4. sub-neg 72.3%

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

   11. Simplified 72.3%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7.2 \cdot 10^{+96}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{-283}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - B}{B}\right)}}\\ \mathbf{elif}\;A \leq 3.25 \cdot 10^{-251}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-37}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - B}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 58.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - B}{B}\right)}}\\ \mathbf{if}\;A \leq -5.8 \cdot 10^{+96}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.2 \cdot 10^{-286}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-30}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ 180.0 (/ PI (atan (/ (- C B) B))))))
   (if (<= A -5.8e+96)
     (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
     (if (<= A 7.2e-286)
       t_0
       (if (<= A 3e-250)
         (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
         (if (<= A 6e-30) t_0 (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 / (((double) M_PI) / atan(((C - B) / B)));
	double tmp;
	if (A <= -5.8e+96) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= 7.2e-286) {
		tmp = t_0;
	} else if (A <= 3e-250) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (A <= 6e-30) {
		tmp = t_0;
	} 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 t_0 = 180.0 / (Math.PI / Math.atan(((C - B) / B)));
	double tmp;
	if (A <= -5.8e+96) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= 7.2e-286) {
		tmp = t_0;
	} else if (A <= 3e-250) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (A <= 6e-30) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 / (math.pi / math.atan(((C - B) / B)))
	tmp = 0
	if A <= -5.8e+96:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= 7.2e-286:
		tmp = t_0
	elif A <= 3e-250:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif A <= 6e-30:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - B) / B))))
	tmp = 0.0
	if (A <= -5.8e+96)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= 7.2e-286)
		tmp = t_0;
	elseif (A <= 3e-250)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (A <= 6e-30)
		tmp = t_0;
	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)
	t_0 = 180.0 / (pi / atan(((C - B) / B)));
	tmp = 0.0;
	if (A <= -5.8e+96)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= 7.2e-286)
		tmp = t_0;
	elseif (A <= 3e-250)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (A <= 6e-30)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -5.8e+96], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 7.2e-286], t$95$0, If[LessEqual[A, 3e-250], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6e-30], t$95$0, 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 < -5.79999999999999955e96

   1. Initial program 27.2%

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

   3. Taylor expanded in A around -inf 62.9%

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

   4. Taylor expanded in B around 0 74.1%

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

      1. associate-*r/ 74.3%

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

   6. Simplified 74.3%

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

   if -5.79999999999999955e96 < A < 7.20000000000000027e-286 or 3.00000000000000016e-250 < A < 5.9999999999999998e-30

   1. Initial program 56.5%

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

   4. Applied egg-rr 76.2%

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

   5. Taylor expanded in A around 0 55.2%

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

      1. unpow2 55.2%

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

      2. unpow2 55.2%

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

      3. hypot-define 75.0%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in C around 0 55.6%

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

   if 7.20000000000000027e-286 < A < 3.00000000000000016e-250

   1. Initial program 60.9%

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

   3. Taylor expanded in B around -inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. div-sub 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in C around inf 78.2%

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

   if 5.9999999999999998e-30 < A

   1. Initial program 69.1%

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

   3. Taylor expanded in B around -inf 71.8%

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

      1. associate--l+ 71.8%

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

      2. div-sub 74.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in C around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

   8. Simplified 72.3%

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

   9. Taylor expanded in A around 0 72.3%

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

       1. mul-1-neg 72.3%

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

       2. distribute-frac-neg 72.3%

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

       3. distribute-frac-neg 72.3%

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

       4. sub-neg 72.3%

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

   11. Simplified 72.3%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.8 \cdot 10^{+96}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.2 \cdot 10^{-286}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - B}{B}\right)}}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-30}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - B}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;A \leq -5.8 \cdot 10^{+96}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-286}:\\ \;\;\;\;\frac{\frac{t\_0}{\pi}}{0.005555555555555556}\\ \mathbf{elif}\;A \leq 10^{-251}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{-33}:\\ \;\;\;\;\frac{180}{\frac{\pi}{t\_0}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (/ (- C B) B))))
   (if (<= A -5.8e+96)
     (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
     (if (<= A 5e-286)
       (/ (/ t_0 PI) 0.005555555555555556)
       (if (<= A 1e-251)
         (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
         (if (<= A 4.2e-33)
           (/ 180.0 (/ PI t_0))
           (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((C - B) / B));
	double tmp;
	if (A <= -5.8e+96) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= 5e-286) {
		tmp = (t_0 / ((double) M_PI)) / 0.005555555555555556;
	} else if (A <= 1e-251) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (A <= 4.2e-33) {
		tmp = 180.0 / (((double) M_PI) / t_0);
	} 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 t_0 = Math.atan(((C - B) / B));
	double tmp;
	if (A <= -5.8e+96) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= 5e-286) {
		tmp = (t_0 / Math.PI) / 0.005555555555555556;
	} else if (A <= 1e-251) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (A <= 4.2e-33) {
		tmp = 180.0 / (Math.PI / t_0);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((C - B) / B))
	tmp = 0
	if A <= -5.8e+96:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= 5e-286:
		tmp = (t_0 / math.pi) / 0.005555555555555556
	elif A <= 1e-251:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif A <= 4.2e-33:
		tmp = 180.0 / (math.pi / t_0)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(Float64(C - B) / B))
	tmp = 0.0
	if (A <= -5.8e+96)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= 5e-286)
		tmp = Float64(Float64(t_0 / pi) / 0.005555555555555556);
	elseif (A <= 1e-251)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (A <= 4.2e-33)
		tmp = Float64(180.0 / Float64(pi / t_0));
	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)
	t_0 = atan(((C - B) / B));
	tmp = 0.0;
	if (A <= -5.8e+96)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= 5e-286)
		tmp = (t_0 / pi) / 0.005555555555555556;
	elseif (A <= 1e-251)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (A <= 4.2e-33)
		tmp = 180.0 / (pi / t_0);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -5.8e+96], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 5e-286], N[(N[(t$95$0 / Pi), $MachinePrecision] / 0.005555555555555556), $MachinePrecision], If[LessEqual[A, 1e-251], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.2e-33], N[(180.0 / N[(Pi / t$95$0), $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 5 regimes

2. if A < -5.79999999999999955e96

   1. Initial program 27.2%

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

   3. Taylor expanded in A around -inf 62.9%

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

   4. Taylor expanded in B around 0 74.1%

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

      1. associate-*r/ 74.3%

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

   6. Simplified 74.3%

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

   if -5.79999999999999955e96 < A < 5.00000000000000037e-286

   1. Initial program 57.3%

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

   4. Applied egg-rr 77.5%

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

      1. clear-num 77.5%

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

      2. inv-pow 77.5%

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

      3. div-inv 77.5%

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

      4. associate--l- 77.3%

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

      5. metadata-eval 77.3%

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

   6. Applied egg-rr 77.3%

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

   8. Simplified 77.5%

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

   9. Taylor expanded in A around 0 56.4%

      \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{\color{blue}{C - \sqrt{{B}^{2} + {C}^{2}}}}{B}\right)}{\pi}}{0.005555555555555556} \]
   10. Step-by-step derivation

       1. unpow2 56.4%

          \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi}}{0.005555555555555556} \]

       2. unpow2 56.4%

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

       3. hypot-undefine 76.6%

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

   11. Simplified 76.6%

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

   12. Taylor expanded in C around 0 53.1%

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

   if 5.00000000000000037e-286 < A < 1.00000000000000002e-251

   1. Initial program 60.9%

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

   3. Taylor expanded in B around -inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. div-sub 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in C around inf 78.2%

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

   if 1.00000000000000002e-251 < A < 4.2e-33

   1. Initial program 54.8%

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

   4. Applied egg-rr 73.6%

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

   5. Taylor expanded in A around 0 52.8%

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

      1. unpow2 52.8%

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

      2. unpow2 52.8%

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

      3. hypot-define 71.7%

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

   7. Simplified 71.7%

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

   8. Taylor expanded in C around 0 60.7%

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

   if 4.2e-33 < A

   1. Initial program 69.1%

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

   3. Taylor expanded in B around -inf 71.8%

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

      1. associate--l+ 71.8%

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

      2. div-sub 74.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in C around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

   8. Simplified 72.3%

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

   9. Taylor expanded in A around 0 72.3%

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

       1. mul-1-neg 72.3%

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

       2. distribute-frac-neg 72.3%

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

       3. distribute-frac-neg 72.3%

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

       4. sub-neg 72.3%

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

   11. Simplified 72.3%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.8 \cdot 10^{+96}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-286}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}}{0.005555555555555556}\\ \mathbf{elif}\;A \leq 10^{-251}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{-33}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - B}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 60.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{-223}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-308}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.8 \cdot 10^{-216}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-110}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}}{0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B -1.55e-223)
     t_0
     (if (<= B 2e-308)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (if (<= B 9.8e-216)
         t_0
         (if (<= B 2.55e-110)
           (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
           (/ (/ (atan (/ (- C B) B)) PI) 0.005555555555555556)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (B <= -1.55e-223) {
		tmp = t_0;
	} else if (B <= 2e-308) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 9.8e-216) {
		tmp = t_0;
	} else if (B <= 2.55e-110) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else {
		tmp = (atan(((C - B) / B)) / ((double) M_PI)) / 0.005555555555555556;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= -1.55e-223) {
		tmp = t_0;
	} else if (B <= 2e-308) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 9.8e-216) {
		tmp = t_0;
	} else if (B <= 2.55e-110) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else {
		tmp = (Math.atan(((C - B) / B)) / Math.PI) / 0.005555555555555556;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= -1.55e-223:
		tmp = t_0
	elif B <= 2e-308:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 9.8e-216:
		tmp = t_0
	elif B <= 2.55e-110:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	else:
		tmp = (math.atan(((C - B) / B)) / math.pi) / 0.005555555555555556
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= -1.55e-223)
		tmp = t_0;
	elseif (B <= 2e-308)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 9.8e-216)
		tmp = t_0;
	elseif (B <= 2.55e-110)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	else
		tmp = Float64(Float64(atan(Float64(Float64(C - B) / B)) / pi) / 0.005555555555555556);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= -1.55e-223)
		tmp = t_0;
	elseif (B <= 2e-308)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 9.8e-216)
		tmp = t_0;
	elseif (B <= 2.55e-110)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	else
		tmp = (atan(((C - B) / B)) / pi) / 0.005555555555555556;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.55e-223], t$95$0, If[LessEqual[B, 2e-308], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.8e-216], t$95$0, If[LessEqual[B, 2.55e-110], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] / 0.005555555555555556), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.55000000000000009e-223 or 1.9999999999999998e-308 < B < 9.8000000000000003e-216

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf 66.9%

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

      1. associate--l+ 66.9%

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

      2. div-sub 68.4%

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

   5. Simplified 68.4%

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

   if -1.55000000000000009e-223 < B < 1.9999999999999998e-308

   1. Initial program 55.4%

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

   3. Taylor expanded in C around inf 70.3%

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

      1. associate-*r/ 70.3%

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

      2. distribute-rgt1-in 70.3%

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

      3. metadata-eval 70.3%

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

      4. mul0-lft 70.3%

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

      5. metadata-eval 70.3%

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

   5. Simplified 70.3%

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

   if 9.8000000000000003e-216 < B < 2.5500000000000001e-110

   1. Initial program 30.7%

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

   3. Taylor expanded in A around -inf 54.3%

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

   4. Taylor expanded in B around 0 62.3%

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

      1. associate-*r/ 62.4%

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

   6. Simplified 62.4%

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

   if 2.5500000000000001e-110 < B

   1. Initial program 53.1%

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

   4. Applied egg-rr 75.7%

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

      1. clear-num 75.7%

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

      2. inv-pow 75.7%

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

      3. div-inv 75.7%

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

      4. associate--l- 74.9%

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

      5. metadata-eval 74.9%

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

   6. Applied egg-rr 74.9%

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

   8. Simplified 75.7%

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

   9. Taylor expanded in A around 0 47.4%

      \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{\color{blue}{C - \sqrt{{B}^{2} + {C}^{2}}}}{B}\right)}{\pi}}{0.005555555555555556} \]
   10. Step-by-step derivation

       1. unpow2 47.4%

          \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi}}{0.005555555555555556} \]

       2. unpow2 47.4%

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

       3. hypot-undefine 68.1%

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

   11. Simplified 68.1%

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

   12. Taylor expanded in C around 0 66.3%

       \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{\color{blue}{C - B}}{B}\right)}{\pi}}{0.005555555555555556} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.55 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-308}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.8 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-110}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}}{0.005555555555555556}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 56.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.5 \cdot 10^{+78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{-247}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.2 \cdot 10^{-97}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.5e+78)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 1.35e-247)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (if (<= A 3.2e-97)
       (* 180.0 (/ (atan -1.0) PI))
       (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.5e+78) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 1.35e-247) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (A <= 3.2e-97) {
		tmp = 180.0 * (atan(-1.0) / ((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 <= -3.5e+78) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 1.35e-247) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (A <= 3.2e-97) {
		tmp = 180.0 * (Math.atan(-1.0) / 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 <= -3.5e+78:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 1.35e-247:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif A <= 3.2e-97:
		tmp = 180.0 * (math.atan(-1.0) / 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 <= -3.5e+78)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 1.35e-247)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (A <= 3.2e-97)
		tmp = Float64(180.0 * Float64(atan(-1.0) / 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 <= -3.5e+78)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 1.35e-247)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (A <= 3.2e-97)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.5e+78], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.35e-247], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.2e-97], N[(180.0 * N[(N[ArcTan[-1.0], $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 < -3.5000000000000001e78

   1. Initial program 29.7%

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

   3. Taylor expanded in A around -inf 70.4%

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

      1. associate-*r/ 70.4%

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

   5. Simplified 70.4%

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

   if -3.5000000000000001e78 < A < 1.35000000000000004e-247

   1. Initial program 58.4%

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

   3. Taylor expanded in B around -inf 47.4%

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

      1. associate--l+ 47.4%

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

      2. div-sub 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in C around inf 48.6%

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

   if 1.35000000000000004e-247 < A < 3.1999999999999998e-97

   1. Initial program 37.2%

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

   3. Taylor expanded in B around inf 40.8%

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

   if 3.1999999999999998e-97 < A

   1. Initial program 71.9%

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

   3. Taylor expanded in B around -inf 70.3%

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

      1. associate--l+ 70.3%

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

      2. div-sub 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in C around 0 68.7%

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

      1. associate-*r/ 68.7%

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

      2. neg-mul-1 68.7%

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

   8. Simplified 68.7%

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

   9. Taylor expanded in A around 0 68.7%

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

       1. mul-1-neg 68.7%

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

       2. distribute-frac-neg 68.7%

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

       3. distribute-frac-neg 68.7%

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

       4. sub-neg 68.7%

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

   11. Simplified 68.7%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.5 \cdot 10^{+78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{-247}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.2 \cdot 10^{-97}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 56.7% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -7.5 \cdot 10^{+78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.95 \cdot 10^{-248}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -7.5e+78)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 1.95e-248)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (if (<= A 9.6e-99)
       (/ 180.0 (/ PI (atan (* -0.5 (/ B C)))))
       (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -7.5e+78) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 1.95e-248) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (A <= 9.6e-99) {
		tmp = 180.0 / (((double) M_PI) / atan((-0.5 * (B / C))));
	} 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 <= -7.5e+78) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 1.95e-248) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (A <= 9.6e-99) {
		tmp = 180.0 / (Math.PI / Math.atan((-0.5 * (B / C))));
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -7.5e+78:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 1.95e-248:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif A <= 9.6e-99:
		tmp = 180.0 / (math.pi / math.atan((-0.5 * (B / C))))
	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 <= -7.5e+78)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 1.95e-248)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (A <= 9.6e-99)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-0.5 * Float64(B / C)))));
	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 <= -7.5e+78)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 1.95e-248)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (A <= 9.6e-99)
		tmp = 180.0 / (pi / atan((-0.5 * (B / C))));
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -7.5e+78], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.95e-248], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9.6e-99], N[(180.0 / N[(Pi / N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $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 < -7.49999999999999934e78

   1. Initial program 29.7%

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

   3. Taylor expanded in A around -inf 70.4%

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

      1. associate-*r/ 70.4%

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

   5. Simplified 70.4%

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

   if -7.49999999999999934e78 < A < 1.95e-248

   1. Initial program 58.4%

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

   3. Taylor expanded in B around -inf 47.4%

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

      1. associate--l+ 47.4%

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

      2. div-sub 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in C around inf 48.6%

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

   if 1.95e-248 < A < 9.6000000000000002e-99

   1. Initial program 34.7%

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

   4. Applied egg-rr 61.7%

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

   5. Taylor expanded in A around 0 34.7%

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

      1. unpow2 34.7%

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

      2. unpow2 34.7%

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

      3. hypot-define 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in C around inf 47.7%

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

   if 9.6000000000000002e-99 < A

   1. Initial program 72.2%

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

   3. Taylor expanded in B around -inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. div-sub 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in C around 0 67.9%

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

      1. associate-*r/ 67.9%

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

      2. neg-mul-1 67.9%

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

   8. Simplified 67.9%

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

   9. Taylor expanded in A around 0 67.9%

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

       1. mul-1-neg 67.9%

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

       2. distribute-frac-neg 67.9%

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

       3. distribute-frac-neg 67.9%

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

       4. sub-neg 67.9%

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

   11. Simplified 67.9%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7.5 \cdot 10^{+78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.95 \cdot 10^{-248}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 56.8% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{+78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{-248}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C}{B}\right)}}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-105}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.1e+78)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 9e-248)
     (/ 180.0 (/ PI (atan (+ 1.0 (/ C B)))))
     (if (<= A 1.25e-105)
       (/ 180.0 (/ PI (atan (* -0.5 (/ B C)))))
       (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.1e+78) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 9e-248) {
		tmp = 180.0 / (((double) M_PI) / atan((1.0 + (C / B))));
	} else if (A <= 1.25e-105) {
		tmp = 180.0 / (((double) M_PI) / atan((-0.5 * (B / C))));
	} 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 <= -2.1e+78) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 9e-248) {
		tmp = 180.0 / (Math.PI / Math.atan((1.0 + (C / B))));
	} else if (A <= 1.25e-105) {
		tmp = 180.0 / (Math.PI / Math.atan((-0.5 * (B / C))));
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.1e+78:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 9e-248:
		tmp = 180.0 / (math.pi / math.atan((1.0 + (C / B))))
	elif A <= 1.25e-105:
		tmp = 180.0 / (math.pi / math.atan((-0.5 * (B / C))))
	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 <= -2.1e+78)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 9e-248)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(1.0 + Float64(C / B)))));
	elseif (A <= 1.25e-105)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-0.5 * Float64(B / C)))));
	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 <= -2.1e+78)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 9e-248)
		tmp = 180.0 / (pi / atan((1.0 + (C / B))));
	elseif (A <= 1.25e-105)
		tmp = 180.0 / (pi / atan((-0.5 * (B / C))));
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.1e+78], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9e-248], N[(180.0 / N[(Pi / N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.25e-105], N[(180.0 / N[(Pi / N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $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 < -2.1000000000000001e78

   1. Initial program 29.7%

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

   3. Taylor expanded in A around -inf 70.4%

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

      1. associate-*r/ 70.4%

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

   5. Simplified 70.4%

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

   if -2.1000000000000001e78 < A < 8.9999999999999992e-248

   1. Initial program 58.4%

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

   4. Applied egg-rr 78.7%

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

   5. Taylor expanded in A around 0 58.3%

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

      1. unpow2 58.3%

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

      2. unpow2 58.3%

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

      3. hypot-define 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in B around -inf 48.6%

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

   if 8.9999999999999992e-248 < A < 1.24999999999999991e-105

   1. Initial program 34.7%

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

   4. Applied egg-rr 61.7%

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

   5. Taylor expanded in A around 0 34.7%

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

      1. unpow2 34.7%

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

      2. unpow2 34.7%

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

      3. hypot-define 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in C around inf 47.7%

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

   if 1.24999999999999991e-105 < A

   1. Initial program 72.2%

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

   3. Taylor expanded in B around -inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. div-sub 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in C around 0 67.9%

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

      1. associate-*r/ 67.9%

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

      2. neg-mul-1 67.9%

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

   8. Simplified 67.9%

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

   9. Taylor expanded in A around 0 67.9%

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

       1. mul-1-neg 67.9%

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

       2. distribute-frac-neg 67.9%

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

       3. distribute-frac-neg 67.9%

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

       4. sub-neg 67.9%

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

   11. Simplified 67.9%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{+78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9 \cdot 10^{-248}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C}{B}\right)}}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-105}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 45.6% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.9 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.58 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.9e-60)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -1.58e-223)
     (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
     (if (<= B 2.1e-106)
       (* 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 <= -1.9e-60) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -1.58e-223) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 2.1e-106) {
		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 <= -1.9e-60) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -1.58e-223) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 2.1e-106) {
		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 <= -1.9e-60:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -1.58e-223:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 2.1e-106:
		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 <= -1.9e-60)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -1.58e-223)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 2.1e-106)
		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 <= -1.9e-60)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -1.58e-223)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 2.1e-106)
		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, -1.9e-60], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.58e-223], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.1e-106], 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 < -1.89999999999999997e-60

   1. Initial program 47.3%

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

   3. Taylor expanded in B around -inf 47.0%

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

   if -1.89999999999999997e-60 < B < -1.58e-223

   1. Initial program 75.5%

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

   3. Taylor expanded in A around inf 56.6%

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

   if -1.58e-223 < B < 2.10000000000000003e-106

   1. Initial program 48.8%

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

   3. Taylor expanded in C around inf 44.5%

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

      1. associate-*r/ 44.5%

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

      2. distribute-rgt1-in 44.5%

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

      3. metadata-eval 44.5%

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

      4. mul0-lft 44.5%

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

      5. metadata-eval 44.5%

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

   5. Simplified 44.5%

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

   if 2.10000000000000003e-106 < B

   1. Initial program 53.1%

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

   3. Taylor expanded in B around inf 55.5%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.9 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.58 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 44.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.6 \cdot 10^{-153}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.6e-153)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.75e-106)
     (* 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 <= -3.6e-153) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.75e-106) {
		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 <= -3.6e-153) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.75e-106) {
		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 <= -3.6e-153:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.75e-106:
		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 <= -3.6e-153)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.75e-106)
		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 <= -3.6e-153)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.75e-106)
		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, -3.6e-153], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.75e-106], 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 < -3.5999999999999998e-153

   1. Initial program 51.9%

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

   3. Taylor expanded in B around -inf 43.1%

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

   if -3.5999999999999998e-153 < B < 1.75e-106

   1. Initial program 55.1%

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

   3. Taylor expanded in C around inf 41.4%

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

      1. associate-*r/ 41.4%

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

      2. distribute-rgt1-in 41.4%

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

      3. metadata-eval 41.4%

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

      4. mul0-lft 41.4%

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

      5. metadata-eval 41.4%

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

   5. Simplified 41.4%

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

   if 1.75e-106 < B

   1. Initial program 53.1%

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

   3. Taylor expanded in B around inf 55.5%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.6 \cdot 10^{-153}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-106}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 40.1% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.8 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.8e-302)
   (* 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 <= -3.8e-302) {
		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 <= -3.8e-302) {
		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 <= -3.8e-302:
		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 <= -3.8e-302)
		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 <= -3.8e-302)
		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, -3.8e-302], 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 < -3.8e-302

   1. Initial program 54.7%

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

   3. Taylor expanded in B around -inf 36.4%

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

   if -3.8e-302 < B

   1. Initial program 51.8%

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

   3. Taylor expanded in B around inf 43.2%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.8 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 20.9% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 53.2%

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

3. Taylor expanded in B around inf 23.0%

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

4. Final simplification 23.0%

   \[\leadsto 180 \cdot \frac{\tan^{-1} -1}{\pi} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024080 
(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)))