ABCF->ab-angle angle

Percentage Accurate: 53.1% → 80.7%

Time: 15.5s

Alternatives: 21

Speedup: 2.4×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 2.65 \cdot 10^{+29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - \mathsf{hypot}\left(B, A - C\right)\right) - A\right)\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.9 \cdot 10^{+34}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.3 \cdot 10^{+65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\frac{\pi}{180}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 2.65e+29)
   (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C (hypot B (- A C))) A))) PI))
   (if (<= C 3.9e+34)
     (/ (* 180.0 (atan (/ (* B -0.5) C))) PI)
     (if (<= C 2.3e+65)
       (* 180.0 (/ (atan (/ (- (- A) (hypot B A)) B)) PI))
       (/ (atan (/ -0.5 (/ C B))) (/ PI 180.0))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.65e+29) {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - hypot(B, (A - C))) - A))) / ((double) M_PI));
	} else if (C <= 3.9e+34) {
		tmp = (180.0 * atan(((B * -0.5) / C))) / ((double) M_PI);
	} else if (C <= 2.3e+65) {
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / ((double) M_PI));
	} else {
		tmp = atan((-0.5 / (C / B))) / (((double) M_PI) / 180.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.65e+29) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C - Math.hypot(B, (A - C))) - A))) / Math.PI);
	} else if (C <= 3.9e+34) {
		tmp = (180.0 * Math.atan(((B * -0.5) / C))) / Math.PI;
	} else if (C <= 2.3e+65) {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(B, A)) / B)) / Math.PI);
	} else {
		tmp = Math.atan((-0.5 / (C / B))) / (Math.PI / 180.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 2.65e+29:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C - math.hypot(B, (A - C))) - A))) / math.pi)
	elif C <= 3.9e+34:
		tmp = (180.0 * math.atan(((B * -0.5) / C))) / math.pi
	elif C <= 2.3e+65:
		tmp = 180.0 * (math.atan(((-A - math.hypot(B, A)) / B)) / math.pi)
	else:
		tmp = math.atan((-0.5 / (C / B))) / (math.pi / 180.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 2.65e+29)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - hypot(B, Float64(A - C))) - A))) / pi));
	elseif (C <= 3.9e+34)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / C))) / pi);
	elseif (C <= 2.3e+65)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(B, A)) / B)) / pi));
	else
		tmp = Float64(atan(Float64(-0.5 / Float64(C / B))) / Float64(pi / 180.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 2.65e+29)
		tmp = 180.0 * (atan(((1.0 / B) * ((C - hypot(B, (A - C))) - A))) / pi);
	elseif (C <= 3.9e+34)
		tmp = (180.0 * atan(((B * -0.5) / C))) / pi;
	elseif (C <= 2.3e+65)
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / pi);
	else
		tmp = atan((-0.5 / (C / B))) / (pi / 180.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 2.65e+29], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.9e+34], N[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 2.3e+65], 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[ArcTan[N[(-0.5 / N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < 2.65e29

   1. Initial program 64.9%

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

      1. associate--l- 63.5%

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

      2. sub-neg 63.5%

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

      3. unpow2 63.5%

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

      4. unpow2 63.5%

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

      5. hypot-def 79.0%

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

   3. Applied egg-rr 79.0%

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

      1. unsub-neg 79.0%

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

      2. +-commutative 79.0%

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

      3. associate--r+ 84.8%

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

   5. Simplified 84.8%

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

   if 2.65e29 < C < 3.90000000000000019e34

   1. Initial program 4.4%

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

   2. Taylor expanded in A around 0 4.4%

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

      1. unpow2 4.4%

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

      2. unpow2 4.4%

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

      3. hypot-def 4.4%

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

   4. Simplified 4.4%

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

   5. Taylor expanded in C around inf 97.2%

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

      1. associate-*r/ 97.2%

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

   7. Simplified 97.2%

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

      1. associate-*r/ 97.8%

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

      2. *-commutative 97.8%

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

   9. Applied egg-rr 97.8%

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

   if 3.90000000000000019e34 < C < 2.3e65

   1. Initial program 24.5%

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

   2. Taylor expanded in C around 0 24.5%

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

      1. associate-*r/ 24.5%

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

      2. mul-1-neg 24.5%

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

      3. unpow2 24.5%

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

      4. unpow2 24.5%

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

      5. hypot-def 73.2%

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

   4. Simplified 73.2%

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

   if 2.3e65 < C

   1. Initial program 14.3%

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

   2. Taylor expanded in A around 0 11.5%

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

      1. unpow2 11.5%

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

      2. unpow2 11.5%

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

      3. hypot-def 56.5%

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

   4. Simplified 56.5%

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

   5. Taylor expanded in C around -inf 56.5%

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

      1. associate-*r/ 56.5%

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

      2. distribute-lft-in 56.5%

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

      3. neg-mul-1 56.5%

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

      4. mul-1-neg 56.5%

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

      5. remove-double-neg 56.5%

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

      6. neg-mul-1 56.5%

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

      7. sub-neg 56.5%

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

      8. associate-*r/ 56.5%

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

      9. *-commutative 56.5%

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

      10. associate-/l* 56.5%

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

   7. Simplified 56.5%

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

   8. Taylor expanded in C around inf 72.4%

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

      1. associate-*r/ 72.4%

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

      2. associate-/l* 72.4%

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

   10. Simplified 72.4%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 2.65 \cdot 10^{+29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - \mathsf{hypot}\left(B, A - C\right)\right) - A\right)\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.9 \cdot 10^{+34}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.3 \cdot 10^{+65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\frac{\pi}{180}}\\ \end{array} \]

Alternative 2: 76.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -1.02 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -6.2 \cdot 10^{+101}:\\ \;\;\;\;180 \cdot \frac{t_0}{\pi}\\ \mathbf{elif}\;A \leq -1.7 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 5.5 \cdot 10^{+117}:\\ \;\;\;\;\frac{t_0}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (/ (- C (hypot B C)) B)))
        (t_1 (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))))
   (if (<= A -1.02e+151)
     t_1
     (if (<= A -6.2e+101)
       (* 180.0 (/ t_0 PI))
       (if (<= A -1.7e+70)
         t_1
         (if (<= A 5.5e+117)
           (/ t_0 (/ PI 180.0))
           (* 180.0 (/ (atan (/ (- (- A) (hypot B A)) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((C - hypot(B, C)) / B));
	double t_1 = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	double tmp;
	if (A <= -1.02e+151) {
		tmp = t_1;
	} else if (A <= -6.2e+101) {
		tmp = 180.0 * (t_0 / ((double) M_PI));
	} else if (A <= -1.7e+70) {
		tmp = t_1;
	} else if (A <= 5.5e+117) {
		tmp = t_0 / (((double) M_PI) / 180.0);
	} else {
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((C - Math.hypot(B, C)) / B));
	double t_1 = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	double tmp;
	if (A <= -1.02e+151) {
		tmp = t_1;
	} else if (A <= -6.2e+101) {
		tmp = 180.0 * (t_0 / Math.PI);
	} else if (A <= -1.7e+70) {
		tmp = t_1;
	} else if (A <= 5.5e+117) {
		tmp = t_0 / (Math.PI / 180.0);
	} else {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(B, A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((C - math.hypot(B, C)) / B))
	t_1 = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	tmp = 0
	if A <= -1.02e+151:
		tmp = t_1
	elif A <= -6.2e+101:
		tmp = 180.0 * (t_0 / math.pi)
	elif A <= -1.7e+70:
		tmp = t_1
	elif A <= 5.5e+117:
		tmp = t_0 / (math.pi / 180.0)
	else:
		tmp = 180.0 * (math.atan(((-A - math.hypot(B, A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(Float64(C - hypot(B, C)) / B))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi))
	tmp = 0.0
	if (A <= -1.02e+151)
		tmp = t_1;
	elseif (A <= -6.2e+101)
		tmp = Float64(180.0 * Float64(t_0 / pi));
	elseif (A <= -1.7e+70)
		tmp = t_1;
	elseif (A <= 5.5e+117)
		tmp = Float64(t_0 / Float64(pi / 180.0));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(B, A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((C - hypot(B, C)) / B));
	t_1 = 180.0 * (atan(((B * 0.5) / A)) / pi);
	tmp = 0.0;
	if (A <= -1.02e+151)
		tmp = t_1;
	elseif (A <= -6.2e+101)
		tmp = 180.0 * (t_0 / pi);
	elseif (A <= -1.7e+70)
		tmp = t_1;
	elseif (A <= 5.5e+117)
		tmp = t_0 / (pi / 180.0);
	else
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.02e+151], t$95$1, If[LessEqual[A, -6.2e+101], N[(180.0 * N[(t$95$0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.7e+70], t$95$1, If[LessEqual[A, 5.5e+117], N[(t$95$0 / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.02000000000000002e151 or -6.19999999999999998e101 < A < -1.7e70

   1. Initial program 12.1%

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

   2. Taylor expanded in A around -inf 89.1%

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

      1. associate-*r/ 89.1%

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

   4. Simplified 89.1%

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

   if -1.02000000000000002e151 < A < -6.19999999999999998e101

   1. Initial program 37.1%

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

   2. Taylor expanded in A around 0 37.1%

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

      1. unpow2 37.1%

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

      2. unpow2 37.1%

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

      3. hypot-def 100.0%

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

   4. Simplified 100.0%

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

   if -1.7e70 < A < 5.49999999999999965e117

   1. Initial program 55.8%

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

   2. Taylor expanded in A around 0 52.1%

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

      1. unpow2 52.1%

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

      2. unpow2 52.1%

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

      3. hypot-def 76.6%

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

   4. Simplified 76.6%

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

   5. Taylor expanded in C around -inf 76.6%

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

      1. associate-*r/ 76.6%

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

      2. distribute-lft-in 76.6%

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

      3. neg-mul-1 76.6%

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

      4. mul-1-neg 76.6%

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

      5. remove-double-neg 76.6%

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

      6. neg-mul-1 76.6%

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

      7. sub-neg 76.6%

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

      8. associate-*r/ 76.6%

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

      9. *-commutative 76.6%

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

      10. associate-/l* 76.6%

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

   7. Simplified 76.6%

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

   if 5.49999999999999965e117 < A

   1. Initial program 72.8%

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

   2. Taylor expanded in C around 0 72.8%

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

      1. associate-*r/ 72.8%

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

      2. mul-1-neg 72.8%

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

      3. unpow2 72.8%

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

      4. unpow2 72.8%

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

      5. hypot-def 91.2%

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

   4. Simplified 91.2%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.02 \cdot 10^{+151}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -6.2 \cdot 10^{+101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.7 \cdot 10^{+70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.5 \cdot 10^{+117}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3: 75.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -2.4 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -6.5 \cdot 10^{+101}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -4.2 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 3 \cdot 10^{+122}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI)))
        (t_1 (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))))
   (if (<= A -2.4e+151)
     t_1
     (if (<= A -6.5e+101)
       t_0
       (if (<= A -4.2e+71)
         t_1
         (if (<= A 3e+122) t_0 (* 180.0 (/ (atan (/ (- B A) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	double tmp;
	if (A <= -2.4e+151) {
		tmp = t_1;
	} else if (A <= -6.5e+101) {
		tmp = t_0;
	} else if (A <= -4.2e+71) {
		tmp = t_1;
	} else if (A <= 3e+122) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	double tmp;
	if (A <= -2.4e+151) {
		tmp = t_1;
	} else if (A <= -6.5e+101) {
		tmp = t_0;
	} else if (A <= -4.2e+71) {
		tmp = t_1;
	} else if (A <= 3e+122) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	t_1 = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	tmp = 0
	if A <= -2.4e+151:
		tmp = t_1
	elif A <= -6.5e+101:
		tmp = t_0
	elif A <= -4.2e+71:
		tmp = t_1
	elif A <= 3e+122:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi))
	tmp = 0.0
	if (A <= -2.4e+151)
		tmp = t_1;
	elseif (A <= -6.5e+101)
		tmp = t_0;
	elseif (A <= -4.2e+71)
		tmp = t_1;
	elseif (A <= 3e+122)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	t_1 = 180.0 * (atan(((B * 0.5) / A)) / pi);
	tmp = 0.0;
	if (A <= -2.4e+151)
		tmp = t_1;
	elseif (A <= -6.5e+101)
		tmp = t_0;
	elseif (A <= -4.2e+71)
		tmp = t_1;
	elseif (A <= 3e+122)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -2.4e+151], t$95$1, If[LessEqual[A, -6.5e+101], t$95$0, If[LessEqual[A, -4.2e+71], t$95$1, If[LessEqual[A, 3e+122], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.4000000000000001e151 or -6.50000000000000016e101 < A < -4.19999999999999978e71

   1. Initial program 12.1%

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

   2. Taylor expanded in A around -inf 89.1%

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

      1. associate-*r/ 89.1%

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

   4. Simplified 89.1%

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

   if -2.4000000000000001e151 < A < -6.50000000000000016e101 or -4.19999999999999978e71 < A < 2.99999999999999986e122

   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. Taylor expanded in A around 0 51.3%

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

      1. unpow2 51.3%

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

      2. unpow2 51.3%

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

      3. hypot-def 77.8%

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

   4. Simplified 77.8%

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

   if 2.99999999999999986e122 < A

   1. Initial program 74.1%

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

      1. associate--l- 74.1%

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

      2. sub-neg 74.1%

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

      3. unpow2 74.1%

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

      4. unpow2 74.1%

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

      5. hypot-def 95.6%

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

   3. Applied egg-rr 95.6%

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

      1. unsub-neg 95.6%

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

      2. +-commutative 95.6%

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

      3. associate--r+ 91.0%

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

   5. Simplified 91.0%

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

   6. Taylor expanded in C around 0 74.0%

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

      1. associate-*r/ 74.0%

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

      2. mul-1-neg 74.0%

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

      3. distribute-neg-in 74.0%

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

      4. unsub-neg 74.0%

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

      5. unpow2 74.0%

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

      6. unpow2 74.0%

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

      7. hypot-def 91.0%

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

   8. Simplified 91.0%

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

   9. Taylor expanded in B around -inf 86.5%

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

       1. neg-mul-1 86.5%

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

       2. +-commutative 86.5%

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

       3. unsub-neg 86.5%

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

   11. Simplified 86.5%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.4 \cdot 10^{+151}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -6.5 \cdot 10^{+101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.2 \cdot 10^{+71}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{+122}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 74.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -5 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -6.5 \cdot 10^{+101}:\\ \;\;\;\;180 \cdot \frac{t_0}{\pi}\\ \mathbf{elif}\;A \leq -1.6 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 7 \cdot 10^{+121}:\\ \;\;\;\;\frac{t_0}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (/ (- C (hypot B C)) B)))
        (t_1 (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))))
   (if (<= A -5e+150)
     t_1
     (if (<= A -6.5e+101)
       (* 180.0 (/ t_0 PI))
       (if (<= A -1.6e+73)
         t_1
         (if (<= A 7e+121)
           (/ t_0 (/ PI 180.0))
           (* 180.0 (/ (atan (/ (- B A) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((C - hypot(B, C)) / B));
	double t_1 = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	double tmp;
	if (A <= -5e+150) {
		tmp = t_1;
	} else if (A <= -6.5e+101) {
		tmp = 180.0 * (t_0 / ((double) M_PI));
	} else if (A <= -1.6e+73) {
		tmp = t_1;
	} else if (A <= 7e+121) {
		tmp = t_0 / (((double) M_PI) / 180.0);
	} else {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((C - Math.hypot(B, C)) / B));
	double t_1 = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	double tmp;
	if (A <= -5e+150) {
		tmp = t_1;
	} else if (A <= -6.5e+101) {
		tmp = 180.0 * (t_0 / Math.PI);
	} else if (A <= -1.6e+73) {
		tmp = t_1;
	} else if (A <= 7e+121) {
		tmp = t_0 / (Math.PI / 180.0);
	} else {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((C - math.hypot(B, C)) / B))
	t_1 = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	tmp = 0
	if A <= -5e+150:
		tmp = t_1
	elif A <= -6.5e+101:
		tmp = 180.0 * (t_0 / math.pi)
	elif A <= -1.6e+73:
		tmp = t_1
	elif A <= 7e+121:
		tmp = t_0 / (math.pi / 180.0)
	else:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(Float64(C - hypot(B, C)) / B))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi))
	tmp = 0.0
	if (A <= -5e+150)
		tmp = t_1;
	elseif (A <= -6.5e+101)
		tmp = Float64(180.0 * Float64(t_0 / pi));
	elseif (A <= -1.6e+73)
		tmp = t_1;
	elseif (A <= 7e+121)
		tmp = Float64(t_0 / Float64(pi / 180.0));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((C - hypot(B, C)) / B));
	t_1 = 180.0 * (atan(((B * 0.5) / A)) / pi);
	tmp = 0.0;
	if (A <= -5e+150)
		tmp = t_1;
	elseif (A <= -6.5e+101)
		tmp = 180.0 * (t_0 / pi);
	elseif (A <= -1.6e+73)
		tmp = t_1;
	elseif (A <= 7e+121)
		tmp = t_0 / (pi / 180.0);
	else
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -5e+150], t$95$1, If[LessEqual[A, -6.5e+101], N[(180.0 * N[(t$95$0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.6e+73], t$95$1, If[LessEqual[A, 7e+121], N[(t$95$0 / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -5.00000000000000009e150 or -6.50000000000000016e101 < A < -1.59999999999999991e73

   1. Initial program 12.1%

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

   2. Taylor expanded in A around -inf 89.1%

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

      1. associate-*r/ 89.1%

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

   4. Simplified 89.1%

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

   if -5.00000000000000009e150 < A < -6.50000000000000016e101

   1. Initial program 37.1%

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

   2. Taylor expanded in A around 0 37.1%

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

      1. unpow2 37.1%

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

      2. unpow2 37.1%

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

      3. hypot-def 100.0%

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

   4. Simplified 100.0%

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

   if -1.59999999999999991e73 < A < 6.9999999999999999e121

   1. Initial program 55.6%

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

   2. Taylor expanded in A around 0 51.9%

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

      1. unpow2 51.9%

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

      2. unpow2 51.9%

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

      3. hypot-def 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in C around -inf 76.7%

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

      1. associate-*r/ 76.7%

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

      2. distribute-lft-in 76.7%

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

      3. neg-mul-1 76.7%

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

      4. mul-1-neg 76.7%

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

      5. remove-double-neg 76.7%

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

      6. neg-mul-1 76.7%

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

      7. sub-neg 76.7%

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

      8. associate-*r/ 76.7%

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

      9. *-commutative 76.7%

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

      10. associate-/l* 76.7%

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

   7. Simplified 76.7%

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

   if 6.9999999999999999e121 < A

   1. Initial program 74.1%

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

      1. associate--l- 74.1%

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

      2. sub-neg 74.1%

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

      3. unpow2 74.1%

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

      4. unpow2 74.1%

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

      5. hypot-def 95.6%

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

   3. Applied egg-rr 95.6%

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

      1. unsub-neg 95.6%

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

      2. +-commutative 95.6%

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

      3. associate--r+ 91.0%

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

   5. Simplified 91.0%

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

   6. Taylor expanded in C around 0 74.0%

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

      1. associate-*r/ 74.0%

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

      2. mul-1-neg 74.0%

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

      3. distribute-neg-in 74.0%

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

      4. unsub-neg 74.0%

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

      5. unpow2 74.0%

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

      6. unpow2 74.0%

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

      7. hypot-def 91.0%

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

   8. Simplified 91.0%

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

   9. Taylor expanded in B around -inf 86.5%

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

       1. neg-mul-1 86.5%

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

       2. +-commutative 86.5%

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

       3. unsub-neg 86.5%

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

   11. Simplified 86.5%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{+150}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -6.5 \cdot 10^{+101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.6 \cdot 10^{+73}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7 \cdot 10^{+121}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 80.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 1.55 \cdot 10^{+29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - \mathsf{hypot}\left(B, A - C\right)\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.8 \cdot 10^{+65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\frac{\pi}{180}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 1.55e+29)
   (* 180.0 (/ (atan (/ (- (- C (hypot B (- A C))) A) B)) PI))
   (if (<= C 4.1e+34)
     (/ (* 180.0 (atan (/ (* B -0.5) C))) PI)
     (if (<= C 3.8e+65)
       (* 180.0 (/ (atan (/ (- (- A) (hypot B A)) B)) PI))
       (/ (atan (/ -0.5 (/ C B))) (/ PI 180.0))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.55e+29) {
		tmp = 180.0 * (atan((((C - hypot(B, (A - C))) - A) / B)) / ((double) M_PI));
	} else if (C <= 4.1e+34) {
		tmp = (180.0 * atan(((B * -0.5) / C))) / ((double) M_PI);
	} else if (C <= 3.8e+65) {
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / ((double) M_PI));
	} else {
		tmp = atan((-0.5 / (C / B))) / (((double) M_PI) / 180.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.55e+29) {
		tmp = 180.0 * (Math.atan((((C - Math.hypot(B, (A - C))) - A) / B)) / Math.PI);
	} else if (C <= 4.1e+34) {
		tmp = (180.0 * Math.atan(((B * -0.5) / C))) / Math.PI;
	} else if (C <= 3.8e+65) {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(B, A)) / B)) / Math.PI);
	} else {
		tmp = Math.atan((-0.5 / (C / B))) / (Math.PI / 180.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 1.55e+29:
		tmp = 180.0 * (math.atan((((C - math.hypot(B, (A - C))) - A) / B)) / math.pi)
	elif C <= 4.1e+34:
		tmp = (180.0 * math.atan(((B * -0.5) / C))) / math.pi
	elif C <= 3.8e+65:
		tmp = 180.0 * (math.atan(((-A - math.hypot(B, A)) / B)) / math.pi)
	else:
		tmp = math.atan((-0.5 / (C / B))) / (math.pi / 180.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 1.55e+29)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - hypot(B, Float64(A - C))) - A) / B)) / pi));
	elseif (C <= 4.1e+34)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / C))) / pi);
	elseif (C <= 3.8e+65)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(B, A)) / B)) / pi));
	else
		tmp = Float64(atan(Float64(-0.5 / Float64(C / B))) / Float64(pi / 180.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 1.55e+29)
		tmp = 180.0 * (atan((((C - hypot(B, (A - C))) - A) / B)) / pi);
	elseif (C <= 4.1e+34)
		tmp = (180.0 * atan(((B * -0.5) / C))) / pi;
	elseif (C <= 3.8e+65)
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / pi);
	else
		tmp = atan((-0.5 / (C / B))) / (pi / 180.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 1.55e+29], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.1e+34], N[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 3.8e+65], 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[ArcTan[N[(-0.5 / N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < 1.5499999999999999e29

   1. Initial program 64.9%

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

   2. Taylor expanded in B around 0 63.5%

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

      1. +-commutative 63.5%

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

   4. Simplified 84.8%

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

   if 1.5499999999999999e29 < C < 4.0999999999999998e34

   1. Initial program 4.4%

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

   2. Taylor expanded in A around 0 4.4%

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

      1. unpow2 4.4%

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

      2. unpow2 4.4%

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

      3. hypot-def 4.4%

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

   4. Simplified 4.4%

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

   5. Taylor expanded in C around inf 97.2%

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

      1. associate-*r/ 97.2%

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

   7. Simplified 97.2%

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

      1. associate-*r/ 97.8%

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

      2. *-commutative 97.8%

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

   9. Applied egg-rr 97.8%

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

   if 4.0999999999999998e34 < C < 3.80000000000000011e65

   1. Initial program 24.5%

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

   2. Taylor expanded in C around 0 24.5%

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

      1. associate-*r/ 24.5%

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

      2. mul-1-neg 24.5%

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

      3. unpow2 24.5%

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

      4. unpow2 24.5%

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

      5. hypot-def 73.2%

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

   4. Simplified 73.2%

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

   if 3.80000000000000011e65 < C

   1. Initial program 14.3%

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

   2. Taylor expanded in A around 0 11.5%

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

      1. unpow2 11.5%

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

      2. unpow2 11.5%

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

      3. hypot-def 56.5%

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

   4. Simplified 56.5%

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

   5. Taylor expanded in C around -inf 56.5%

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

      1. associate-*r/ 56.5%

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

      2. distribute-lft-in 56.5%

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

      3. neg-mul-1 56.5%

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

      4. mul-1-neg 56.5%

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

      5. remove-double-neg 56.5%

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

      6. neg-mul-1 56.5%

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

      7. sub-neg 56.5%

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

      8. associate-*r/ 56.5%

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

      9. *-commutative 56.5%

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

      10. associate-/l* 56.5%

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

   7. Simplified 56.5%

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

   8. Taylor expanded in C around inf 72.4%

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

      1. associate-*r/ 72.4%

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

      2. associate-/l* 72.4%

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

   10. Simplified 72.4%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 1.55 \cdot 10^{+29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - \mathsf{hypot}\left(B, A - C\right)\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.8 \cdot 10^{+65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\frac{\pi}{180}}\\ \end{array} \]

Alternative 6: 65.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq 1.8 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-151}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-104}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{C} + t_0 \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t_0 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B 1.8e-202)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 2.4e-151)
       (/ (* 180.0 (atan (/ (* B -0.5) C))) PI)
       (if (<= B 3.9e-104)
         (* 180.0 (/ (atan (+ (/ (* B 0.5) C) (* t_0 2.0))) PI))
         (if (<= B 1.3e-87)
           (* 180.0 (/ (atan (/ -0.5 (/ C B))) PI))
           (* 180.0 (/ (atan (+ t_0 -1.0)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 1.8e-202) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 2.4e-151) {
		tmp = (180.0 * atan(((B * -0.5) / C))) / ((double) M_PI);
	} else if (B <= 3.9e-104) {
		tmp = 180.0 * (atan((((B * 0.5) / C) + (t_0 * 2.0))) / ((double) M_PI));
	} else if (B <= 1.3e-87) {
		tmp = 180.0 * (atan((-0.5 / (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((t_0 + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 1.8e-202) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 2.4e-151) {
		tmp = (180.0 * Math.atan(((B * -0.5) / C))) / Math.PI;
	} else if (B <= 3.9e-104) {
		tmp = 180.0 * (Math.atan((((B * 0.5) / C) + (t_0 * 2.0))) / Math.PI);
	} else if (B <= 1.3e-87) {
		tmp = 180.0 * (Math.atan((-0.5 / (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((t_0 + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= 1.8e-202:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 2.4e-151:
		tmp = (180.0 * math.atan(((B * -0.5) / C))) / math.pi
	elif B <= 3.9e-104:
		tmp = 180.0 * (math.atan((((B * 0.5) / C) + (t_0 * 2.0))) / math.pi)
	elif B <= 1.3e-87:
		tmp = 180.0 * (math.atan((-0.5 / (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((t_0 + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= 1.8e-202)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 2.4e-151)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / C))) / pi);
	elseif (B <= 3.9e-104)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(B * 0.5) / C) + Float64(t_0 * 2.0))) / pi));
	elseif (B <= 1.3e-87)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 / Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= 1.8e-202)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 2.4e-151)
		tmp = (180.0 * atan(((B * -0.5) / C))) / pi;
	elseif (B <= 3.9e-104)
		tmp = 180.0 * (atan((((B * 0.5) / C) + (t_0 * 2.0))) / pi);
	elseif (B <= 1.3e-87)
		tmp = 180.0 * (atan((-0.5 / (C / B))) / pi);
	else
		tmp = 180.0 * (atan((t_0 + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, 1.8e-202], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.4e-151], N[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 3.9e-104], N[(180.0 * N[(N[ArcTan[N[(N[(N[(B * 0.5), $MachinePrecision] / C), $MachinePrecision] + N[(t$95$0 * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.3e-87], N[(180.0 * N[(N[ArcTan[N[(-0.5 / N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < 1.8000000000000001e-202

   1. Initial program 53.3%

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

   2. Taylor expanded in B around -inf 63.2%

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

      1. associate--l+ 63.2%

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

      2. div-sub 64.6%

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

   4. Simplified 64.6%

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

   if 1.8000000000000001e-202 < B < 2.4e-151

   1. Initial program 19.3%

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

   2. Taylor expanded in A around 0 18.6%

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

      1. unpow2 18.6%

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

      2. unpow2 18.6%

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

      3. hypot-def 68.4%

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

   4. Simplified 68.4%

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

   5. Taylor expanded in C around inf 59.8%

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

      1. associate-*r/ 59.8%

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

   7. Simplified 59.8%

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

      1. associate-*r/ 60.0%

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

      2. *-commutative 60.0%

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

   9. Applied egg-rr 60.0%

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

   if 2.4e-151 < B < 3.9000000000000002e-104

   1. Initial program 70.4%

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

   2. Taylor expanded in C around -inf 70.6%

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

      1. +-commutative 70.6%

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

      2. +-commutative 70.6%

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

      3. associate-+l+ 70.6%

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

      4. associate-*r/ 70.6%

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

      5. metadata-eval 70.6%

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

      6. cancel-sign-sub-inv 70.6%

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

      7. distribute-lft-out-- 70.6%

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

      8. div-sub 70.6%

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

   4. Simplified 70.6%

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

   if 3.9000000000000002e-104 < B < 1.30000000000000001e-87

   1. Initial program 20.0%

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

   2. Taylor expanded in A around 0 3.8%

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

      1. unpow2 3.8%

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

      2. unpow2 3.8%

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

      3. hypot-def 5.7%

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

   4. Simplified 5.7%

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

   5. Taylor expanded in C around inf 84.2%

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

      1. associate-*r/ 84.5%

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

      2. associate-/l* 84.2%

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

   7. Simplified 84.2%

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

   if 1.30000000000000001e-87 < B

   1. Initial program 51.4%

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

   2. Taylor expanded in B around inf 75.5%

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

      1. +-commutative 75.5%

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

      2. associate--r+ 75.5%

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

      3. div-sub 75.5%

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

   4. Simplified 75.5%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.8 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-151}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-104}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{C} + \frac{C - A}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 7: 59.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{if}\;A \leq -2.5 \cdot 10^{+60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.15 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.8 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-173}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI))))
   (if (<= A -2.5e+60)
     (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
     (if (<= A -2.15e-11)
       t_0
       (if (<= A -1.8e-85)
         (* 180.0 (/ (atan (/ -0.5 (/ C B))) PI))
         (if (<= A 2.6e-173)
           t_0
           (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	double tmp;
	if (A <= -2.5e+60) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= -2.15e-11) {
		tmp = t_0;
	} else if (A <= -1.8e-85) {
		tmp = 180.0 * (atan((-0.5 / (C / B))) / ((double) M_PI));
	} else if (A <= 2.6e-173) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	double tmp;
	if (A <= -2.5e+60) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= -2.15e-11) {
		tmp = t_0;
	} else if (A <= -1.8e-85) {
		tmp = 180.0 * (Math.atan((-0.5 / (C / B))) / Math.PI);
	} else if (A <= 2.6e-173) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	tmp = 0
	if A <= -2.5e+60:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= -2.15e-11:
		tmp = t_0
	elif A <= -1.8e-85:
		tmp = 180.0 * (math.atan((-0.5 / (C / B))) / math.pi)
	elif A <= 2.6e-173:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi))
	tmp = 0.0
	if (A <= -2.5e+60)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= -2.15e-11)
		tmp = t_0;
	elseif (A <= -1.8e-85)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 / Float64(C / B))) / pi));
	elseif (A <= 2.6e-173)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C / B) + -1.0)) / pi);
	tmp = 0.0;
	if (A <= -2.5e+60)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= -2.15e-11)
		tmp = t_0;
	elseif (A <= -1.8e-85)
		tmp = 180.0 * (atan((-0.5 / (C / B))) / pi);
	elseif (A <= 2.6e-173)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / 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] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -2.5e+60], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.15e-11], t$95$0, If[LessEqual[A, -1.8e-85], N[(180.0 * N[(N[ArcTan[N[(-0.5 / N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.6e-173], t$95$0, N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -2.49999999999999987e60

   1. Initial program 15.7%

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

   2. Taylor expanded in A around -inf 76.6%

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

      1. associate-*r/ 76.6%

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

   4. Simplified 76.6%

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

   if -2.49999999999999987e60 < A < -2.15000000000000001e-11 or -1.7999999999999999e-85 < A < 2.60000000000000003e-173

   1. Initial program 60.5%

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

   2. Taylor expanded in A around 0 59.9%

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

      1. unpow2 59.9%

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

      2. unpow2 59.9%

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

      3. hypot-def 79.7%

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

   4. Simplified 79.7%

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

   5. Taylor expanded in C around 0 62.0%

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

   if -2.15000000000000001e-11 < A < -1.7999999999999999e-85

   1. Initial program 27.0%

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

   2. Taylor expanded in A around 0 27.2%

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

      1. unpow2 27.2%

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

      2. unpow2 27.2%

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

      3. hypot-def 66.0%

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

   4. Simplified 66.0%

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

   5. Taylor expanded in C around inf 59.7%

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

      1. associate-*r/ 59.7%

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

      2. associate-/l* 59.7%

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

   7. Simplified 59.7%

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

   if 2.60000000000000003e-173 < A

   1. Initial program 64.9%

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

   2. Taylor expanded in B around -inf 69.8%

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

      1. associate--l+ 69.8%

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

      2. div-sub 70.9%

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

   4. Simplified 70.9%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.5 \cdot 10^{+60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.15 \cdot 10^{-11}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.8 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 46.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{if}\;B \leq -8 \cdot 10^{+48}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-198}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-156}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-78}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))))
   (if (<= B -8e+48)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 3.1e-198)
       t_0
       (if (<= B 9.2e-156)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 1.8e-78) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	double tmp;
	if (B <= -8e+48) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 3.1e-198) {
		tmp = t_0;
	} else if (B <= 9.2e-156) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 1.8e-78) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	double tmp;
	if (B <= -8e+48) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 3.1e-198) {
		tmp = t_0;
	} else if (B <= 9.2e-156) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 1.8e-78) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	tmp = 0
	if B <= -8e+48:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 3.1e-198:
		tmp = t_0
	elif B <= 9.2e-156:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 1.8e-78:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi))
	tmp = 0.0
	if (B <= -8e+48)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 3.1e-198)
		tmp = t_0;
	elseif (B <= 9.2e-156)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 1.8e-78)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C / B) * 2.0)) / pi);
	tmp = 0.0;
	if (B <= -8e+48)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 3.1e-198)
		tmp = t_0;
	elseif (B <= 9.2e-156)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 1.8e-78)
		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[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -8e+48], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.1e-198], t$95$0, If[LessEqual[B, 9.2e-156], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.8e-78], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -8.00000000000000035e48

   1. Initial program 44.6%

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

   2. Taylor expanded in B around -inf 76.4%

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

   if -8.00000000000000035e48 < B < 3.0999999999999998e-198 or 9.1999999999999998e-156 < B < 1.8000000000000001e-78

   1. Initial program 57.8%

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

   2. Taylor expanded in C around -inf 40.0%

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

   if 3.0999999999999998e-198 < B < 9.1999999999999998e-156

   1. Initial program 19.3%

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

   2. Taylor expanded in C around inf 52.8%

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

      1. associate-*r/ 52.8%

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

      2. distribute-rgt1-in 52.8%

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

      3. metadata-eval 52.8%

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

      4. mul0-lft 52.8%

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

      5. metadata-eval 52.8%

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

   4. Simplified 52.8%

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

   if 1.8000000000000001e-78 < B

   1. Initial program 50.2%

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

   2. Taylor expanded in B around inf 57.3%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8 \cdot 10^{+48}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-198}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-156}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 9: 59.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -3.45 \cdot 10^{-87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -3 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.25 \cdot 10^{-268}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4 \cdot 10^{-21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\frac{\pi}{180}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -3.45e-87)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= C -3e-289)
     (* 180.0 (/ (atan (/ (- (- A) B) B)) PI))
     (if (<= C 1.25e-268)
       (* 180.0 (/ (atan (/ 0.5 (/ A B))) PI))
       (if (<= C 4e-21)
         (* 180.0 (/ (atan (/ (- B A) B)) PI))
         (/ (atan (/ -0.5 (/ C B))) (/ PI 180.0)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.45e-87) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (C <= -3e-289) {
		tmp = 180.0 * (atan(((-A - B) / B)) / ((double) M_PI));
	} else if (C <= 1.25e-268) {
		tmp = 180.0 * (atan((0.5 / (A / B))) / ((double) M_PI));
	} else if (C <= 4e-21) {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	} else {
		tmp = atan((-0.5 / (C / B))) / (((double) M_PI) / 180.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.45e-87) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (C <= -3e-289) {
		tmp = 180.0 * (Math.atan(((-A - B) / B)) / Math.PI);
	} else if (C <= 1.25e-268) {
		tmp = 180.0 * (Math.atan((0.5 / (A / B))) / Math.PI);
	} else if (C <= 4e-21) {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	} else {
		tmp = Math.atan((-0.5 / (C / B))) / (Math.PI / 180.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -3.45e-87:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif C <= -3e-289:
		tmp = 180.0 * (math.atan(((-A - B) / B)) / math.pi)
	elif C <= 1.25e-268:
		tmp = 180.0 * (math.atan((0.5 / (A / B))) / math.pi)
	elif C <= 4e-21:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	else:
		tmp = math.atan((-0.5 / (C / B))) / (math.pi / 180.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -3.45e-87)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (C <= -3e-289)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - B) / B)) / pi));
	elseif (C <= 1.25e-268)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 / Float64(A / B))) / pi));
	elseif (C <= 4e-21)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	else
		tmp = Float64(atan(Float64(-0.5 / Float64(C / B))) / Float64(pi / 180.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -3.45e-87)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (C <= -3e-289)
		tmp = 180.0 * (atan(((-A - B) / B)) / pi);
	elseif (C <= 1.25e-268)
		tmp = 180.0 * (atan((0.5 / (A / B))) / pi);
	elseif (C <= 4e-21)
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	else
		tmp = atan((-0.5 / (C / B))) / (pi / 180.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -3.45e-87], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -3e-289], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.25e-268], N[(180.0 * N[(N[ArcTan[N[(0.5 / N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4e-21], N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(-0.5 / N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -3.45000000000000021e-87

   1. Initial program 68.6%

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

   2. Taylor expanded in A around 0 67.8%

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

      1. unpow2 67.8%

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

      2. unpow2 67.8%

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

      3. hypot-def 86.2%

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

   4. Simplified 86.2%

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

   5. Taylor expanded in B around -inf 73.4%

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

   if -3.45000000000000021e-87 < C < -2.9999999999999998e-289

   1. Initial program 67.2%

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

      1. associate--l- 63.8%

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

      2. sub-neg 63.8%

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

      3. unpow2 63.8%

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

      4. unpow2 63.8%

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

      5. hypot-def 82.4%

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

   3. Applied egg-rr 82.4%

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

      1. unsub-neg 82.4%

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

      2. +-commutative 82.4%

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

      3. associate--r+ 92.9%

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

   5. Simplified 92.9%

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

   6. Taylor expanded in C around 0 60.2%

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

      1. associate-*r/ 60.2%

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

      2. mul-1-neg 60.2%

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

      3. distribute-neg-in 60.2%

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

      4. unsub-neg 60.2%

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

      5. unpow2 60.2%

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

      6. unpow2 60.2%

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

      7. hypot-def 86.1%

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

   8. Simplified 86.1%

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

   9. Taylor expanded in A around 0 63.6%

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

       1. neg-mul-1 63.6%

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

       2. +-commutative 63.6%

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

       3. mul-1-neg 63.6%

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

       4. unsub-neg 63.6%

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

   11. Simplified 63.6%

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

   if -2.9999999999999998e-289 < C < 1.25e-268

   1. Initial program 47.6%

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

      1. associate--l- 40.7%

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

      2. sub-neg 40.7%

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

      3. unpow2 40.7%

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

      4. unpow2 40.7%

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

      5. hypot-def 54.2%

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

   3. Applied egg-rr 54.2%

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

      1. unsub-neg 54.2%

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

      2. +-commutative 54.2%

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

      3. associate--r+ 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in C around 0 47.6%

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

      1. associate-*r/ 47.6%

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

      2. mul-1-neg 47.6%

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

      3. distribute-neg-in 47.6%

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

      4. unsub-neg 47.6%

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

      5. unpow2 47.6%

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

      6. unpow2 47.6%

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

      7. hypot-def 68.2%

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

   8. Simplified 68.2%

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

   9. Taylor expanded in A around -inf 51.9%

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

       1. associate-*r/ 51.9%

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

       2. associate-/l* 51.9%

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

   11. Simplified 51.9%

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

   if 1.25e-268 < C < 3.99999999999999963e-21

   1. Initial program 67.3%

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

      1. associate--l- 67.1%

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

      2. sub-neg 67.1%

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

      3. unpow2 67.1%

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

      4. unpow2 67.1%

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

      5. hypot-def 74.3%

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

   3. Applied egg-rr 74.3%

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

      1. unsub-neg 74.3%

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

      2. +-commutative 74.3%

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

      3. associate--r+ 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in C around 0 65.9%

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

      1. associate-*r/ 65.9%

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

      2. mul-1-neg 65.9%

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

      3. distribute-neg-in 65.9%

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

      4. unsub-neg 65.9%

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

      5. unpow2 65.9%

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

      6. unpow2 65.9%

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

      7. hypot-def 79.7%

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

   8. Simplified 79.7%

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

   9. Taylor expanded in B around -inf 53.0%

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

       1. neg-mul-1 53.0%

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

       2. +-commutative 53.0%

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

       3. unsub-neg 53.0%

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

   11. Simplified 53.0%

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

   if 3.99999999999999963e-21 < C

   1. Initial program 18.3%

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

   2. Taylor expanded in A around 0 14.1%

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

      1. unpow2 14.1%

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

      2. unpow2 14.1%

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

      3. hypot-def 51.4%

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

   4. Simplified 51.4%

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

   5. Taylor expanded in C around -inf 51.4%

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

      1. associate-*r/ 51.4%

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

      2. distribute-lft-in 51.4%

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

      3. neg-mul-1 51.4%

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

      4. mul-1-neg 51.4%

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

      5. remove-double-neg 51.4%

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

      6. neg-mul-1 51.4%

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

      7. sub-neg 51.4%

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

      8. associate-*r/ 51.4%

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

      9. *-commutative 51.4%

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

      10. associate-/l* 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in C around inf 65.0%

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

      1. associate-*r/ 65.0%

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

      2. associate-/l* 64.9%

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

   10. Simplified 64.9%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -3.45 \cdot 10^{-87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -3 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.25 \cdot 10^{-268}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4 \cdot 10^{-21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\frac{\pi}{180}}\\ \end{array} \]

Alternative 10: 51.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 3.9 \cdot 10^{-205}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-156}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.05 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 3.9e-205)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= B 1.6e-156)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (if (<= B 2.05e-78)
       (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 3.9e-205) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (B <= 1.6e-156) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 2.05e-78) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((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 <= 3.9e-205) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (B <= 1.6e-156) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 2.05e-78) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 3.9e-205:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif B <= 1.6e-156:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 2.05e-78:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / 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 <= 3.9e-205)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (B <= 1.6e-156)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 2.05e-78)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / 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 <= 3.9e-205)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (B <= 1.6e-156)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 2.05e-78)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 3.9e-205], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.6e-156], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.05e-78], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $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 < 3.90000000000000018e-205

   1. Initial program 53.3%

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

   2. Taylor expanded in A around 0 45.8%

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

      1. unpow2 45.8%

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

      2. unpow2 45.8%

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

      3. hypot-def 66.8%

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

   4. Simplified 66.8%

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

   5. Taylor expanded in B around -inf 56.8%

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

   if 3.90000000000000018e-205 < B < 1.59999999999999991e-156

   1. Initial program 19.3%

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

   2. Taylor expanded in C around inf 52.8%

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

      1. associate-*r/ 52.8%

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

      2. distribute-rgt1-in 52.8%

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

      3. metadata-eval 52.8%

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

      4. mul0-lft 52.8%

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

      5. metadata-eval 52.8%

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

   4. Simplified 52.8%

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

   if 1.59999999999999991e-156 < B < 2.0499999999999999e-78

   1. Initial program 58.8%

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

   2. Taylor expanded in C around -inf 38.3%

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

   if 2.0499999999999999e-78 < B

   1. Initial program 50.2%

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

   2. Taylor expanded in B around inf 57.3%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 3.9 \cdot 10^{-205}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-156}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.05 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11: 53.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 3 \cdot 10^{-255}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 1.4 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 3e-255)
   (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI))
   (if (<= C 9.5e-168)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= C 1.4e-67)
       (* 180.0 (/ (atan -1.0) PI))
       (* 180.0 (/ (atan (/ -0.5 (/ C B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 3e-255) {
		tmp = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	} else if (C <= 9.5e-168) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (C <= 1.4e-67) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 / (C / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 3e-255) {
		tmp = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	} else if (C <= 9.5e-168) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (C <= 1.4e-67) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 / (C / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 3e-255:
		tmp = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	elif C <= 9.5e-168:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif C <= 1.4e-67:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 / (C / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 3e-255)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi));
	elseif (C <= 9.5e-168)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (C <= 1.4e-67)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 / Float64(C / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 3e-255)
		tmp = 180.0 * (atan(((C / B) + -1.0)) / pi);
	elseif (C <= 9.5e-168)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (C <= 1.4e-67)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-0.5 / (C / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 3e-255], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 9.5e-168], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.4e-67], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 / N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < 3.00000000000000002e-255

   1. Initial program 66.5%

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

   2. Taylor expanded in A around 0 59.0%

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

      1. unpow2 59.0%

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

      2. unpow2 59.0%

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

      3. hypot-def 76.8%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in C around 0 60.8%

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

   if 3.00000000000000002e-255 < C < 9.49999999999999918e-168

   1. Initial program 58.1%

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

   2. Taylor expanded in B around -inf 46.8%

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

   if 9.49999999999999918e-168 < C < 1.40000000000000005e-67

   1. Initial program 67.8%

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

   2. Taylor expanded in B around inf 40.6%

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

   if 1.40000000000000005e-67 < C

   1. Initial program 25.5%

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

   2. Taylor expanded in A around 0 17.7%

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

      1. unpow2 17.7%

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

      2. unpow2 17.7%

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

      3. hypot-def 48.9%

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

   4. Simplified 48.9%

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

   5. Taylor expanded in C around inf 63.0%

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

      1. associate-*r/ 63.1%

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

      2. associate-/l* 63.0%

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

   7. Simplified 63.0%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 3 \cdot 10^{-255}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 1.4 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi}\\ \end{array} \]

Alternative 12: 66.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq 1.1 \cdot 10^{-198}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-158}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t_0 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B 1.1e-198)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 1.75e-158)
       (/ (* 180.0 (atan (/ (* B -0.5) C))) PI)
       (* 180.0 (/ (atan (+ t_0 -1.0)) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 1.1e-198) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 1.75e-158) {
		tmp = (180.0 * atan(((B * -0.5) / C))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((t_0 + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 1.1e-198) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 1.75e-158) {
		tmp = (180.0 * Math.atan(((B * -0.5) / C))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((t_0 + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= 1.1e-198:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 1.75e-158:
		tmp = (180.0 * math.atan(((B * -0.5) / C))) / math.pi
	else:
		tmp = 180.0 * (math.atan((t_0 + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= 1.1e-198)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 1.75e-158)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / C))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= 1.1e-198)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 1.75e-158)
		tmp = (180.0 * atan(((B * -0.5) / C))) / pi;
	else
		tmp = 180.0 * (atan((t_0 + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, 1.1e-198], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.75e-158], N[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < 1.1e-198

   1. Initial program 53.3%

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

   2. Taylor expanded in B around -inf 63.2%

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

      1. associate--l+ 63.2%

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

      2. div-sub 64.6%

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

   4. Simplified 64.6%

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

   if 1.1e-198 < B < 1.75000000000000006e-158

   1. Initial program 14.3%

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

   2. Taylor expanded in A around 0 13.5%

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

      1. unpow2 13.5%

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

      2. unpow2 13.5%

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

      3. hypot-def 62.1%

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

   4. Simplified 62.1%

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

   5. Taylor expanded in C around inf 61.6%

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

      1. associate-*r/ 61.6%

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

   7. Simplified 61.6%

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

      1. associate-*r/ 61.8%

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

      2. *-commutative 61.8%

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

   9. Applied egg-rr 61.8%

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

   if 1.75000000000000006e-158 < 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. Taylor expanded in B around inf 70.3%

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

      1. +-commutative 70.3%

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

      2. associate--r+ 70.3%

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

      3. div-sub 70.3%

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

   4. Simplified 70.3%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.1 \cdot 10^{-198}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.75 \cdot 10^{-158}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 13: 55.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.7 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-156}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.7e-202)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= B 2e-156)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.7e-202) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (B <= 2e-156) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.7e-202) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (B <= 2e-156) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 1.7e-202:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif B <= 2e-156:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 1.7e-202)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (B <= 2e-156)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 1.7e-202)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (B <= 2e-156)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(((C / B) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 1.7e-202], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2e-156], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 1.70000000000000006e-202

   1. Initial program 53.3%

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

   2. Taylor expanded in A around 0 45.8%

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

      1. unpow2 45.8%

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

      2. unpow2 45.8%

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

      3. hypot-def 66.8%

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

   4. Simplified 66.8%

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

   5. Taylor expanded in B around -inf 56.8%

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

   if 1.70000000000000006e-202 < B < 2.00000000000000008e-156

   1. Initial program 19.3%

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

   2. Taylor expanded in C around inf 52.8%

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

      1. associate-*r/ 52.8%

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

      2. distribute-rgt1-in 52.8%

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

      3. metadata-eval 52.8%

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

      4. mul0-lft 52.8%

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

      5. metadata-eval 52.8%

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

   4. Simplified 52.8%

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

   if 2.00000000000000008e-156 < B

   1. Initial program 52.0%

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

   2. Taylor expanded in A around 0 41.3%

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

      1. unpow2 41.3%

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

      2. unpow2 41.3%

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

      3. hypot-def 60.8%

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

   4. Simplified 60.8%

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

   5. Taylor expanded in C around 0 59.5%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.7 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-156}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 14: 54.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.15 \cdot 10^{-287}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.95 \cdot 10^{-178}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.15e-287)
   (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI))
   (if (<= C 1.95e-178)
     (* 180.0 (/ (atan (/ 0.5 (/ A B))) PI))
     (* 180.0 (/ (atan (/ -0.5 (/ C B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.15e-287) {
		tmp = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	} else if (C <= 1.95e-178) {
		tmp = 180.0 * (atan((0.5 / (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 / (C / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.15e-287) {
		tmp = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	} else if (C <= 1.95e-178) {
		tmp = 180.0 * (Math.atan((0.5 / (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 / (C / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.15e-287:
		tmp = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	elif C <= 1.95e-178:
		tmp = 180.0 * (math.atan((0.5 / (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 / (C / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.15e-287)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi));
	elseif (C <= 1.95e-178)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 / Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 / Float64(C / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.15e-287)
		tmp = 180.0 * (atan(((C / B) + -1.0)) / pi);
	elseif (C <= 1.95e-178)
		tmp = 180.0 * (atan((0.5 / (A / B))) / pi);
	else
		tmp = 180.0 * (atan((-0.5 / (C / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.15e-287], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.95e-178], N[(180.0 * N[(N[ArcTan[N[(0.5 / N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 / N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.14999999999999993e-287

   1. Initial program 68.3%

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

   2. Taylor expanded in A around 0 62.6%

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

      1. unpow2 62.6%

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

      2. unpow2 62.6%

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

      3. hypot-def 81.1%

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

   4. Simplified 81.1%

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

   5. Taylor expanded in C around 0 66.0%

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

   if -1.14999999999999993e-287 < C < 1.95000000000000013e-178

   1. Initial program 54.0%

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

      1. associate--l- 50.0%

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

      2. sub-neg 50.0%

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

      3. unpow2 50.0%

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

      4. unpow2 50.0%

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

      5. hypot-def 60.5%

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

   3. Applied egg-rr 60.5%

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

      1. unsub-neg 60.5%

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

      2. +-commutative 60.5%

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

      3. associate--r+ 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in C around 0 54.0%

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

      1. associate-*r/ 54.0%

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

      2. mul-1-neg 54.0%

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

      3. distribute-neg-in 54.0%

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

      4. unsub-neg 54.0%

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

      5. unpow2 54.0%

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

      6. unpow2 54.0%

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

      7. hypot-def 75.2%

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

   8. Simplified 75.2%

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

   9. Taylor expanded in A around -inf 46.1%

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

       1. associate-*r/ 46.1%

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

       2. associate-/l* 45.9%

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

   11. Simplified 45.9%

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

   if 1.95000000000000013e-178 < C

   1. Initial program 33.1%

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

   2. Taylor expanded in A around 0 23.5%

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

      1. unpow2 23.5%

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

      2. unpow2 23.5%

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

      3. hypot-def 51.4%

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

   4. Simplified 51.4%

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

   5. Taylor expanded in C around inf 56.7%

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

      1. associate-*r/ 56.7%

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

      2. associate-/l* 56.7%

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

   7. Simplified 56.6%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.15 \cdot 10^{-287}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.95 \cdot 10^{-178}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\pi}\\ \end{array} \]

Alternative 15: 54.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -4 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 6 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -4e-289)
   (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI))
   (if (<= C 6e-184)
     (* 180.0 (/ (atan (/ 0.5 (/ A B))) PI))
     (* 180.0 (/ (atan (/ (* B -0.5) C)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -4e-289) {
		tmp = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	} else if (C <= 6e-184) {
		tmp = 180.0 * (atan((0.5 / (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -4e-289) {
		tmp = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	} else if (C <= 6e-184) {
		tmp = 180.0 * (Math.atan((0.5 / (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -4e-289:
		tmp = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	elif C <= 6e-184:
		tmp = 180.0 * (math.atan((0.5 / (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -4e-289)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi));
	elseif (C <= 6e-184)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 / Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -4e-289)
		tmp = 180.0 * (atan(((C / B) + -1.0)) / pi);
	elseif (C <= 6e-184)
		tmp = 180.0 * (atan((0.5 / (A / B))) / pi);
	else
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -4e-289], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6e-184], N[(180.0 * N[(N[ArcTan[N[(0.5 / N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -4e-289

   1. Initial program 68.3%

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

   2. Taylor expanded in A around 0 62.6%

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

      1. unpow2 62.6%

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

      2. unpow2 62.6%

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

      3. hypot-def 81.1%

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

   4. Simplified 81.1%

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

   5. Taylor expanded in C around 0 66.0%

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

   if -4e-289 < C < 5.99999999999999982e-184

   1. Initial program 54.0%

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

      1. associate--l- 50.0%

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

      2. sub-neg 50.0%

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

      3. unpow2 50.0%

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

      4. unpow2 50.0%

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

      5. hypot-def 60.5%

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

   3. Applied egg-rr 60.5%

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

      1. unsub-neg 60.5%

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

      2. +-commutative 60.5%

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

      3. associate--r+ 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in C around 0 54.0%

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

      1. associate-*r/ 54.0%

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

      2. mul-1-neg 54.0%

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

      3. distribute-neg-in 54.0%

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

      4. unsub-neg 54.0%

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

      5. unpow2 54.0%

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

      6. unpow2 54.0%

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

      7. hypot-def 75.2%

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

   8. Simplified 75.2%

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

   9. Taylor expanded in A around -inf 46.1%

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

       1. associate-*r/ 46.1%

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

       2. associate-/l* 45.9%

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

   11. Simplified 45.9%

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

   if 5.99999999999999982e-184 < C

   1. Initial program 33.1%

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

   2. Taylor expanded in A around 0 23.5%

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

      1. unpow2 23.5%

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

      2. unpow2 23.5%

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

      3. hypot-def 51.4%

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

   4. Simplified 51.4%

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

   5. Taylor expanded in C around inf 56.7%

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

      1. associate-*r/ 56.7%

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

   7. Simplified 56.7%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -4 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 6 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \]

Alternative 16: 54.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -9.5 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.1 \cdot 10^{-178}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -9.5e-289)
   (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI))
   (if (<= C 2.1e-178)
     (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
     (* 180.0 (/ (atan (/ (* B -0.5) C)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -9.5e-289) {
		tmp = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	} else if (C <= 2.1e-178) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -9.5e-289) {
		tmp = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	} else if (C <= 2.1e-178) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -9.5e-289:
		tmp = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	elif C <= 2.1e-178:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -9.5e-289)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi));
	elseif (C <= 2.1e-178)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -9.5e-289)
		tmp = 180.0 * (atan(((C / B) + -1.0)) / pi);
	elseif (C <= 2.1e-178)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	else
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -9.5e-289], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.1e-178], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -9.4999999999999995e-289

   1. Initial program 68.3%

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

   2. Taylor expanded in A around 0 62.6%

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

      1. unpow2 62.6%

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

      2. unpow2 62.6%

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

      3. hypot-def 81.1%

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

   4. Simplified 81.1%

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

   5. Taylor expanded in C around 0 66.0%

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

   if -9.4999999999999995e-289 < C < 2.1e-178

   1. Initial program 54.0%

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

   2. Taylor expanded in A around -inf 46.1%

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

      1. associate-*r/ 46.1%

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

   4. Simplified 46.1%

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

   if 2.1e-178 < C

   1. Initial program 33.1%

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

   2. Taylor expanded in A around 0 23.5%

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

      1. unpow2 23.5%

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

      2. unpow2 23.5%

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

      3. hypot-def 51.4%

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

   4. Simplified 51.4%

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

   5. Taylor expanded in C around inf 56.7%

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

      1. associate-*r/ 56.7%

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

   7. Simplified 56.7%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -9.5 \cdot 10^{-289}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.1 \cdot 10^{-178}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \]

Alternative 17: 59.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -2.85 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -2.85e-223)
   (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI))
   (if (<= C 2.1e-26)
     (* 180.0 (/ (atan (/ (- B A) B)) PI))
     (* 180.0 (/ (atan (/ (* B -0.5) C)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.85e-223) {
		tmp = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	} else if (C <= 2.1e-26) {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.85e-223) {
		tmp = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	} else if (C <= 2.1e-26) {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -2.85e-223:
		tmp = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	elif C <= 2.1e-26:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -2.85e-223)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi));
	elseif (C <= 2.1e-26)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -2.85e-223)
		tmp = 180.0 * (atan(((C / B) + -1.0)) / pi);
	elseif (C <= 2.1e-26)
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	else
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -2.85e-223], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.1e-26], N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -2.8499999999999999e-223

   1. Initial program 66.7%

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

   2. Taylor expanded in A around 0 64.4%

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

      1. unpow2 64.4%

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

      2. unpow2 64.4%

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

      3. hypot-def 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in C around 0 68.7%

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

   if -2.8499999999999999e-223 < C < 2.10000000000000008e-26

   1. Initial program 65.8%

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

      1. associate--l- 64.3%

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

      2. sub-neg 64.3%

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

      3. unpow2 64.3%

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

      4. unpow2 64.3%

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

      5. hypot-def 73.2%

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

   3. Applied egg-rr 73.2%

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

      1. unsub-neg 73.2%

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

      2. +-commutative 73.2%

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

      3. associate--r+ 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in C around 0 64.9%

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

      1. associate-*r/ 64.9%

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

      2. mul-1-neg 64.9%

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

      3. distribute-neg-in 64.9%

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

      4. unsub-neg 64.9%

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

      5. unpow2 64.9%

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

      6. unpow2 64.9%

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

      7. hypot-def 79.7%

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

   8. Simplified 79.7%

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

   9. Taylor expanded in B around -inf 52.4%

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

       1. neg-mul-1 52.4%

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

       2. +-commutative 52.4%

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

       3. unsub-neg 52.4%

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

   11. Simplified 52.4%

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

   if 2.10000000000000008e-26 < C

   1. Initial program 18.3%

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

   2. Taylor expanded in A around 0 14.1%

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

      1. unpow2 14.1%

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

      2. unpow2 14.1%

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

      3. hypot-def 51.4%

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

   4. Simplified 51.4%

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

   5. Taylor expanded in C around inf 64.9%

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

      1. associate-*r/ 64.9%

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

   7. Simplified 64.9%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.85 \cdot 10^{-223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \]

Alternative 18: 59.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -6.2 \cdot 10^{-221}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.15 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\frac{\pi}{180}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -6.2e-221)
   (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI))
   (if (<= C 1.15e-20)
     (* 180.0 (/ (atan (/ (- B A) B)) PI))
     (/ (atan (/ -0.5 (/ C B))) (/ PI 180.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -6.2e-221) {
		tmp = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	} else if (C <= 1.15e-20) {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	} else {
		tmp = atan((-0.5 / (C / B))) / (((double) M_PI) / 180.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -6.2e-221) {
		tmp = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	} else if (C <= 1.15e-20) {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	} else {
		tmp = Math.atan((-0.5 / (C / B))) / (Math.PI / 180.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -6.2e-221:
		tmp = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	elif C <= 1.15e-20:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	else:
		tmp = math.atan((-0.5 / (C / B))) / (math.pi / 180.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -6.2e-221)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi));
	elseif (C <= 1.15e-20)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	else
		tmp = Float64(atan(Float64(-0.5 / Float64(C / B))) / Float64(pi / 180.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -6.2e-221)
		tmp = 180.0 * (atan(((C / B) + -1.0)) / pi);
	elseif (C <= 1.15e-20)
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	else
		tmp = atan((-0.5 / (C / B))) / (pi / 180.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -6.2e-221], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.15e-20], N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(-0.5 / N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -6.1999999999999998e-221

   1. Initial program 66.7%

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

   2. Taylor expanded in A around 0 64.4%

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

      1. unpow2 64.4%

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

      2. unpow2 64.4%

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

      3. hypot-def 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in C around 0 68.7%

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

   if -6.1999999999999998e-221 < C < 1.15e-20

   1. Initial program 65.8%

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

      1. associate--l- 64.3%

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

      2. sub-neg 64.3%

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

      3. unpow2 64.3%

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

      4. unpow2 64.3%

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

      5. hypot-def 73.2%

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

   3. Applied egg-rr 73.2%

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

      1. unsub-neg 73.2%

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

      2. +-commutative 73.2%

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

      3. associate--r+ 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in C around 0 64.9%

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

      1. associate-*r/ 64.9%

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

      2. mul-1-neg 64.9%

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

      3. distribute-neg-in 64.9%

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

      4. unsub-neg 64.9%

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

      5. unpow2 64.9%

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

      6. unpow2 64.9%

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

      7. hypot-def 79.7%

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

   8. Simplified 79.7%

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

   9. Taylor expanded in B around -inf 52.4%

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

       1. neg-mul-1 52.4%

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

       2. +-commutative 52.4%

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

       3. unsub-neg 52.4%

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

   11. Simplified 52.4%

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

   if 1.15e-20 < C

   1. Initial program 18.3%

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

   2. Taylor expanded in A around 0 14.1%

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

      1. unpow2 14.1%

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

      2. unpow2 14.1%

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

      3. hypot-def 51.4%

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

   4. Simplified 51.4%

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

   5. Taylor expanded in C around -inf 51.4%

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

      1. associate-*r/ 51.4%

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

      2. distribute-lft-in 51.4%

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

      3. neg-mul-1 51.4%

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

      4. mul-1-neg 51.4%

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

      5. remove-double-neg 51.4%

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

      6. neg-mul-1 51.4%

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

      7. sub-neg 51.4%

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

      8. associate-*r/ 51.4%

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

      9. *-commutative 51.4%

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

      10. associate-/l* 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in C around inf 65.0%

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

      1. associate-*r/ 65.0%

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

      2. associate-/l* 64.9%

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

   10. Simplified 64.9%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -6.2 \cdot 10^{-221}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.15 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-0.5}{\frac{C}{B}}\right)}{\frac{\pi}{180}}\\ \end{array} \]

Alternative 19: 45.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.2 \cdot 10^{-57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-157}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.2e-57)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.6e-157)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.2e-57) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.6e-157) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.2e-57) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.6e-157) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5.2e-57:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.6e-157:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5.2e-57)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.6e-157)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5.2e-57)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.6e-157)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5.2e-57], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.6e-157], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -5.19999999999999971e-57

   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. Taylor expanded in B around -inf 56.0%

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

   if -5.19999999999999971e-57 < B < 4.59999999999999977e-157

   1. Initial program 54.1%

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

   2. Taylor expanded in C around inf 37.8%

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

      1. associate-*r/ 37.8%

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

      2. distribute-rgt1-in 37.8%

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

      3. metadata-eval 37.8%

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

      4. mul0-lft 37.8%

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

      5. metadata-eval 37.8%

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

   4. Simplified 37.8%

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

   if 4.59999999999999977e-157 < 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. Taylor expanded in B around inf 48.1%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.2 \cdot 10^{-57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-157}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 20: 40.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.999999999999994e-310

   1. Initial program 50.2%

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

   2. Taylor expanded in B around -inf 39.7%

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

   if -1.999999999999994e-310 < B

   1. Initial program 52.0%

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

   2. Taylor expanded in B around inf 39.2%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 21: 21.0% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 51.2%

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

2. Taylor expanded in B around inf 21.3%

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

3. Final simplification 21.3%

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

Reproduce

herbie shell --seed 2023187 
(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)))