ABCF->ab-angle angle

Percentage Accurate: 53.7% → 78.1%

Time: 24.2s

Alternatives: 23

Speedup: 2.5×

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: 53.7% 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: 78.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -1.1 \cdot 10^{+148}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_1\\ \mathbf{elif}\;A \leq -1.35 \cdot 10^{-15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - t_0}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.75 \cdot 10^{-100}:\\ \;\;\;\;\frac{1}{\frac{\pi}{t_1} \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + t_0\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (hypot B (- A C))) (t_1 (atan (* 0.5 (/ B A)))))
   (if (<= A -1.1e+148)
     (* (/ 180.0 PI) t_1)
     (if (<= A -1.35e-15)
       (* 180.0 (/ (atan (/ (- (- C A) t_0) B)) PI))
       (if (<= A -1.75e-100)
         (/ 1.0 (* (/ PI t_1) 0.005555555555555556))
         (* 180.0 (/ (atan (/ (- C (+ A t_0)) B)) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = hypot(B, (A - C));
	double t_1 = atan((0.5 * (B / A)));
	double tmp;
	if (A <= -1.1e+148) {
		tmp = (180.0 / ((double) M_PI)) * t_1;
	} else if (A <= -1.35e-15) {
		tmp = 180.0 * (atan((((C - A) - t_0) / B)) / ((double) M_PI));
	} else if (A <= -1.75e-100) {
		tmp = 1.0 / ((((double) M_PI) / t_1) * 0.005555555555555556);
	} else {
		tmp = 180.0 * (atan(((C - (A + t_0)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.hypot(B, (A - C));
	double t_1 = Math.atan((0.5 * (B / A)));
	double tmp;
	if (A <= -1.1e+148) {
		tmp = (180.0 / Math.PI) * t_1;
	} else if (A <= -1.35e-15) {
		tmp = 180.0 * (Math.atan((((C - A) - t_0) / B)) / Math.PI);
	} else if (A <= -1.75e-100) {
		tmp = 1.0 / ((Math.PI / t_1) * 0.005555555555555556);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + t_0)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.hypot(B, (A - C))
	t_1 = math.atan((0.5 * (B / A)))
	tmp = 0
	if A <= -1.1e+148:
		tmp = (180.0 / math.pi) * t_1
	elif A <= -1.35e-15:
		tmp = 180.0 * (math.atan((((C - A) - t_0) / B)) / math.pi)
	elif A <= -1.75e-100:
		tmp = 1.0 / ((math.pi / t_1) * 0.005555555555555556)
	else:
		tmp = 180.0 * (math.atan(((C - (A + t_0)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = hypot(B, Float64(A - C))
	t_1 = atan(Float64(0.5 * Float64(B / A)))
	tmp = 0.0
	if (A <= -1.1e+148)
		tmp = Float64(Float64(180.0 / pi) * t_1);
	elseif (A <= -1.35e-15)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - t_0) / B)) / pi));
	elseif (A <= -1.75e-100)
		tmp = Float64(1.0 / Float64(Float64(pi / t_1) * 0.005555555555555556));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + t_0)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = hypot(B, (A - C));
	t_1 = atan((0.5 * (B / A)));
	tmp = 0.0;
	if (A <= -1.1e+148)
		tmp = (180.0 / pi) * t_1;
	elseif (A <= -1.35e-15)
		tmp = 180.0 * (atan((((C - A) - t_0) / B)) / pi);
	elseif (A <= -1.75e-100)
		tmp = 1.0 / ((pi / t_1) * 0.005555555555555556);
	else
		tmp = 180.0 * (atan(((C - (A + t_0)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -1.1e+148], N[(N[(180.0 / Pi), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[A, -1.35e-15], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - t$95$0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.75e-100], N[(1.0 / N[(N[(Pi / t$95$1), $MachinePrecision] * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + t$95$0), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.0999999999999999e148

   1. Initial program 9.0%

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

      1. associate-*l/ 9.0%

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

      2. *-lft-identity 9.0%

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

      3. +-commutative 9.0%

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

      4. unpow2 9.0%

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

      5. unpow2 9.0%

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

      6. hypot-def 55.0%

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

   3. Simplified 55.0%

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

      1. clear-num 55.0%

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

      2. un-div-inv 55.0%

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

      3. div-inv 55.0%

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

      4. associate--r+ 18.0%

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

      5. hypot-udef 8.9%

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

      6. unpow2 8.9%

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

      7. unpow2 8.9%

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

      8. +-commutative 8.9%

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

      9. associate--l- 9.0%

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

      10. *-commutative 9.0%

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

   5. Applied egg-rr 55.0%

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

   6. Taylor expanded in A around -inf 87.3%

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

      1. associate-/r/ 87.4%

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

   8. Applied egg-rr 87.4%

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

   if -1.0999999999999999e148 < A < -1.35000000000000005e-15

   1. Initial program 43.9%

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

      1. associate-*l/ 43.9%

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

      2. *-lft-identity 43.9%

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

      3. +-commutative 43.9%

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

      4. unpow2 43.9%

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

      5. unpow2 43.9%

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

      6. hypot-def 71.6%

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

   3. Simplified 71.6%

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

   if -1.35000000000000005e-15 < A < -1.75e-100

   1. Initial program 13.5%

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

      1. associate-*l/ 13.5%

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

      2. *-lft-identity 13.5%

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

      3. +-commutative 13.5%

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

      4. unpow2 13.5%

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

      5. unpow2 13.5%

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

      6. hypot-def 23.9%

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

   3. Simplified 23.9%

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

      1. clear-num 23.9%

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

      2. un-div-inv 23.9%

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

      3. div-inv 23.9%

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

      4. associate--r+ 23.1%

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

      5. hypot-udef 12.7%

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

      6. unpow2 12.7%

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

      7. unpow2 12.7%

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

      8. +-commutative 12.7%

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

      9. associate--l- 13.5%

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

      10. *-commutative 13.5%

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

   5. Applied egg-rr 23.9%

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

   6. Taylor expanded in A around -inf 61.1%

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

      1. clear-num 61.1%

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

      2. inv-pow 61.1%

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

   8. Applied egg-rr 61.1%

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

      1. unpow-1 61.1%

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

      2. div-inv 61.4%

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

      3. metadata-eval 61.4%

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

   10. Applied egg-rr 61.4%

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

   if -1.75e-100 < A

   1. Initial program 69.4%

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

   3. Simplified 89.3%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.1 \cdot 10^{+148}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq -1.35 \cdot 10^{-15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.75 \cdot 10^{-100}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)} \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 2: 82.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -5e-67)
     (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))
     (if (<= t_0 0.0)
       (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
       (/ 180.0 (/ PI (atan (/ (- (- C A) (hypot (- A C) B)) B))))))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -5e-67) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	} else if (t_0 <= 0.0) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((C - A) - hypot((A - C), B)) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_0 <= -5e-67) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	} else if (t_0 <= 0.0) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((C - A) - Math.hypot((A - C), B)) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_0 <= -5e-67:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	elif t_0 <= 0.0:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = 180.0 / (math.pi / math.atan((((C - A) - math.hypot((A - C), B)) / B)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_0 <= -5e-67)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -5e-67)
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	elseif (t_0 <= 0.0)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 / (pi / atan((((C - A) - hypot((A - C), B)) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e-67], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -4.9999999999999999e-67

   1. Initial program 54.5%

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

      1. associate-*l/ 54.5%

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

      2. *-lft-identity 54.5%

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

      3. +-commutative 54.5%

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

      4. unpow2 54.5%

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

      5. unpow2 54.5%

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

      6. hypot-def 86.5%

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

   3. Simplified 86.5%

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

   if -4.9999999999999999e-67 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 0.0

   1. Initial program 10.9%

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

      1. associate-*l/ 10.9%

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

      2. *-lft-identity 10.9%

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

      3. +-commutative 10.9%

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

      4. unpow2 10.9%

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

      5. unpow2 10.9%

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

      6. hypot-def 10.9%

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

   3. Simplified 10.9%

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

      1. clear-num 10.9%

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

      2. un-div-inv 10.9%

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

      3. div-inv 10.9%

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

      4. associate--r+ 4.0%

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

      5. hypot-udef 4.0%

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

      6. unpow2 4.0%

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

      7. unpow2 4.0%

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

      8. +-commutative 4.0%

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

      9. associate--l- 10.9%

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

      10. *-commutative 10.9%

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

   5. Applied egg-rr 10.9%

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

   6. Taylor expanded in A around -inf 62.0%

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

      1. associate-/r/ 62.1%

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

   8. Applied egg-rr 62.1%

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

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

   1. Initial program 67.6%

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

      1. associate-*l/ 67.6%

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

      2. *-lft-identity 67.6%

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

      3. +-commutative 67.6%

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

      4. unpow2 67.6%

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

      5. unpow2 67.6%

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

      6. hypot-def 90.3%

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

   3. Simplified 90.3%

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

      1. clear-num 90.4%

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

      2. un-div-inv 90.4%

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

      3. div-inv 90.4%

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

      4. associate--r+ 85.5%

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

      5. hypot-udef 67.6%

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

      6. unpow2 67.6%

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

      7. unpow2 67.6%

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

      8. +-commutative 67.6%

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

      9. associate--l- 67.6%

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

      10. *-commutative 67.6%

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

   5. Applied egg-rr 90.4%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -5 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}\\ \end{array} \]

Alternative 3: 77.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -7.2 \cdot 10^{+147}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_0\\ \mathbf{elif}\;A \leq -7.2 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.75 \cdot 10^{-100}:\\ \;\;\;\;\frac{1}{\frac{\pi}{t_0} \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (* 0.5 (/ B A)))))
   (if (<= A -7.2e+147)
     (* (/ 180.0 PI) t_0)
     (if (<= A -7.2e-16)
       (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
       (if (<= A -1.75e-100)
         (/ 1.0 (* (/ PI t_0) 0.005555555555555556))
         (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = atan((0.5 * (B / A)));
	double tmp;
	if (A <= -7.2e+147) {
		tmp = (180.0 / ((double) M_PI)) * t_0;
	} else if (A <= -7.2e-16) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else if (A <= -1.75e-100) {
		tmp = 1.0 / ((((double) M_PI) / t_0) * 0.005555555555555556);
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan((0.5 * (B / A)));
	double tmp;
	if (A <= -7.2e+147) {
		tmp = (180.0 / Math.PI) * t_0;
	} else if (A <= -7.2e-16) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else if (A <= -1.75e-100) {
		tmp = 1.0 / ((Math.PI / t_0) * 0.005555555555555556);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan((0.5 * (B / A)))
	tmp = 0
	if A <= -7.2e+147:
		tmp = (180.0 / math.pi) * t_0
	elif A <= -7.2e-16:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	elif A <= -1.75e-100:
		tmp = 1.0 / ((math.pi / t_0) * 0.005555555555555556)
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(0.5 * Float64(B / A)))
	tmp = 0.0
	if (A <= -7.2e+147)
		tmp = Float64(Float64(180.0 / pi) * t_0);
	elseif (A <= -7.2e-16)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	elseif (A <= -1.75e-100)
		tmp = Float64(1.0 / Float64(Float64(pi / t_0) * 0.005555555555555556));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan((0.5 * (B / A)));
	tmp = 0.0;
	if (A <= -7.2e+147)
		tmp = (180.0 / pi) * t_0;
	elseif (A <= -7.2e-16)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	elseif (A <= -1.75e-100)
		tmp = 1.0 / ((pi / t_0) * 0.005555555555555556);
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -7.2e+147], N[(N[(180.0 / Pi), $MachinePrecision] * t$95$0), $MachinePrecision], If[LessEqual[A, -7.2e-16], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.75e-100], N[(1.0 / N[(N[(Pi / t$95$0), $MachinePrecision] * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -7.20000000000000041e147

   1. Initial program 9.0%

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

      1. associate-*l/ 9.0%

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

      2. *-lft-identity 9.0%

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

      3. +-commutative 9.0%

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

      4. unpow2 9.0%

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

      5. unpow2 9.0%

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

      6. hypot-def 55.0%

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

   3. Simplified 55.0%

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

      1. clear-num 55.0%

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

      2. un-div-inv 55.0%

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

      3. div-inv 55.0%

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

      4. associate--r+ 18.0%

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

      5. hypot-udef 8.9%

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

      6. unpow2 8.9%

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

      7. unpow2 8.9%

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

      8. +-commutative 8.9%

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

      9. associate--l- 9.0%

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

      10. *-commutative 9.0%

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

   5. Applied egg-rr 55.0%

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

   6. Taylor expanded in A around -inf 87.3%

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

      1. associate-/r/ 87.4%

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

   8. Applied egg-rr 87.4%

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

   if -7.20000000000000041e147 < A < -7.19999999999999965e-16

   1. Initial program 43.9%

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

   2. Taylor expanded in A around 0 39.2%

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

      1. unpow2 39.2%

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

      2. unpow2 39.2%

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

      3. hypot-def 66.9%

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

   4. Simplified 66.9%

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

   if -7.19999999999999965e-16 < A < -1.75e-100

   1. Initial program 13.5%

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

      1. associate-*l/ 13.5%

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

      2. *-lft-identity 13.5%

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

      3. +-commutative 13.5%

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

      4. unpow2 13.5%

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

      5. unpow2 13.5%

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

      6. hypot-def 23.9%

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

   3. Simplified 23.9%

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

      1. clear-num 23.9%

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

      2. un-div-inv 23.9%

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

      3. div-inv 23.9%

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

      4. associate--r+ 23.1%

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

      5. hypot-udef 12.7%

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

      6. unpow2 12.7%

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

      7. unpow2 12.7%

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

      8. +-commutative 12.7%

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

      9. associate--l- 13.5%

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

      10. *-commutative 13.5%

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

   5. Applied egg-rr 23.9%

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

   6. Taylor expanded in A around -inf 61.1%

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

      1. clear-num 61.1%

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

      2. inv-pow 61.1%

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

   8. Applied egg-rr 61.1%

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

      1. unpow-1 61.1%

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

      2. div-inv 61.4%

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

      3. metadata-eval 61.4%

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

   10. Applied egg-rr 61.4%

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

   if -1.75e-100 < A

   1. Initial program 69.4%

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

   3. Simplified 89.3%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7.2 \cdot 10^{+147}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq -7.2 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.75 \cdot 10^{-100}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)} \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 74.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -2.4 \cdot 10^{+151}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_1\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.75 \cdot 10^{-100}:\\ \;\;\;\;\frac{1}{\frac{\pi}{t_1} \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 3.3 \cdot 10^{-26}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI)))
        (t_1 (atan (* 0.5 (/ B A)))))
   (if (<= A -2.4e+151)
     (* (/ 180.0 PI) t_1)
     (if (<= A -8.5e-15)
       t_0
       (if (<= A -1.75e-100)
         (/ 1.0 (* (/ PI t_1) 0.005555555555555556))
         (if (<= A 3.3e-26)
           t_0
           (* 180.0 (/ (atan (/ (- (- A) (hypot 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 = atan((0.5 * (B / A)));
	double tmp;
	if (A <= -2.4e+151) {
		tmp = (180.0 / ((double) M_PI)) * t_1;
	} else if (A <= -8.5e-15) {
		tmp = t_0;
	} else if (A <= -1.75e-100) {
		tmp = 1.0 / ((((double) M_PI) / t_1) * 0.005555555555555556);
	} else if (A <= 3.3e-26) {
		tmp = t_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 = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	double t_1 = Math.atan((0.5 * (B / A)));
	double tmp;
	if (A <= -2.4e+151) {
		tmp = (180.0 / Math.PI) * t_1;
	} else if (A <= -8.5e-15) {
		tmp = t_0;
	} else if (A <= -1.75e-100) {
		tmp = 1.0 / ((Math.PI / t_1) * 0.005555555555555556);
	} else if (A <= 3.3e-26) {
		tmp = t_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 = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	t_1 = math.atan((0.5 * (B / A)))
	tmp = 0
	if A <= -2.4e+151:
		tmp = (180.0 / math.pi) * t_1
	elif A <= -8.5e-15:
		tmp = t_0
	elif A <= -1.75e-100:
		tmp = 1.0 / ((math.pi / t_1) * 0.005555555555555556)
	elif A <= 3.3e-26:
		tmp = t_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 = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi))
	t_1 = atan(Float64(0.5 * Float64(B / A)))
	tmp = 0.0
	if (A <= -2.4e+151)
		tmp = Float64(Float64(180.0 / pi) * t_1);
	elseif (A <= -8.5e-15)
		tmp = t_0;
	elseif (A <= -1.75e-100)
		tmp = Float64(1.0 / Float64(Float64(pi / t_1) * 0.005555555555555556));
	elseif (A <= 3.3e-26)
		tmp = t_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 = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	t_1 = atan((0.5 * (B / A)));
	tmp = 0.0;
	if (A <= -2.4e+151)
		tmp = (180.0 / pi) * t_1;
	elseif (A <= -8.5e-15)
		tmp = t_0;
	elseif (A <= -1.75e-100)
		tmp = 1.0 / ((pi / t_1) * 0.005555555555555556);
	elseif (A <= 3.3e-26)
		tmp = t_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[(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[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -2.4e+151], N[(N[(180.0 / Pi), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[A, -8.5e-15], t$95$0, If[LessEqual[A, -1.75e-100], N[(1.0 / N[(N[(Pi / t$95$1), $MachinePrecision] * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.3e-26], t$95$0, 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 < -2.4000000000000001e151

   1. Initial program 9.0%

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

      1. associate-*l/ 9.0%

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

      2. *-lft-identity 9.0%

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

      3. +-commutative 9.0%

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

      4. unpow2 9.0%

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

      5. unpow2 9.0%

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

      6. hypot-def 55.0%

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

   3. Simplified 55.0%

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

      1. clear-num 55.0%

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

      2. un-div-inv 55.0%

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

      3. div-inv 55.0%

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

      4. associate--r+ 18.0%

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

      5. hypot-udef 8.9%

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

      6. unpow2 8.9%

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

      7. unpow2 8.9%

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

      8. +-commutative 8.9%

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

      9. associate--l- 9.0%

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

      10. *-commutative 9.0%

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

   5. Applied egg-rr 55.0%

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

   6. Taylor expanded in A around -inf 87.3%

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

      1. associate-/r/ 87.4%

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

   8. Applied egg-rr 87.4%

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

   if -2.4000000000000001e151 < A < -8.50000000000000007e-15 or -1.75e-100 < A < 3.2999999999999998e-26

   1. Initial program 56.1%

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

   2. Taylor expanded in A around 0 52.7%

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

      1. unpow2 52.7%

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

      2. unpow2 52.7%

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

      3. hypot-def 78.4%

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

   4. Simplified 78.4%

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

   if -8.50000000000000007e-15 < A < -1.75e-100

   1. Initial program 13.5%

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

      1. associate-*l/ 13.5%

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

      2. *-lft-identity 13.5%

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

      3. +-commutative 13.5%

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

      4. unpow2 13.5%

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

      5. unpow2 13.5%

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

      6. hypot-def 23.9%

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

   3. Simplified 23.9%

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

      1. clear-num 23.9%

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

      2. un-div-inv 23.9%

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

      3. div-inv 23.9%

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

      4. associate--r+ 23.1%

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

      5. hypot-udef 12.7%

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

      6. unpow2 12.7%

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

      7. unpow2 12.7%

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

      8. +-commutative 12.7%

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

      9. associate--l- 13.5%

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

      10. *-commutative 13.5%

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

   5. Applied egg-rr 23.9%

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

   6. Taylor expanded in A around -inf 61.1%

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

      1. clear-num 61.1%

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

      2. inv-pow 61.1%

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

   8. Applied egg-rr 61.1%

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

      1. unpow-1 61.1%

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

      2. div-inv 61.4%

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

      3. metadata-eval 61.4%

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

   10. Applied egg-rr 61.4%

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

   if 3.2999999999999998e-26 < A

   1. Initial program 83.2%

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

   2. Taylor expanded in C around 0 81.0%

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

      1. associate-*r/ 81.0%

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

      2. mul-1-neg 81.0%

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

      3. +-commutative 81.0%

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

      4. unpow2 81.0%

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

      5. unpow2 81.0%

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

      6. hypot-def 89.7%

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

   4. Simplified 89.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.4 \cdot 10^{+151}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.75 \cdot 10^{-100}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)} \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 3.3 \cdot 10^{-26}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 74.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -3.8 \cdot 10^{+146}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_1\\ \mathbf{elif}\;A \leq -6.8 \cdot 10^{-16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.75 \cdot 10^{-100}:\\ \;\;\;\;\frac{1}{\frac{\pi}{t_1} \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 2.75 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI)))
        (t_1 (atan (* 0.5 (/ B A)))))
   (if (<= A -3.8e+146)
     (* (/ 180.0 PI) t_1)
     (if (<= A -6.8e-16)
       t_0
       (if (<= A -1.75e-100)
         (/ 1.0 (* (/ PI t_1) 0.005555555555555556))
         (if (<= A 2.75e-25)
           t_0
           (/ 180.0 (/ PI (atan (/ (- (- A) (hypot A B)) B))))))))))

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 = atan((0.5 * (B / A)));
	double tmp;
	if (A <= -3.8e+146) {
		tmp = (180.0 / ((double) M_PI)) * t_1;
	} else if (A <= -6.8e-16) {
		tmp = t_0;
	} else if (A <= -1.75e-100) {
		tmp = 1.0 / ((((double) M_PI) / t_1) * 0.005555555555555556);
	} else if (A <= 2.75e-25) {
		tmp = t_0;
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((-A - hypot(A, B)) / B)));
	}
	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 = Math.atan((0.5 * (B / A)));
	double tmp;
	if (A <= -3.8e+146) {
		tmp = (180.0 / Math.PI) * t_1;
	} else if (A <= -6.8e-16) {
		tmp = t_0;
	} else if (A <= -1.75e-100) {
		tmp = 1.0 / ((Math.PI / t_1) * 0.005555555555555556);
	} else if (A <= 2.75e-25) {
		tmp = t_0;
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((-A - Math.hypot(A, B)) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	t_1 = math.atan((0.5 * (B / A)))
	tmp = 0
	if A <= -3.8e+146:
		tmp = (180.0 / math.pi) * t_1
	elif A <= -6.8e-16:
		tmp = t_0
	elif A <= -1.75e-100:
		tmp = 1.0 / ((math.pi / t_1) * 0.005555555555555556)
	elif A <= 2.75e-25:
		tmp = t_0
	else:
		tmp = 180.0 / (math.pi / math.atan(((-A - math.hypot(A, B)) / B)))
	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 = atan(Float64(0.5 * Float64(B / A)))
	tmp = 0.0
	if (A <= -3.8e+146)
		tmp = Float64(Float64(180.0 / pi) * t_1);
	elseif (A <= -6.8e-16)
		tmp = t_0;
	elseif (A <= -1.75e-100)
		tmp = Float64(1.0 / Float64(Float64(pi / t_1) * 0.005555555555555556));
	elseif (A <= 2.75e-25)
		tmp = t_0;
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(-A) - hypot(A, B)) / B))));
	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 = atan((0.5 * (B / A)));
	tmp = 0.0;
	if (A <= -3.8e+146)
		tmp = (180.0 / pi) * t_1;
	elseif (A <= -6.8e-16)
		tmp = t_0;
	elseif (A <= -1.75e-100)
		tmp = 1.0 / ((pi / t_1) * 0.005555555555555556);
	elseif (A <= 2.75e-25)
		tmp = t_0;
	else
		tmp = 180.0 / (pi / atan(((-A - hypot(A, B)) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -3.8e+146], N[(N[(180.0 / Pi), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[A, -6.8e-16], t$95$0, If[LessEqual[A, -1.75e-100], N[(1.0 / N[(N[(Pi / t$95$1), $MachinePrecision] * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.75e-25], t$95$0, N[(180.0 / N[(Pi / N[ArcTan[N[(N[((-A) - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -3.79999999999999979e146

   1. Initial program 9.0%

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

      1. associate-*l/ 9.0%

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

      2. *-lft-identity 9.0%

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

      3. +-commutative 9.0%

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

      4. unpow2 9.0%

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

      5. unpow2 9.0%

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

      6. hypot-def 55.0%

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

   3. Simplified 55.0%

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

      1. clear-num 55.0%

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

      2. un-div-inv 55.0%

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

      3. div-inv 55.0%

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

      4. associate--r+ 18.0%

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

      5. hypot-udef 8.9%

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

      6. unpow2 8.9%

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

      7. unpow2 8.9%

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

      8. +-commutative 8.9%

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

      9. associate--l- 9.0%

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

      10. *-commutative 9.0%

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

   5. Applied egg-rr 55.0%

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

   6. Taylor expanded in A around -inf 87.3%

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

      1. associate-/r/ 87.4%

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

   8. Applied egg-rr 87.4%

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

   if -3.79999999999999979e146 < A < -6.8e-16 or -1.75e-100 < A < 2.75000000000000002e-25

   1. Initial program 56.1%

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

   2. Taylor expanded in A around 0 52.7%

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

      1. unpow2 52.7%

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

      2. unpow2 52.7%

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

      3. hypot-def 78.4%

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

   4. Simplified 78.4%

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

   if -6.8e-16 < A < -1.75e-100

   1. Initial program 13.5%

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

      1. associate-*l/ 13.5%

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

      2. *-lft-identity 13.5%

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

      3. +-commutative 13.5%

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

      4. unpow2 13.5%

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

      5. unpow2 13.5%

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

      6. hypot-def 23.9%

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

   3. Simplified 23.9%

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

      1. clear-num 23.9%

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

      2. un-div-inv 23.9%

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

      3. div-inv 23.9%

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

      4. associate--r+ 23.1%

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

      5. hypot-udef 12.7%

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

      6. unpow2 12.7%

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

      7. unpow2 12.7%

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

      8. +-commutative 12.7%

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

      9. associate--l- 13.5%

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

      10. *-commutative 13.5%

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

   5. Applied egg-rr 23.9%

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

   6. Taylor expanded in A around -inf 61.1%

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

      1. clear-num 61.1%

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

      2. inv-pow 61.1%

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

   8. Applied egg-rr 61.1%

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

      1. unpow-1 61.1%

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

      2. div-inv 61.4%

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

      3. metadata-eval 61.4%

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

   10. Applied egg-rr 61.4%

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

   if 2.75000000000000002e-25 < A

   1. Initial program 83.2%

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

      1. associate-*l/ 83.2%

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

      2. *-lft-identity 83.2%

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

      3. +-commutative 83.2%

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

      4. unpow2 83.2%

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

      5. unpow2 83.2%

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

      6. hypot-def 96.2%

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

   3. Simplified 96.2%

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

      1. clear-num 96.2%

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

      2. un-div-inv 96.2%

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

      3. div-inv 96.2%

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

      4. associate--r+ 96.2%

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

      5. hypot-udef 83.3%

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

      6. unpow2 83.3%

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

      7. unpow2 83.3%

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

      8. +-commutative 83.3%

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

      9. associate--l- 83.3%

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

      10. *-commutative 83.3%

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

   5. Applied egg-rr 96.2%

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

   6. Taylor expanded in C around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. unpow2 81.0%

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

      3. unpow2 81.0%

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

      4. hypot-def 89.7%

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

   8. Simplified 89.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.8 \cdot 10^{+146}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq -6.8 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.75 \cdot 10^{-100}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)} \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 2.75 \cdot 10^{-25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}}\\ \end{array} \]

Alternative 6: 72.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -1.55 \cdot 10^{+146}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_1\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.75 \cdot 10^{-100}:\\ \;\;\;\;\frac{1}{\frac{\pi}{t_1} \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 5.9 \cdot 10^{-41}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI)))
        (t_1 (atan (* 0.5 (/ B A)))))
   (if (<= A -1.55e+146)
     (* (/ 180.0 PI) t_1)
     (if (<= A -8.5e-15)
       t_0
       (if (<= A -1.75e-100)
         (/ 1.0 (* (/ PI t_1) 0.005555555555555556))
         (if (<= A 5.9e-41)
           t_0
           (* 180.0 (/ (atan (/ (- C (+ 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 = atan((0.5 * (B / A)));
	double tmp;
	if (A <= -1.55e+146) {
		tmp = (180.0 / ((double) M_PI)) * t_1;
	} else if (A <= -8.5e-15) {
		tmp = t_0;
	} else if (A <= -1.75e-100) {
		tmp = 1.0 / ((((double) M_PI) / t_1) * 0.005555555555555556);
	} else if (A <= 5.9e-41) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	double t_1 = Math.atan((0.5 * (B / A)));
	double tmp;
	if (A <= -1.55e+146) {
		tmp = (180.0 / Math.PI) * t_1;
	} else if (A <= -8.5e-15) {
		tmp = t_0;
	} else if (A <= -1.75e-100) {
		tmp = 1.0 / ((Math.PI / t_1) * 0.005555555555555556);
	} else if (A <= 5.9e-41) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((C - (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 = math.atan((0.5 * (B / A)))
	tmp = 0
	if A <= -1.55e+146:
		tmp = (180.0 / math.pi) * t_1
	elif A <= -8.5e-15:
		tmp = t_0
	elif A <= -1.75e-100:
		tmp = 1.0 / ((math.pi / t_1) * 0.005555555555555556)
	elif A <= 5.9e-41:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((C - (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 = atan(Float64(0.5 * Float64(B / A)))
	tmp = 0.0
	if (A <= -1.55e+146)
		tmp = Float64(Float64(180.0 / pi) * t_1);
	elseif (A <= -8.5e-15)
		tmp = t_0;
	elseif (A <= -1.75e-100)
		tmp = Float64(1.0 / Float64(Float64(pi / t_1) * 0.005555555555555556));
	elseif (A <= 5.9e-41)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	t_1 = atan((0.5 * (B / A)));
	tmp = 0.0;
	if (A <= -1.55e+146)
		tmp = (180.0 / pi) * t_1;
	elseif (A <= -8.5e-15)
		tmp = t_0;
	elseif (A <= -1.75e-100)
		tmp = 1.0 / ((pi / t_1) * 0.005555555555555556);
	elseif (A <= 5.9e-41)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((C - (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[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -1.55e+146], N[(N[(180.0 / Pi), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[A, -8.5e-15], t$95$0, If[LessEqual[A, -1.75e-100], N[(1.0 / N[(N[(Pi / t$95$1), $MachinePrecision] * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.9e-41], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.5500000000000001e146

   1. Initial program 9.0%

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

      1. associate-*l/ 9.0%

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

      2. *-lft-identity 9.0%

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

      3. +-commutative 9.0%

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

      4. unpow2 9.0%

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

      5. unpow2 9.0%

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

      6. hypot-def 55.0%

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

   3. Simplified 55.0%

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

      1. clear-num 55.0%

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

      2. un-div-inv 55.0%

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

      3. div-inv 55.0%

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

      4. associate--r+ 18.0%

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

      5. hypot-udef 8.9%

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

      6. unpow2 8.9%

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

      7. unpow2 8.9%

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

      8. +-commutative 8.9%

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

      9. associate--l- 9.0%

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

      10. *-commutative 9.0%

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

   5. Applied egg-rr 55.0%

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

   6. Taylor expanded in A around -inf 87.3%

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

      1. associate-/r/ 87.4%

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

   8. Applied egg-rr 87.4%

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

   if -1.5500000000000001e146 < A < -8.50000000000000007e-15 or -1.75e-100 < A < 5.8999999999999997e-41

   1. Initial program 55.7%

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

   2. Taylor expanded in A around 0 52.3%

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

      1. unpow2 52.3%

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

      2. unpow2 52.3%

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

      3. hypot-def 77.9%

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

   4. Simplified 77.9%

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

   if -8.50000000000000007e-15 < A < -1.75e-100

   1. Initial program 13.5%

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

      1. associate-*l/ 13.5%

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

      2. *-lft-identity 13.5%

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

      3. +-commutative 13.5%

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

      4. unpow2 13.5%

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

      5. unpow2 13.5%

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

      6. hypot-def 23.9%

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

   3. Simplified 23.9%

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

      1. clear-num 23.9%

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

      2. un-div-inv 23.9%

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

      3. div-inv 23.9%

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

      4. associate--r+ 23.1%

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

      5. hypot-udef 12.7%

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

      6. unpow2 12.7%

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

      7. unpow2 12.7%

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

      8. +-commutative 12.7%

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

      9. associate--l- 13.5%

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

      10. *-commutative 13.5%

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

   5. Applied egg-rr 23.9%

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

   6. Taylor expanded in A around -inf 61.1%

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

      1. clear-num 61.1%

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

      2. inv-pow 61.1%

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

   8. Applied egg-rr 61.1%

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

      1. unpow-1 61.1%

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

      2. div-inv 61.4%

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

      3. metadata-eval 61.4%

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

   10. Applied egg-rr 61.4%

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

   if 5.8999999999999997e-41 < A

   1. Initial program 82.8%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in B around inf 87.7%

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

      1. +-commutative 87.7%

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

   6. Simplified 87.7%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.55 \cdot 10^{+146}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.75 \cdot 10^{-100}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)} \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 5.9 \cdot 10^{-41}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 74.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -1.5 \cdot 10^{+146}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_1\\ \mathbf{elif}\;A \leq -6.8 \cdot 10^{-16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.75 \cdot 10^{-100}:\\ \;\;\;\;\frac{1}{\frac{\pi}{t_1} \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 8.6 \cdot 10^{-28}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI)))
        (t_1 (atan (* 0.5 (/ B A)))))
   (if (<= A -1.5e+146)
     (* (/ 180.0 PI) t_1)
     (if (<= A -6.8e-16)
       t_0
       (if (<= A -1.75e-100)
         (/ 1.0 (* (/ PI t_1) 0.005555555555555556))
         (if (<= A 8.6e-28)
           t_0
           (/ (* -180.0 (atan (/ (+ A (hypot A B)) 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 = atan((0.5 * (B / A)));
	double tmp;
	if (A <= -1.5e+146) {
		tmp = (180.0 / ((double) M_PI)) * t_1;
	} else if (A <= -6.8e-16) {
		tmp = t_0;
	} else if (A <= -1.75e-100) {
		tmp = 1.0 / ((((double) M_PI) / t_1) * 0.005555555555555556);
	} else if (A <= 8.6e-28) {
		tmp = t_0;
	} else {
		tmp = (-180.0 * atan(((A + hypot(A, B)) / 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 = Math.atan((0.5 * (B / A)));
	double tmp;
	if (A <= -1.5e+146) {
		tmp = (180.0 / Math.PI) * t_1;
	} else if (A <= -6.8e-16) {
		tmp = t_0;
	} else if (A <= -1.75e-100) {
		tmp = 1.0 / ((Math.PI / t_1) * 0.005555555555555556);
	} else if (A <= 8.6e-28) {
		tmp = t_0;
	} else {
		tmp = (-180.0 * Math.atan(((A + Math.hypot(A, B)) / 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 = math.atan((0.5 * (B / A)))
	tmp = 0
	if A <= -1.5e+146:
		tmp = (180.0 / math.pi) * t_1
	elif A <= -6.8e-16:
		tmp = t_0
	elif A <= -1.75e-100:
		tmp = 1.0 / ((math.pi / t_1) * 0.005555555555555556)
	elif A <= 8.6e-28:
		tmp = t_0
	else:
		tmp = (-180.0 * math.atan(((A + math.hypot(A, B)) / 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 = atan(Float64(0.5 * Float64(B / A)))
	tmp = 0.0
	if (A <= -1.5e+146)
		tmp = Float64(Float64(180.0 / pi) * t_1);
	elseif (A <= -6.8e-16)
		tmp = t_0;
	elseif (A <= -1.75e-100)
		tmp = Float64(1.0 / Float64(Float64(pi / t_1) * 0.005555555555555556));
	elseif (A <= 8.6e-28)
		tmp = t_0;
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(A + hypot(A, B)) / 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 = atan((0.5 * (B / A)));
	tmp = 0.0;
	if (A <= -1.5e+146)
		tmp = (180.0 / pi) * t_1;
	elseif (A <= -6.8e-16)
		tmp = t_0;
	elseif (A <= -1.75e-100)
		tmp = 1.0 / ((pi / t_1) * 0.005555555555555556);
	elseif (A <= 8.6e-28)
		tmp = t_0;
	else
		tmp = (-180.0 * atan(((A + hypot(A, B)) / 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[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -1.5e+146], N[(N[(180.0 / Pi), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[A, -6.8e-16], t$95$0, If[LessEqual[A, -1.75e-100], N[(1.0 / N[(N[(Pi / t$95$1), $MachinePrecision] * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 8.6e-28], t$95$0, N[(N[(-180.0 * N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.50000000000000001e146

   1. Initial program 9.0%

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

      1. associate-*l/ 9.0%

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

      2. *-lft-identity 9.0%

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

      3. +-commutative 9.0%

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

      4. unpow2 9.0%

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

      5. unpow2 9.0%

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

      6. hypot-def 55.0%

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

   3. Simplified 55.0%

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

      1. clear-num 55.0%

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

      2. un-div-inv 55.0%

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

      3. div-inv 55.0%

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

      4. associate--r+ 18.0%

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

      5. hypot-udef 8.9%

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

      6. unpow2 8.9%

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

      7. unpow2 8.9%

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

      8. +-commutative 8.9%

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

      9. associate--l- 9.0%

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

      10. *-commutative 9.0%

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

   5. Applied egg-rr 55.0%

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

   6. Taylor expanded in A around -inf 87.3%

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

      1. associate-/r/ 87.4%

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

   8. Applied egg-rr 87.4%

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

   if -1.50000000000000001e146 < A < -6.8e-16 or -1.75e-100 < A < 8.6e-28

   1. Initial program 56.1%

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

   2. Taylor expanded in A around 0 52.7%

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

      1. unpow2 52.7%

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

      2. unpow2 52.7%

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

      3. hypot-def 78.4%

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

   4. Simplified 78.4%

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

   if -6.8e-16 < A < -1.75e-100

   1. Initial program 13.5%

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

      1. associate-*l/ 13.5%

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

      2. *-lft-identity 13.5%

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

      3. +-commutative 13.5%

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

      4. unpow2 13.5%

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

      5. unpow2 13.5%

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

      6. hypot-def 23.9%

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

   3. Simplified 23.9%

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

      1. clear-num 23.9%

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

      2. un-div-inv 23.9%

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

      3. div-inv 23.9%

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

      4. associate--r+ 23.1%

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

      5. hypot-udef 12.7%

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

      6. unpow2 12.7%

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

      7. unpow2 12.7%

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

      8. +-commutative 12.7%

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

      9. associate--l- 13.5%

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

      10. *-commutative 13.5%

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

   5. Applied egg-rr 23.9%

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

   6. Taylor expanded in A around -inf 61.1%

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

      1. clear-num 61.1%

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

      2. inv-pow 61.1%

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

   8. Applied egg-rr 61.1%

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

      1. unpow-1 61.1%

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

      2. div-inv 61.4%

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

      3. metadata-eval 61.4%

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

   10. Applied egg-rr 61.4%

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

   if 8.6e-28 < A

   1. Initial program 83.2%

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

      1. associate-*l/ 83.2%

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

      2. *-lft-identity 83.2%

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

      3. +-commutative 83.2%

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

      4. unpow2 83.2%

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

      5. unpow2 83.2%

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

      6. hypot-def 96.2%

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

   3. Simplified 96.2%

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

      1. clear-num 96.2%

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

      2. un-div-inv 96.2%

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

      3. div-inv 96.2%

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

      4. associate--r+ 96.2%

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

      5. hypot-udef 83.3%

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

      6. unpow2 83.3%

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

      7. unpow2 83.3%

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

      8. +-commutative 83.3%

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

      9. associate--l- 83.3%

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

      10. *-commutative 83.3%

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

   5. Applied egg-rr 96.2%

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

   6. Taylor expanded in C around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. unpow2 81.0%

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

      3. unpow2 81.0%

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

      4. hypot-def 89.7%

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

   8. Simplified 89.7%

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

      1. expm1-log1p-u 50.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)}}\right)\right)} \]

      2. expm1-udef 50.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)}}\right)} - 1} \]

      3. associate-/r/ 50.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)}\right)} - 1 \]

      4. distribute-frac-neg 50.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(-\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}\right)} - 1 \]

      5. atan-neg 50.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \color{blue}{\left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)}\right)} - 1 \]

   10. Applied egg-rr 50.0%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 50.0%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\pi} \cdot \left(-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)\right)\right)\right)} \]

       2. expm1-log1p 89.7%

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

       3. associate-*l/ 89.7%

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

       4. neg-mul-1 89.7%

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

       5. associate-*r* 89.7%

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

       6. metadata-eval 89.7%

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

   12. Simplified 89.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+146}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq -6.8 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.75 \cdot 10^{-100}:\\ \;\;\;\;\frac{1}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)} \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 8.6 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 44.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;B \leq -2.5 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.2 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.8 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.9 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-86}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* (/ A B) -2.0)) PI)))
        (t_1 (* 180.0 (/ (atan 1.0) PI))))
   (if (<= B -2.5e+94)
     t_1
     (if (<= B -1.2e-113)
       t_0
       (if (<= B -1.8e-192)
         t_1
         (if (<= B -1.9e-256)
           (* 180.0 (/ (atan (/ 0.0 B)) PI))
           (if (<= B 8.5e-86) t_0 (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	double t_1 = 180.0 * (atan(1.0) / ((double) M_PI));
	double tmp;
	if (B <= -2.5e+94) {
		tmp = t_1;
	} else if (B <= -1.2e-113) {
		tmp = t_0;
	} else if (B <= -1.8e-192) {
		tmp = t_1;
	} else if (B <= -1.9e-256) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 8.5e-86) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	double t_1 = 180.0 * (Math.atan(1.0) / Math.PI);
	double tmp;
	if (B <= -2.5e+94) {
		tmp = t_1;
	} else if (B <= -1.2e-113) {
		tmp = t_0;
	} else if (B <= -1.8e-192) {
		tmp = t_1;
	} else if (B <= -1.9e-256) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 8.5e-86) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	t_1 = 180.0 * (math.atan(1.0) / math.pi)
	tmp = 0
	if B <= -2.5e+94:
		tmp = t_1
	elif B <= -1.2e-113:
		tmp = t_0
	elif B <= -1.8e-192:
		tmp = t_1
	elif B <= -1.9e-256:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 8.5e-86:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi))
	t_1 = Float64(180.0 * Float64(atan(1.0) / pi))
	tmp = 0.0
	if (B <= -2.5e+94)
		tmp = t_1;
	elseif (B <= -1.2e-113)
		tmp = t_0;
	elseif (B <= -1.8e-192)
		tmp = t_1;
	elseif (B <= -1.9e-256)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 8.5e-86)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((A / B) * -2.0)) / pi);
	t_1 = 180.0 * (atan(1.0) / pi);
	tmp = 0.0;
	if (B <= -2.5e+94)
		tmp = t_1;
	elseif (B <= -1.2e-113)
		tmp = t_0;
	elseif (B <= -1.8e-192)
		tmp = t_1;
	elseif (B <= -1.9e-256)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 8.5e-86)
		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[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.5e+94], t$95$1, If[LessEqual[B, -1.2e-113], t$95$0, If[LessEqual[B, -1.8e-192], t$95$1, If[LessEqual[B, -1.9e-256], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.5e-86], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.50000000000000005e94 or -1.20000000000000006e-113 < B < -1.7999999999999999e-192

   1. Initial program 51.0%

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

   2. Taylor expanded in B around -inf 54.7%

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

   if -2.50000000000000005e94 < B < -1.20000000000000006e-113 or -1.89999999999999988e-256 < B < 8.499999999999999e-86

   1. Initial program 62.9%

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

   2. Taylor expanded in A around inf 38.8%

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

   if -1.7999999999999999e-192 < B < -1.89999999999999988e-256

   1. Initial program 59.9%

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

   2. Taylor expanded in C around inf 37.6%

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

      1. associate-*r/ 37.6%

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

      2. distribute-rgt1-in 37.6%

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

      3. metadata-eval 37.6%

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

      4. mul0-lft 37.6%

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

      5. metadata-eval 37.6%

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

   4. Simplified 37.6%

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

   if 8.499999999999999e-86 < B

   1. Initial program 45.5%

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

   2. Taylor expanded in B around inf 61.5%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.5 \cdot 10^{+94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.2 \cdot 10^{-113}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.8 \cdot 10^{-192}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.9 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-86}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 9: 65.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8 \cdot 10^{-128}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(0.5 \cdot \left(B \cdot \frac{B}{A}\right)\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8e-128)
   (/ (* 180.0 (atan (/ (- (+ B C) A) B))) PI)
   (if (<= B -2.1e-148)
     (* 180.0 (/ (atan (* (/ 1.0 B) (* 0.5 (* B (/ B A))))) PI))
     (if (<= B -2e-302)
       (* 180.0 (/ (atan (- 1.0 (/ (- A C) B))) PI))
       (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -8e-128) {
		tmp = (180.0 * atan((((B + C) - A) / B))) / ((double) M_PI);
	} else if (B <= -2.1e-148) {
		tmp = 180.0 * (atan(((1.0 / B) * (0.5 * (B * (B / A))))) / ((double) M_PI));
	} else if (B <= -2e-302) {
		tmp = 180.0 * (atan((1.0 - ((A - C) / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -8e-128) {
		tmp = (180.0 * Math.atan((((B + C) - A) / B))) / Math.PI;
	} else if (B <= -2.1e-148) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * (0.5 * (B * (B / A))))) / Math.PI);
	} else if (B <= -2e-302) {
		tmp = 180.0 * (Math.atan((1.0 - ((A - C) / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -8e-128:
		tmp = (180.0 * math.atan((((B + C) - A) / B))) / math.pi
	elif B <= -2.1e-148:
		tmp = 180.0 * (math.atan(((1.0 / B) * (0.5 * (B * (B / A))))) / math.pi)
	elif B <= -2e-302:
		tmp = 180.0 * (math.atan((1.0 - ((A - C) / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -8e-128)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(B + C) - A) / B))) / pi);
	elseif (B <= -2.1e-148)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(0.5 * Float64(B * Float64(B / A))))) / pi));
	elseif (B <= -2e-302)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(Float64(A - C) / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -8e-128)
		tmp = (180.0 * atan((((B + C) - A) / B))) / pi;
	elseif (B <= -2.1e-148)
		tmp = 180.0 * (atan(((1.0 / B) * (0.5 * (B * (B / A))))) / pi);
	elseif (B <= -2e-302)
		tmp = 180.0 * (atan((1.0 - ((A - C) / B))) / pi);
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -8e-128], N[(N[(180.0 * N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, -2.1e-148], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(0.5 * N[(B * N[(B / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2e-302], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -8.00000000000000043e-128

   1. Initial program 62.8%

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

      1. associate-*l/ 62.8%

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

      2. *-lft-identity 62.8%

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

      3. +-commutative 62.8%

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

      4. unpow2 62.8%

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

      5. unpow2 62.8%

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

      6. hypot-def 84.6%

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

   3. Simplified 84.6%

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

      1. *-commutative 84.6%

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

      2. associate-*l/ 84.6%

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

      3. hypot-udef 62.8%

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

      4. unpow2 62.8%

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

      5. unpow2 62.8%

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

      6. +-commutative 62.8%

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

      7. unpow2 62.8%

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

      8. unpow2 62.8%

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

      9. hypot-def 84.6%

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

   5. Applied egg-rr 84.6%

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

   6. Taylor expanded in B around -inf 81.3%

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

   if -8.00000000000000043e-128 < B < -2.1e-148

   1. Initial program 14.4%

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

   2. Taylor expanded in A around -inf 57.4%

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

      1. unpow2 57.4%

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

      2. *-un-lft-identity 57.4%

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

      3. times-frac 57.9%

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

   4. Applied egg-rr 57.9%

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

   if -2.1e-148 < B < -1.9999999999999999e-302

   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 62.4%

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

      1. associate--l+ 62.4%

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

      2. div-sub 64.9%

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

   4. Simplified 64.9%

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

   if -1.9999999999999999e-302 < B

   1. Initial program 48.4%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in B around inf 65.1%

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

      1. +-commutative 65.1%

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

   6. Simplified 65.1%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8 \cdot 10^{-128}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(0.5 \cdot \left(B \cdot \frac{B}{A}\right)\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10: 44.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-A}{B}\right)}}\\ t_1 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;B \leq -2.5 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -2.25 \cdot 10^{-116}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -2.25 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.26 \cdot 10^{-85}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ 180.0 (/ PI (atan (/ (- A) B)))))
        (t_1 (* 180.0 (/ (atan 1.0) PI))))
   (if (<= B -2.5e+94)
     t_1
     (if (<= B -2.25e-116)
       t_0
       (if (<= B -8.2e-189)
         t_1
         (if (<= B -2.25e-256)
           (* 180.0 (/ (atan (/ 0.0 B)) PI))
           (if (<= B 1.26e-85) t_0 (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 / (((double) M_PI) / atan((-A / B)));
	double t_1 = 180.0 * (atan(1.0) / ((double) M_PI));
	double tmp;
	if (B <= -2.5e+94) {
		tmp = t_1;
	} else if (B <= -2.25e-116) {
		tmp = t_0;
	} else if (B <= -8.2e-189) {
		tmp = t_1;
	} else if (B <= -2.25e-256) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 1.26e-85) {
		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.PI / Math.atan((-A / B)));
	double t_1 = 180.0 * (Math.atan(1.0) / Math.PI);
	double tmp;
	if (B <= -2.5e+94) {
		tmp = t_1;
	} else if (B <= -2.25e-116) {
		tmp = t_0;
	} else if (B <= -8.2e-189) {
		tmp = t_1;
	} else if (B <= -2.25e-256) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 1.26e-85) {
		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.pi / math.atan((-A / B)))
	t_1 = 180.0 * (math.atan(1.0) / math.pi)
	tmp = 0
	if B <= -2.5e+94:
		tmp = t_1
	elif B <= -2.25e-116:
		tmp = t_0
	elif B <= -8.2e-189:
		tmp = t_1
	elif B <= -2.25e-256:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 1.26e-85:
		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(pi / atan(Float64(Float64(-A) / B))))
	t_1 = Float64(180.0 * Float64(atan(1.0) / pi))
	tmp = 0.0
	if (B <= -2.5e+94)
		tmp = t_1;
	elseif (B <= -2.25e-116)
		tmp = t_0;
	elseif (B <= -8.2e-189)
		tmp = t_1;
	elseif (B <= -2.25e-256)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 1.26e-85)
		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 / (pi / atan((-A / B)));
	t_1 = 180.0 * (atan(1.0) / pi);
	tmp = 0.0;
	if (B <= -2.5e+94)
		tmp = t_1;
	elseif (B <= -2.25e-116)
		tmp = t_0;
	elseif (B <= -8.2e-189)
		tmp = t_1;
	elseif (B <= -2.25e-256)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 1.26e-85)
		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[(Pi / N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.5e+94], t$95$1, If[LessEqual[B, -2.25e-116], t$95$0, If[LessEqual[B, -8.2e-189], t$95$1, If[LessEqual[B, -2.25e-256], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.26e-85], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.50000000000000005e94 or -2.25000000000000006e-116 < B < -8.2000000000000006e-189

   1. Initial program 51.0%

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

   2. Taylor expanded in B around -inf 54.7%

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

   if -2.50000000000000005e94 < B < -2.25000000000000006e-116 or -2.2500000000000001e-256 < B < 1.26e-85

   1. Initial program 62.9%

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

      1. associate-*l/ 62.9%

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

      2. *-lft-identity 62.9%

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

      3. +-commutative 62.9%

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

      4. unpow2 62.9%

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

      5. unpow2 62.9%

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

      6. hypot-def 76.8%

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

   3. Simplified 76.8%

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

      1. clear-num 76.7%

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

      2. un-div-inv 76.7%

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

      3. div-inv 76.7%

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

      4. associate--r+ 67.5%

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

      5. hypot-udef 61.8%

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

      6. unpow2 61.8%

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

      7. unpow2 61.8%

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

      8. +-commutative 61.8%

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

      9. associate--l- 62.9%

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

      10. *-commutative 62.9%

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

   5. Applied egg-rr 76.7%

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

   6. Taylor expanded in C around 0 49.0%

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

      1. mul-1-neg 49.0%

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

      2. unpow2 49.0%

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

      3. unpow2 49.0%

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

      4. hypot-def 59.5%

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

   8. Simplified 59.5%

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

   9. Taylor expanded in A around 0 41.0%

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

   10. Taylor expanded in A around inf 38.8%

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

       1. associate-*r/ 38.8%

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

       2. mul-1-neg 38.8%

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

   12. Simplified 38.8%

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

   if -8.2000000000000006e-189 < B < -2.2500000000000001e-256

   1. Initial program 59.9%

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

   2. Taylor expanded in C around inf 37.6%

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

      1. associate-*r/ 37.6%

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

      2. distribute-rgt1-in 37.6%

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

      3. metadata-eval 37.6%

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

      4. mul0-lft 37.6%

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

      5. metadata-eval 37.6%

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

   4. Simplified 37.6%

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

   if 1.26e-85 < B

   1. Initial program 45.5%

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

   2. Taylor expanded in B around inf 61.5%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.5 \cdot 10^{+94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.25 \cdot 10^{-116}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-A}{B}\right)}}\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-189}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.25 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.26 \cdot 10^{-85}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-A}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11: 46.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -0.0275:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -4.7 \cdot 10^{-256}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.32 \cdot 10^{-249}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-A}{B}\right)}}\\ \mathbf{elif}\;B \leq 2.05 \cdot 10^{-91}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))))
   (if (<= B -0.0275)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -4.7e-256)
       t_0
       (if (<= B 1.32e-249)
         (/ 180.0 (/ PI (atan (/ (- A) B))))
         (if (<= B 2.05e-91) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	double tmp;
	if (B <= -0.0275) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -4.7e-256) {
		tmp = t_0;
	} else if (B <= 1.32e-249) {
		tmp = 180.0 / (((double) M_PI) / atan((-A / B)));
	} else if (B <= 2.05e-91) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	double tmp;
	if (B <= -0.0275) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -4.7e-256) {
		tmp = t_0;
	} else if (B <= 1.32e-249) {
		tmp = 180.0 / (Math.PI / Math.atan((-A / B)));
	} else if (B <= 2.05e-91) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	tmp = 0
	if B <= -0.0275:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -4.7e-256:
		tmp = t_0
	elif B <= 1.32e-249:
		tmp = 180.0 / (math.pi / math.atan((-A / B)))
	elif B <= 2.05e-91:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi))
	tmp = 0.0
	if (B <= -0.0275)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -4.7e-256)
		tmp = t_0;
	elseif (B <= 1.32e-249)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(-A) / B))));
	elseif (B <= 2.05e-91)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((2.0 * (C / B))) / pi);
	tmp = 0.0;
	if (B <= -0.0275)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -4.7e-256)
		tmp = t_0;
	elseif (B <= 1.32e-249)
		tmp = 180.0 / (pi / atan((-A / B)));
	elseif (B <= 2.05e-91)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -0.0275], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4.7e-256], t$95$0, If[LessEqual[B, 1.32e-249], N[(180.0 / N[(Pi / N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.05e-91], 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 < -0.0275000000000000001

   1. Initial program 56.3%

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

   2. Taylor expanded in B around -inf 58.1%

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

   if -0.0275000000000000001 < B < -4.69999999999999982e-256 or 1.32e-249 < B < 2.05000000000000012e-91

   1. Initial program 57.4%

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

   2. Taylor expanded in C around -inf 37.2%

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

   if -4.69999999999999982e-256 < B < 1.32e-249

   1. Initial program 65.7%

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

      1. associate-*l/ 65.7%

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

      2. *-lft-identity 65.7%

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

      3. +-commutative 65.7%

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

      4. unpow2 65.7%

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

      5. unpow2 65.7%

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

      6. hypot-def 86.6%

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

   3. Simplified 86.6%

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

      1. clear-num 86.6%

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

      2. un-div-inv 86.6%

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

      3. div-inv 86.6%

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

      4. associate--r+ 65.5%

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

      5. hypot-udef 61.9%

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

      6. unpow2 61.9%

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

      7. unpow2 61.9%

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

      8. +-commutative 61.9%

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

      9. associate--l- 65.7%

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

      10. *-commutative 65.7%

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

   5. Applied egg-rr 86.6%

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

   6. Taylor expanded in C around 0 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unpow2 58.8%

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

      3. unpow2 58.8%

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

      4. hypot-def 76.2%

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

   8. Simplified 76.2%

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

   9. Taylor expanded in A around 0 54.8%

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

   10. Taylor expanded in A around inf 54.8%

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

       1. associate-*r/ 54.8%

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

       2. mul-1-neg 54.8%

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

   12. Simplified 54.8%

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

   if 2.05000000000000012e-91 < B

   1. Initial program 46.3%

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

   2. Taylor expanded in B around inf 60.9%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -0.0275:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -4.7 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.32 \cdot 10^{-249}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-A}{B}\right)}}\\ \mathbf{elif}\;B \leq 2.05 \cdot 10^{-91}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12: 57.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{if}\;A \leq -1.9 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -4500000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -6.2 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2.15 \cdot 10^{-155}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ (/ C B) 1.0)) PI)))
        (t_1 (* 180.0 (/ (atan (/ 0.5 (/ A B))) PI))))
   (if (<= A -1.9e+57)
     t_1
     (if (<= A -4500000000000.0)
       t_0
       (if (<= A -6.2e-101)
         t_1
         (if (<= A 2.15e-155)
           t_0
           (* 180.0 (/ (atan (- -1.0 (/ 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 t_1 = 180.0 * (atan((0.5 / (A / B))) / ((double) M_PI));
	double tmp;
	if (A <= -1.9e+57) {
		tmp = t_1;
	} else if (A <= -4500000000000.0) {
		tmp = t_0;
	} else if (A <= -6.2e-101) {
		tmp = t_1;
	} else if (A <= 2.15e-155) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C / B) + 1.0)) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.5 / (A / B))) / Math.PI);
	double tmp;
	if (A <= -1.9e+57) {
		tmp = t_1;
	} else if (A <= -4500000000000.0) {
		tmp = t_0;
	} else if (A <= -6.2e-101) {
		tmp = t_1;
	} else if (A <= 2.15e-155) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C / B) + 1.0)) / math.pi)
	t_1 = 180.0 * (math.atan((0.5 / (A / B))) / math.pi)
	tmp = 0
	if A <= -1.9e+57:
		tmp = t_1
	elif A <= -4500000000000.0:
		tmp = t_0
	elif A <= -6.2e-101:
		tmp = t_1
	elif A <= 2.15e-155:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + 1.0)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.5 / Float64(A / B))) / pi))
	tmp = 0.0
	if (A <= -1.9e+57)
		tmp = t_1;
	elseif (A <= -4500000000000.0)
		tmp = t_0;
	elseif (A <= -6.2e-101)
		tmp = t_1;
	elseif (A <= 2.15e-155)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C / B) + 1.0)) / pi);
	t_1 = 180.0 * (atan((0.5 / (A / B))) / pi);
	tmp = 0.0;
	if (A <= -1.9e+57)
		tmp = t_1;
	elseif (A <= -4500000000000.0)
		tmp = t_0;
	elseif (A <= -6.2e-101)
		tmp = t_1;
	elseif (A <= 2.15e-155)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.5 / N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.9e+57], t$95$1, If[LessEqual[A, -4500000000000.0], t$95$0, If[LessEqual[A, -6.2e-101], t$95$1, If[LessEqual[A, 2.15e-155], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.8999999999999999e57 or -4.5e12 < A < -6.19999999999999946e-101

   1. Initial program 18.5%

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

      1. associate-*l/ 18.5%

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

      2. *-lft-identity 18.5%

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

      3. +-commutative 18.5%

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

      4. unpow2 18.5%

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

      5. unpow2 18.5%

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

      6. hypot-def 52.4%

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

   3. Simplified 52.4%

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

      1. clear-num 52.4%

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

      2. un-div-inv 52.4%

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

      3. div-inv 52.4%

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

      4. associate--r+ 30.7%

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

      5. hypot-udef 15.3%

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

      6. unpow2 15.3%

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

      7. unpow2 15.3%

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

      8. +-commutative 15.3%

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

      9. associate--l- 18.5%

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

      10. *-commutative 18.5%

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

   5. Applied egg-rr 52.4%

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

   6. Taylor expanded in A around -inf 69.6%

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

   7. Taylor expanded in B around 0 69.0%

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

      1. *-lft-identity 69.0%

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

      2. *-lft-identity 69.0%

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

      3. associate-*r/ 69.0%

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

      4. associate-/l* 69.7%

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

   9. Simplified 69.7%

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

   if -1.8999999999999999e57 < A < -4.5e12 or -6.19999999999999946e-101 < A < 2.15000000000000004e-155

   1. Initial program 57.0%

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

   2. Taylor expanded in B around -inf 56.2%

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

      1. associate--l+ 56.2%

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

      2. div-sub 56.2%

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

   4. Simplified 56.2%

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

   5. Taylor expanded in C around inf 54.5%

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

   if 2.15000000000000004e-155 < A

   1. Initial program 79.9%

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

      1. associate-*l/ 79.9%

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

      2. *-lft-identity 79.9%

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

      3. +-commutative 79.9%

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

      4. unpow2 79.9%

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

      5. unpow2 79.9%

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

      6. hypot-def 94.9%

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

   3. Simplified 94.9%

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

      1. clear-num 94.9%

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

      2. un-div-inv 94.9%

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

      3. div-inv 94.9%

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

      4. associate--r+ 94.9%

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

      5. hypot-udef 79.9%

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

      6. unpow2 79.9%

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

      7. unpow2 79.9%

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

      8. +-commutative 79.9%

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

      9. associate--l- 79.9%

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

      10. *-commutative 79.9%

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

   5. Applied egg-rr 94.9%

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

   6. Taylor expanded in C around 0 76.1%

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

      1. mul-1-neg 76.1%

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

      2. unpow2 76.1%

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

      3. unpow2 76.1%

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

      4. hypot-def 84.7%

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

   8. Simplified 84.7%

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

   9. Taylor expanded in A around 0 77.2%

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

   10. Taylor expanded in A around 0 77.2%

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

       1. neg-mul-1 77.2%

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

       2. distribute-neg-frac 77.2%

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

       3. +-commutative 77.2%

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

       4. distribute-neg-in 77.2%

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

       5. mul-1-neg 77.2%

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

       6. sub-neg 77.2%

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

       7. sub-neg 77.2%

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

       8. mul-1-neg 77.2%

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

       9. distribute-neg-in 77.2%

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

       10. +-commutative 77.2%

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

       11. distribute-neg-in 77.2%

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

       12. mul-1-neg 77.2%

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

       13. sub-neg 77.2%

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

   12. Simplified 77.2%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{+57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4500000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;A \leq -6.2 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.15 \cdot 10^{-155}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 13: 57.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{if}\;A \leq -3.7 \cdot 10^{+58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3800000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.7 \cdot 10^{-101}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-155}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ (/ C B) 1.0)) PI))))
   (if (<= A -3.7e+58)
     (* 180.0 (/ (atan (/ 0.5 (/ A B))) PI))
     (if (<= A -3800000.0)
       t_0
       (if (<= A -2.7e-101)
         (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
         (if (<= A 1.25e-155)
           t_0
           (* 180.0 (/ (atan (- -1.0 (/ 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 <= -3.7e+58) {
		tmp = 180.0 * (atan((0.5 / (A / B))) / ((double) M_PI));
	} else if (A <= -3800000.0) {
		tmp = t_0;
	} else if (A <= -2.7e-101) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (A <= 1.25e-155) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C / B) + 1.0)) / Math.PI);
	double tmp;
	if (A <= -3.7e+58) {
		tmp = 180.0 * (Math.atan((0.5 / (A / B))) / Math.PI);
	} else if (A <= -3800000.0) {
		tmp = t_0;
	} else if (A <= -2.7e-101) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (A <= 1.25e-155) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C / B) + 1.0)) / math.pi)
	tmp = 0
	if A <= -3.7e+58:
		tmp = 180.0 * (math.atan((0.5 / (A / B))) / math.pi)
	elif A <= -3800000.0:
		tmp = t_0
	elif A <= -2.7e-101:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif A <= 1.25e-155:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + 1.0)) / pi))
	tmp = 0.0
	if (A <= -3.7e+58)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 / Float64(A / B))) / pi));
	elseif (A <= -3800000.0)
		tmp = t_0;
	elseif (A <= -2.7e-101)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (A <= 1.25e-155)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C / B) + 1.0)) / pi);
	tmp = 0.0;
	if (A <= -3.7e+58)
		tmp = 180.0 * (atan((0.5 / (A / B))) / pi);
	elseif (A <= -3800000.0)
		tmp = t_0;
	elseif (A <= -2.7e-101)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (A <= 1.25e-155)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -3.7e+58], N[(180.0 * N[(N[ArcTan[N[(0.5 / N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -3800000.0], t$95$0, If[LessEqual[A, -2.7e-101], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.25e-155], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -3.7000000000000002e58

   1. Initial program 20.2%

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

      1. associate-*l/ 20.2%

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

      2. *-lft-identity 20.2%

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

      3. +-commutative 20.2%

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

      4. unpow2 20.2%

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

      5. unpow2 20.2%

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

      6. hypot-def 60.8%

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

   3. Simplified 60.8%

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

      1. clear-num 60.8%

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

      2. un-div-inv 60.8%

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

      3. div-inv 60.8%

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

      4. associate--r+ 32.1%

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

      5. hypot-udef 16.1%

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

      6. unpow2 16.1%

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

      7. unpow2 16.1%

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

      8. +-commutative 16.1%

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

      9. associate--l- 20.2%

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

      10. *-commutative 20.2%

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

   5. Applied egg-rr 60.8%

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

   6. Taylor expanded in A around -inf 74.4%

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

   7. Taylor expanded in B around 0 73.5%

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

      1. *-lft-identity 73.5%

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

      2. *-lft-identity 73.5%

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

      3. associate-*r/ 73.5%

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

      4. associate-/l* 74.4%

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

   9. Simplified 74.4%

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

   if -3.7000000000000002e58 < A < -3.8e6 or -2.7000000000000002e-101 < A < 1.25e-155

   1. Initial program 57.0%

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

   2. Taylor expanded in B around -inf 56.2%

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

      1. associate--l+ 56.2%

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

      2. div-sub 56.2%

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

   4. Simplified 56.2%

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

   5. Taylor expanded in C around inf 54.5%

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

   if -3.8e6 < A < -2.7000000000000002e-101

   1. Initial program 13.4%

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

      1. associate-*l/ 13.4%

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

      2. *-lft-identity 13.4%

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

      3. +-commutative 13.4%

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

      4. unpow2 13.4%

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

      5. unpow2 13.4%

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

      6. hypot-def 27.4%

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

   3. Simplified 27.4%

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

      1. clear-num 27.4%

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

      2. un-div-inv 27.4%

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

      3. div-inv 27.4%

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

      4. associate--r+ 26.7%

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

      5. hypot-udef 12.7%

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

      6. unpow2 12.7%

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

      7. unpow2 12.7%

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

      8. +-commutative 12.7%

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

      9. associate--l- 13.4%

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

      10. *-commutative 13.4%

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

   5. Applied egg-rr 27.4%

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

   6. Taylor expanded in A around -inf 55.3%

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

      1. associate-/r/ 55.5%

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

   8. Applied egg-rr 55.5%

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

   if 1.25e-155 < A

   1. Initial program 79.9%

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

      1. associate-*l/ 79.9%

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

      2. *-lft-identity 79.9%

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

      3. +-commutative 79.9%

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

      4. unpow2 79.9%

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

      5. unpow2 79.9%

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

      6. hypot-def 94.9%

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

   3. Simplified 94.9%

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

      1. clear-num 94.9%

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

      2. un-div-inv 94.9%

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

      3. div-inv 94.9%

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

      4. associate--r+ 94.9%

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

      5. hypot-udef 79.9%

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

      6. unpow2 79.9%

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

      7. unpow2 79.9%

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

      8. +-commutative 79.9%

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

      9. associate--l- 79.9%

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

      10. *-commutative 79.9%

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

   5. Applied egg-rr 94.9%

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

   6. Taylor expanded in C around 0 76.1%

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

      1. mul-1-neg 76.1%

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

      2. unpow2 76.1%

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

      3. unpow2 76.1%

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

      4. hypot-def 84.7%

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

   8. Simplified 84.7%

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

   9. Taylor expanded in A around 0 77.2%

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

   10. Taylor expanded in A around 0 77.2%

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

       1. neg-mul-1 77.2%

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

       2. distribute-neg-frac 77.2%

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

       3. +-commutative 77.2%

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

       4. distribute-neg-in 77.2%

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

       5. mul-1-neg 77.2%

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

       6. sub-neg 77.2%

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

       7. sub-neg 77.2%

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

       8. mul-1-neg 77.2%

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

       9. distribute-neg-in 77.2%

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

       10. +-commutative 77.2%

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

       11. distribute-neg-in 77.2%

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

       12. mul-1-neg 77.2%

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

       13. sub-neg 77.2%

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

   12. Simplified 77.2%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.7 \cdot 10^{+58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3800000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.7 \cdot 10^{-101}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-155}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 14: 62.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.15 \cdot 10^{-127}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.9 \cdot 10^{-148}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-80}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- 1.0 (/ (- A C) B))) PI))))
   (if (<= B -1.15e-127)
     t_0
     (if (<= B -1.9e-148)
       (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
       (if (<= B 1.35e-80) t_0 (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 - ((A - C) / B))) / ((double) M_PI));
	double tmp;
	if (B <= -1.15e-127) {
		tmp = t_0;
	} else if (B <= -1.9e-148) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (B <= 1.35e-80) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 - ((A - C) / B))) / Math.PI);
	double tmp;
	if (B <= -1.15e-127) {
		tmp = t_0;
	} else if (B <= -1.9e-148) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (B <= 1.35e-80) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 - ((A - C) / B))) / math.pi)
	tmp = 0
	if B <= -1.15e-127:
		tmp = t_0
	elif B <= -1.9e-148:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif B <= 1.35e-80:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(Float64(A - C) / B))) / pi))
	tmp = 0.0
	if (B <= -1.15e-127)
		tmp = t_0;
	elseif (B <= -1.9e-148)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (B <= 1.35e-80)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 - ((A - C) / B))) / pi);
	tmp = 0.0;
	if (B <= -1.15e-127)
		tmp = t_0;
	elseif (B <= -1.9e-148)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (B <= 1.35e-80)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.15e-127], t$95$0, If[LessEqual[B, -1.9e-148], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.35e-80], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.15000000000000009e-127 or -1.90000000000000007e-148 < B < 1.3500000000000001e-80

   1. Initial program 60.4%

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

   2. Taylor expanded in B around -inf 65.7%

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

      1. associate--l+ 65.7%

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

      2. div-sub 68.0%

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

   4. Simplified 68.0%

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

   if -1.15000000000000009e-127 < B < -1.90000000000000007e-148

   1. Initial program 14.4%

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

      1. associate-*l/ 14.4%

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

      2. *-lft-identity 14.4%

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

      3. +-commutative 14.4%

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

      4. unpow2 14.4%

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

      5. unpow2 14.4%

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

      6. hypot-def 36.7%

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

   3. Simplified 36.7%

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

      1. clear-num 36.7%

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

      2. un-div-inv 36.7%

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

      3. div-inv 36.7%

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

      4. associate--r+ 26.3%

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

      5. hypot-udef 14.7%

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

      6. unpow2 14.7%

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

      7. unpow2 14.7%

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

      8. +-commutative 14.7%

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

      9. associate--l- 14.4%

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

      10. *-commutative 14.4%

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

   5. Applied egg-rr 36.7%

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

   6. Taylor expanded in A around -inf 57.7%

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

      1. associate-/r/ 57.7%

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

   8. Applied egg-rr 57.7%

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

   if 1.3500000000000001e-80 < B

   1. Initial program 46.1%

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

      1. associate-*l/ 46.1%

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

      2. *-lft-identity 46.1%

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

      3. +-commutative 46.1%

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

      4. unpow2 46.1%

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

      5. unpow2 46.1%

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

      6. hypot-def 76.9%

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

   3. Simplified 76.9%

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

      1. clear-num 76.9%

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

      2. un-div-inv 76.9%

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

      3. div-inv 76.9%

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

      4. associate--r+ 76.8%

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

      5. hypot-udef 46.1%

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

      6. unpow2 46.1%

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

      7. unpow2 46.1%

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

      8. +-commutative 46.1%

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

      9. associate--l- 46.1%

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

      10. *-commutative 46.1%

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

   5. Applied egg-rr 76.9%

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

   6. Taylor expanded in C around 0 42.2%

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

      1. mul-1-neg 42.2%

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

      2. unpow2 42.2%

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

      3. unpow2 42.2%

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

      4. hypot-def 71.4%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\left(A + \color{blue}{\mathsf{hypot}\left(A, B\right)}\right)}{B}\right)}} \]

   8. Simplified 71.4%

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\color{blue}{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}}{B}\right)}} \]

   9. Taylor expanded in A around 0 70.2%

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\color{blue}{\left(A + B\right)}}{B}\right)}} \]

   10. Taylor expanded in A around 0 70.2%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{A + B}{B}\right)}{\pi}} \]
   11. Step-by-step derivation

       1. neg-mul-1 70.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-\frac{A + B}{B}\right)}}{\pi} \]

       2. distribute-neg-frac 70.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-\left(A + B\right)}{B}\right)}}{\pi} \]

       3. +-commutative 70.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-\color{blue}{\left(B + A\right)}}{B}\right)}{\pi} \]

       4. distribute-neg-in 70.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(-B\right) + \left(-A\right)}}{B}\right)}{\pi} \]

       5. mul-1-neg 70.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot B} + \left(-A\right)}{B}\right)}{\pi} \]

       6. sub-neg 70.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot B - A}}{B}\right)}{\pi} \]

       7. sub-neg 70.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot B + \left(-A\right)}}{B}\right)}{\pi} \]

       8. mul-1-neg 70.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(-B\right)} + \left(-A\right)}{B}\right)}{\pi} \]

       9. distribute-neg-in 70.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-\left(B + A\right)}}{B}\right)}{\pi} \]

       10. +-commutative 70.2%

           \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-\color{blue}{\left(A + B\right)}}{B}\right)}{\pi} \]

       11. distribute-neg-in 70.2%

           \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(-A\right) + \left(-B\right)}}{B}\right)}{\pi} \]

       12. mul-1-neg 70.2%

           \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot A} + \left(-B\right)}{B}\right)}{\pi} \]

       13. sub-neg 70.2%

           \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot A - B}}{B}\right)}{\pi} \]

   12. Simplified 70.2%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.15 \cdot 10^{-127}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.9 \cdot 10^{-148}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 15: 65.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -8 \cdot 10^{-128}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-148}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-302}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- 1.0 (/ (- A C) B))) PI))))
   (if (<= B -8e-128)
     t_0
     (if (<= B -2.1e-148)
       (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
       (if (<= B -2e-302) t_0 (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 - ((A - C) / B))) / ((double) M_PI));
	double tmp;
	if (B <= -8e-128) {
		tmp = t_0;
	} else if (B <= -2.1e-148) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (B <= -2e-302) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 - ((A - C) / B))) / Math.PI);
	double tmp;
	if (B <= -8e-128) {
		tmp = t_0;
	} else if (B <= -2.1e-148) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (B <= -2e-302) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 - ((A - C) / B))) / math.pi)
	tmp = 0
	if B <= -8e-128:
		tmp = t_0
	elif B <= -2.1e-148:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif B <= -2e-302:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(Float64(A - C) / B))) / pi))
	tmp = 0.0
	if (B <= -8e-128)
		tmp = t_0;
	elseif (B <= -2.1e-148)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (B <= -2e-302)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 - ((A - C) / B))) / pi);
	tmp = 0.0;
	if (B <= -8e-128)
		tmp = t_0;
	elseif (B <= -2.1e-148)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (B <= -2e-302)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((C - (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[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -8e-128], t$95$0, If[LessEqual[B, -2.1e-148], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2e-302], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -8.00000000000000043e-128 or -2.1e-148 < B < -1.9999999999999999e-302

   1. Initial program 64.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   2. Taylor expanded in B around -inf 75.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   3. Step-by-step derivation

      1. associate--l+ 75.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)}}{\pi} \]

      2. div-sub 76.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\pi} \]

   4. Simplified 76.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   if -8.00000000000000043e-128 < B < -2.1e-148

   1. Initial program 14.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 14.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 14.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 14.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 14.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 14.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 36.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 36.7%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]
   4. Step-by-step derivation

      1. clear-num 36.7%

         \[\leadsto 180 \cdot \color{blue}{\frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}} \]

      2. un-div-inv 36.7%

         \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}} \]

      3. div-inv 36.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \frac{1}{B}\right)}}} \]

      4. associate--r+ 26.3%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{\left(C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \frac{1}{B}\right)}} \]

      5. hypot-udef 14.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      6. unpow2 14.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}} \]

      7. unpow2 14.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      8. +-commutative 14.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      9. associate--l- 14.4%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)} \cdot \frac{1}{B}\right)}} \]

      10. *-commutative 14.4%

          \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}} \]

   5. Applied egg-rr 36.7%

      \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}} \]

   6. Taylor expanded in A around -inf 57.7%

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 57.7%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)} \]

   8. Applied egg-rr 57.7%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)} \]

   if -1.9999999999999999e-302 < B

   1. Initial program 48.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

   3. Simplified 69.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 65.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + B\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. +-commutative 65.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(B + A\right)}}{B}\right)}{\pi} \]

   6. Simplified 65.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(B + A\right)}}{B}\right)}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8 \cdot 10^{-128}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-148}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 16: 65.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.2 \cdot 10^{-125}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -9.2 \cdot 10^{-149}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq -5 \cdot 10^{-182}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.2e-125)
   (* 180.0 (/ (atan (/ (- C (- A B)) B)) PI))
   (if (<= B -9.2e-149)
     (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
     (if (<= B -5e-182)
       (* 180.0 (/ (atan (- 1.0 (/ (- A C) B))) PI))
       (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.2e-125) {
		tmp = 180.0 * (atan(((C - (A - B)) / B)) / ((double) M_PI));
	} else if (B <= -9.2e-149) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (B <= -5e-182) {
		tmp = 180.0 * (atan((1.0 - ((A - C) / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.2e-125) {
		tmp = 180.0 * (Math.atan(((C - (A - B)) / B)) / Math.PI);
	} else if (B <= -9.2e-149) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (B <= -5e-182) {
		tmp = 180.0 * (Math.atan((1.0 - ((A - C) / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.2e-125:
		tmp = 180.0 * (math.atan(((C - (A - B)) / B)) / math.pi)
	elif B <= -9.2e-149:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif B <= -5e-182:
		tmp = 180.0 * (math.atan((1.0 - ((A - C) / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.2e-125)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A - B)) / B)) / pi));
	elseif (B <= -9.2e-149)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (B <= -5e-182)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(Float64(A - C) / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.2e-125)
		tmp = 180.0 * (atan(((C - (A - B)) / B)) / pi);
	elseif (B <= -9.2e-149)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (B <= -5e-182)
		tmp = 180.0 * (atan((1.0 - ((A - C) / B))) / pi);
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.2e-125], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A - B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -9.2e-149], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -5e-182], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.19999999999999995e-125

   1. Initial program 62.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

   3. Simplified 82.4%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around -inf 81.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + -1 \cdot B\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. neg-mul-1 81.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \color{blue}{\left(-B\right)}\right)}{B}\right)}{\pi} \]

      2. unsub-neg 81.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right)}{\pi} \]

   6. Simplified 81.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A - B\right)}}{B}\right)}{\pi} \]

   if -2.19999999999999995e-125 < B < -9.1999999999999999e-149

   1. Initial program 14.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 14.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 14.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 14.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 14.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 14.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 36.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 36.7%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]
   4. Step-by-step derivation

      1. clear-num 36.7%

         \[\leadsto 180 \cdot \color{blue}{\frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}} \]

      2. un-div-inv 36.7%

         \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}} \]

      3. div-inv 36.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \frac{1}{B}\right)}}} \]

      4. associate--r+ 26.3%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{\left(C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \frac{1}{B}\right)}} \]

      5. hypot-udef 14.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      6. unpow2 14.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}} \]

      7. unpow2 14.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      8. +-commutative 14.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      9. associate--l- 14.4%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)} \cdot \frac{1}{B}\right)}} \]

      10. *-commutative 14.4%

          \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}} \]

   5. Applied egg-rr 36.7%

      \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}} \]

   6. Taylor expanded in A around -inf 57.7%

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 57.7%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)} \]

   8. Applied egg-rr 57.7%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)} \]

   if -9.1999999999999999e-149 < B < -5.00000000000000024e-182

   1. Initial program 68.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   2. Taylor expanded in B around -inf 78.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   3. Step-by-step derivation

      1. associate--l+ 78.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)}}{\pi} \]

      2. div-sub 78.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\pi} \]

   4. Simplified 78.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   if -5.00000000000000024e-182 < B

   1. Initial program 52.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

   3. Simplified 70.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 64.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + B\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. +-commutative 64.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(B + A\right)}}{B}\right)}{\pi} \]

   6. Simplified 64.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(B + A\right)}}{B}\right)}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.2 \cdot 10^{-125}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -9.2 \cdot 10^{-149}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq -5 \cdot 10^{-182}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 17: 65.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.5 \cdot 10^{-127}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-148}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.5e-127)
   (/ (* 180.0 (atan (/ (- (+ B C) A) B))) PI)
   (if (<= B -2.1e-148)
     (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
     (if (<= B -2e-302)
       (* 180.0 (/ (atan (- 1.0 (/ (- A C) B))) PI))
       (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.5e-127) {
		tmp = (180.0 * atan((((B + C) - A) / B))) / ((double) M_PI);
	} else if (B <= -2.1e-148) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (B <= -2e-302) {
		tmp = 180.0 * (atan((1.0 - ((A - C) / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.5e-127) {
		tmp = (180.0 * Math.atan((((B + C) - A) / B))) / Math.PI;
	} else if (B <= -2.1e-148) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (B <= -2e-302) {
		tmp = 180.0 * (Math.atan((1.0 - ((A - C) / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.5e-127:
		tmp = (180.0 * math.atan((((B + C) - A) / B))) / math.pi
	elif B <= -2.1e-148:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif B <= -2e-302:
		tmp = 180.0 * (math.atan((1.0 - ((A - C) / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.5e-127)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(B + C) - A) / B))) / pi);
	elseif (B <= -2.1e-148)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (B <= -2e-302)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(Float64(A - C) / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.5e-127)
		tmp = (180.0 * atan((((B + C) - A) / B))) / pi;
	elseif (B <= -2.1e-148)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (B <= -2e-302)
		tmp = 180.0 * (atan((1.0 - ((A - C) / B))) / pi);
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.5e-127], N[(N[(180.0 * N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, -2.1e-148], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2e-302], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.4999999999999999e-127

   1. Initial program 62.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 62.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 62.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 62.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 62.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 62.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 84.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 84.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]
   4. Step-by-step derivation

      1. *-commutative 84.6%

         \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi} \cdot 180} \]

      2. associate-*l/ 84.6%

         \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot 180}{\pi}} \]

      3. hypot-udef 62.8%

         \[\leadsto \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}}{B}\right) \cdot 180}{\pi} \]

      4. unpow2 62.8%

         \[\leadsto \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}}{B}\right) \cdot 180}{\pi} \]

      5. unpow2 62.8%

         \[\leadsto \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}}{B}\right) \cdot 180}{\pi} \]

      6. +-commutative 62.8%

         \[\leadsto \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \cdot 180}{\pi} \]

      7. unpow2 62.8%

         \[\leadsto \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}}{B}\right) \cdot 180}{\pi} \]

      8. unpow2 62.8%

         \[\leadsto \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}}{B}\right) \cdot 180}{\pi} \]

      9. hypot-def 84.6%

         \[\leadsto \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(A - C, B\right)}}{B}\right) \cdot 180}{\pi} \]

   5. Applied egg-rr 84.6%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right) \cdot 180}{\pi}} \]

   6. Taylor expanded in B around -inf 81.3%

      \[\leadsto \frac{\tan^{-1} \left(\frac{\color{blue}{\left(B + C\right) - A}}{B}\right) \cdot 180}{\pi} \]

   if -2.4999999999999999e-127 < B < -2.1e-148

   1. Initial program 14.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 14.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 14.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 14.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 14.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 14.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 36.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 36.7%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]
   4. Step-by-step derivation

      1. clear-num 36.7%

         \[\leadsto 180 \cdot \color{blue}{\frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}} \]

      2. un-div-inv 36.7%

         \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}} \]

      3. div-inv 36.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \frac{1}{B}\right)}}} \]

      4. associate--r+ 26.3%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{\left(C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \frac{1}{B}\right)}} \]

      5. hypot-udef 14.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      6. unpow2 14.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}} \]

      7. unpow2 14.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      8. +-commutative 14.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      9. associate--l- 14.4%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)} \cdot \frac{1}{B}\right)}} \]

      10. *-commutative 14.4%

          \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}} \]

   5. Applied egg-rr 36.7%

      \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}} \]

   6. Taylor expanded in A around -inf 57.7%

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 57.7%

         \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)} \]

   8. Applied egg-rr 57.7%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)} \]

   if -2.1e-148 < B < -1.9999999999999999e-302

   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 62.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   3. Step-by-step derivation

      1. associate--l+ 62.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)}}{\pi} \]

      2. div-sub 64.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\pi} \]

   4. Simplified 64.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   if -1.9999999999999999e-302 < B

   1. Initial program 48.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

   3. Simplified 69.9%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}} \]

   4. Taylor expanded in B around inf 65.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + B\right)}}{B}\right)}{\pi} \]
   5. Step-by-step derivation

      1. +-commutative 65.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(B + A\right)}}{B}\right)}{\pi} \]

   6. Simplified 65.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(B + A\right)}}{B}\right)}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.5 \cdot 10^{-127}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-148}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 18: 50.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.7 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-249}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-A}{B}\right)}}\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-91}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.7e-256)
   (* 180.0 (/ (atan (+ (/ C B) 1.0)) PI))
   (if (<= B 1.45e-249)
     (/ 180.0 (/ PI (atan (/ (- A) B))))
     (if (<= B 1.9e-91)
       (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.7e-256) {
		tmp = 180.0 * (atan(((C / B) + 1.0)) / ((double) M_PI));
	} else if (B <= 1.45e-249) {
		tmp = 180.0 / (((double) M_PI) / atan((-A / B)));
	} else if (B <= 1.9e-91) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.7e-256) {
		tmp = 180.0 * (Math.atan(((C / B) + 1.0)) / Math.PI);
	} else if (B <= 1.45e-249) {
		tmp = 180.0 / (Math.PI / Math.atan((-A / B)));
	} else if (B <= 1.9e-91) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4.7e-256:
		tmp = 180.0 * (math.atan(((C / B) + 1.0)) / math.pi)
	elif B <= 1.45e-249:
		tmp = 180.0 / (math.pi / math.atan((-A / B)))
	elif B <= 1.9e-91:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -4.7e-256)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + 1.0)) / pi));
	elseif (B <= 1.45e-249)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(-A) / B))));
	elseif (B <= 1.9e-91)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -4.7e-256)
		tmp = 180.0 * (atan(((C / B) + 1.0)) / pi);
	elseif (B <= 1.45e-249)
		tmp = 180.0 / (pi / atan((-A / B)));
	elseif (B <= 1.9e-91)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.7e-256], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.45e-249], N[(180.0 / N[(Pi / N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.9e-91], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -4.69999999999999982e-256

   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 B around -inf 72.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   3. Step-by-step derivation

      1. associate--l+ 72.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)}}{\pi} \]

      2. div-sub 73.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\pi} \]

   4. Simplified 73.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   5. Taylor expanded in C around inf 60.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C}{B}}\right)}{\pi} \]

   if -4.69999999999999982e-256 < B < 1.45000000000000011e-249

   1. Initial program 65.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. associate-*l/ 65.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 65.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 65.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 65.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 65.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 86.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 86.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]
   4. Step-by-step derivation

      1. clear-num 86.6%

         \[\leadsto 180 \cdot \color{blue}{\frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}} \]

      2. un-div-inv 86.6%

         \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}} \]

      3. div-inv 86.6%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \frac{1}{B}\right)}}} \]

      4. associate--r+ 65.5%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{\left(C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \frac{1}{B}\right)}} \]

      5. hypot-udef 61.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      6. unpow2 61.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}} \]

      7. unpow2 61.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      8. +-commutative 61.9%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      9. associate--l- 65.7%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)} \cdot \frac{1}{B}\right)}} \]

      10. *-commutative 65.7%

          \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}} \]

   5. Applied egg-rr 86.6%

      \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}} \]

   6. Taylor expanded in C around 0 58.8%

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + \sqrt{{A}^{2} + {B}^{2}}\right)}}{B}\right)}} \]
   7. Step-by-step derivation

      1. mul-1-neg 58.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\color{blue}{-\left(A + \sqrt{{A}^{2} + {B}^{2}}\right)}}{B}\right)}} \]

      2. unpow2 58.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\left(A + \sqrt{\color{blue}{A \cdot A} + {B}^{2}}\right)}{B}\right)}} \]

      3. unpow2 58.8%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\left(A + \sqrt{A \cdot A + \color{blue}{B \cdot B}}\right)}{B}\right)}} \]

      4. hypot-def 76.2%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\left(A + \color{blue}{\mathsf{hypot}\left(A, B\right)}\right)}{B}\right)}} \]

   8. Simplified 76.2%

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\color{blue}{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}}{B}\right)}} \]

   9. Taylor expanded in A around 0 54.8%

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\color{blue}{\left(A + B\right)}}{B}\right)}} \]

   10. Taylor expanded in A around inf 54.8%

       \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A}{B}\right)}}} \]
   11. Step-by-step derivation

       1. associate-*r/ 54.8%

          \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(\frac{-1 \cdot A}{B}\right)}}} \]

       2. mul-1-neg 54.8%

          \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\color{blue}{-A}}{B}\right)}} \]

   12. Simplified 54.8%

       \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(\frac{-A}{B}\right)}}} \]

   if 1.45000000000000011e-249 < B < 1.89999999999999989e-91

   1. Initial program 46.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   2. Taylor expanded in C around -inf 34.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(2 \cdot \frac{C}{B}\right)}}{\pi} \]

   if 1.89999999999999989e-91 < B

   1. Initial program 46.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   2. Taylor expanded in B around inf 60.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.7 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-249}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-A}{B}\right)}}\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-91}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 19: 55.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.26 \cdot 10^{-42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.26e-42)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (if (<= B -5e-256)
     (* 180.0 (/ (atan (+ (/ C B) 1.0)) PI))
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.26e-42) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= -5e-256) {
		tmp = 180.0 * (atan(((C / B) + 1.0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.26e-42) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= -5e-256) {
		tmp = 180.0 * (Math.atan(((C / B) + 1.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.26e-42:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= -5e-256:
		tmp = 180.0 * (math.atan(((C / B) + 1.0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.26e-42)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= -5e-256)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + 1.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.26e-42)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= -5e-256)
		tmp = 180.0 * (atan(((C / B) + 1.0)) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.26e-42], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -5e-256], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.26e-42

   1. Initial program 59.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   2. Taylor expanded in B around -inf 81.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   3. Step-by-step derivation

      1. associate--l+ 81.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)}}{\pi} \]

      2. div-sub 81.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\pi} \]

   4. Simplified 81.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   5. Taylor expanded in C around 0 75.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 - \frac{A}{B}\right)}}{\pi} \]

   if -1.26e-42 < B < -5e-256

   1. Initial program 61.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   2. Taylor expanded in B around -inf 59.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   3. Step-by-step derivation

      1. associate--l+ 59.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)}}{\pi} \]

      2. div-sub 61.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\pi} \]

   4. Simplified 61.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   5. Taylor expanded in C around inf 51.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C}{B}}\right)}{\pi} \]

   if -5e-256 < 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. Step-by-step derivation

      1. associate-*l/ 50.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 50.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 50.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 50.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 50.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 76.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 76.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]
   4. Step-by-step derivation

      1. clear-num 76.1%

         \[\leadsto 180 \cdot \color{blue}{\frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}} \]

      2. un-div-inv 76.1%

         \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}} \]

      3. div-inv 76.1%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \frac{1}{B}\right)}}} \]

      4. associate--r+ 69.4%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{\left(C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \frac{1}{B}\right)}} \]

      5. hypot-udef 49.3%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      6. unpow2 49.3%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}} \]

      7. unpow2 49.3%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      8. +-commutative 49.3%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      9. associate--l- 50.2%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)} \cdot \frac{1}{B}\right)}} \]

      10. *-commutative 50.2%

          \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}} \]

   5. Applied egg-rr 76.1%

      \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}} \]

   6. Taylor expanded in C around 0 41.4%

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + \sqrt{{A}^{2} + {B}^{2}}\right)}}{B}\right)}} \]
   7. Step-by-step derivation

      1. mul-1-neg 41.4%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\color{blue}{-\left(A + \sqrt{{A}^{2} + {B}^{2}}\right)}}{B}\right)}} \]

      2. unpow2 41.4%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\left(A + \sqrt{\color{blue}{A \cdot A} + {B}^{2}}\right)}{B}\right)}} \]

      3. unpow2 41.4%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\left(A + \sqrt{A \cdot A + \color{blue}{B \cdot B}}\right)}{B}\right)}} \]

      4. hypot-def 63.2%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\left(A + \color{blue}{\mathsf{hypot}\left(A, B\right)}\right)}{B}\right)}} \]

   8. Simplified 63.2%

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\color{blue}{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}}{B}\right)}} \]

   9. Taylor expanded in A around 0 55.1%

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\color{blue}{\left(A + B\right)}}{B}\right)}} \]

   10. Taylor expanded in A around 0 55.1%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{A + B}{B}\right)}{\pi}} \]
   11. Step-by-step derivation

       1. neg-mul-1 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-\frac{A + B}{B}\right)}}{\pi} \]

       2. distribute-neg-frac 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-\left(A + B\right)}{B}\right)}}{\pi} \]

       3. +-commutative 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-\color{blue}{\left(B + A\right)}}{B}\right)}{\pi} \]

       4. distribute-neg-in 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(-B\right) + \left(-A\right)}}{B}\right)}{\pi} \]

       5. mul-1-neg 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot B} + \left(-A\right)}{B}\right)}{\pi} \]

       6. sub-neg 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot B - A}}{B}\right)}{\pi} \]

       7. sub-neg 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot B + \left(-A\right)}}{B}\right)}{\pi} \]

       8. mul-1-neg 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(-B\right)} + \left(-A\right)}{B}\right)}{\pi} \]

       9. distribute-neg-in 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-\left(B + A\right)}}{B}\right)}{\pi} \]

       10. +-commutative 55.1%

           \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-\color{blue}{\left(A + B\right)}}{B}\right)}{\pi} \]

       11. distribute-neg-in 55.1%

           \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(-A\right) + \left(-B\right)}}{B}\right)}{\pi} \]

       12. mul-1-neg 55.1%

           \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot A} + \left(-B\right)}{B}\right)}{\pi} \]

       13. sub-neg 55.1%

           \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot A - B}}{B}\right)}{\pi} \]

   12. Simplified 55.1%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.26 \cdot 10^{-42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 20: 44.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.6 \cdot 10^{-190}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5.3 \cdot 10^{-76}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.6e-190)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 5.3e-76)
     (* 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 <= -5.6e-190) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 5.3e-76) {
		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 <= -5.6e-190) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 5.3e-76) {
		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 <= -5.6e-190:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 5.3e-76:
		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 <= -5.6e-190)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 5.3e-76)
		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 <= -5.6e-190)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 5.3e-76)
		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, -5.6e-190], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.3e-76], 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 < -5.60000000000000011e-190

   1. Initial program 59.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   2. Taylor expanded in B around -inf 44.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -5.60000000000000011e-190 < B < 5.3e-76

   1. Initial program 55.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   2. Taylor expanded in C around inf 25.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]
   3. Step-by-step derivation

      1. associate-*r/ 25.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}\right)}}{\pi} \]

      2. distribute-rgt1-in 25.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      3. metadata-eval 25.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      4. mul0-lft 25.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      5. metadata-eval 25.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   4. Simplified 25.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]

   if 5.3e-76 < B

   1. Initial program 46.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   2. Taylor expanded in B around inf 63.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.6 \cdot 10^{-190}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5.3 \cdot 10^{-76}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 21: 55.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.5 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.5e-256)
   (* 180.0 (/ (atan (+ (/ C B) 1.0)) PI))
   (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.5e-256) {
		tmp = 180.0 * (atan(((C / B) + 1.0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.5e-256) {
		tmp = 180.0 * (Math.atan(((C / B) + 1.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5.5e-256:
		tmp = 180.0 * (math.atan(((C / B) + 1.0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5.5e-256)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + 1.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5.5e-256)
		tmp = 180.0 * (atan(((C / B) + 1.0)) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5.5e-256], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -5.4999999999999998e-256

   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 B around -inf 72.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   3. Step-by-step derivation

      1. associate--l+ 72.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)}}{\pi} \]

      2. div-sub 73.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\pi} \]

   4. Simplified 73.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   5. Taylor expanded in C around inf 60.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C}{B}}\right)}{\pi} \]

   if -5.4999999999999998e-256 < 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. Step-by-step derivation

      1. associate-*l/ 50.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)}}{\pi} \]

      2. *-lft-identity 50.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right)}{\pi} \]

      3. +-commutative 50.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right)}{\pi} \]

      4. unpow2 50.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right)}{\pi} \]

      5. unpow2 50.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right)}{\pi} \]

      6. hypot-def 76.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\pi} \]

   3. Simplified 76.1%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}} \]
   4. Step-by-step derivation

      1. clear-num 76.1%

         \[\leadsto 180 \cdot \color{blue}{\frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}} \]

      2. un-div-inv 76.1%

         \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}} \]

      3. div-inv 76.1%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(\left(\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)\right) \cdot \frac{1}{B}\right)}}} \]

      4. associate--r+ 69.4%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{\left(C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)\right)} \cdot \frac{1}{B}\right)}} \]

      5. hypot-udef 49.3%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      6. unpow2 49.3%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}\right)\right) \cdot \frac{1}{B}\right)}} \]

      7. unpow2 49.3%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      8. +-commutative 49.3%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\left(C - \left(A + \sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}\right)\right) \cdot \frac{1}{B}\right)}} \]

      9. associate--l- 50.2%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\color{blue}{\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)} \cdot \frac{1}{B}\right)}} \]

      10. *-commutative 50.2%

          \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{\left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}}} \]

   5. Applied egg-rr 76.1%

      \[\leadsto \color{blue}{\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}} \]

   6. Taylor expanded in C around 0 41.4%

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot \left(A + \sqrt{{A}^{2} + {B}^{2}}\right)}}{B}\right)}} \]
   7. Step-by-step derivation

      1. mul-1-neg 41.4%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\color{blue}{-\left(A + \sqrt{{A}^{2} + {B}^{2}}\right)}}{B}\right)}} \]

      2. unpow2 41.4%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\left(A + \sqrt{\color{blue}{A \cdot A} + {B}^{2}}\right)}{B}\right)}} \]

      3. unpow2 41.4%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\left(A + \sqrt{A \cdot A + \color{blue}{B \cdot B}}\right)}{B}\right)}} \]

      4. hypot-def 63.2%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\left(A + \color{blue}{\mathsf{hypot}\left(A, B\right)}\right)}{B}\right)}} \]

   8. Simplified 63.2%

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\color{blue}{-\left(A + \mathsf{hypot}\left(A, B\right)\right)}}{B}\right)}} \]

   9. Taylor expanded in A around 0 55.1%

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-\color{blue}{\left(A + B\right)}}{B}\right)}} \]

   10. Taylor expanded in A around 0 55.1%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{A + B}{B}\right)}{\pi}} \]
   11. Step-by-step derivation

       1. neg-mul-1 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-\frac{A + B}{B}\right)}}{\pi} \]

       2. distribute-neg-frac 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-\left(A + B\right)}{B}\right)}}{\pi} \]

       3. +-commutative 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-\color{blue}{\left(B + A\right)}}{B}\right)}{\pi} \]

       4. distribute-neg-in 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(-B\right) + \left(-A\right)}}{B}\right)}{\pi} \]

       5. mul-1-neg 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot B} + \left(-A\right)}{B}\right)}{\pi} \]

       6. sub-neg 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot B - A}}{B}\right)}{\pi} \]

       7. sub-neg 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot B + \left(-A\right)}}{B}\right)}{\pi} \]

       8. mul-1-neg 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(-B\right)} + \left(-A\right)}{B}\right)}{\pi} \]

       9. distribute-neg-in 55.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-\left(B + A\right)}}{B}\right)}{\pi} \]

       10. +-commutative 55.1%

           \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-\color{blue}{\left(A + B\right)}}{B}\right)}{\pi} \]

       11. distribute-neg-in 55.1%

           \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(-A\right) + \left(-B\right)}}{B}\right)}{\pi} \]

       12. mul-1-neg 55.1%

           \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot A} + \left(-B\right)}{B}\right)}{\pi} \]

       13. sub-neg 55.1%

           \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-1 \cdot A - B}}{B}\right)}{\pi} \]

   12. Simplified 55.1%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.5 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 22: 39.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-309}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e-309) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-309) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-309) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1e-309:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1e-309)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1e-309)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1e-309], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.000000000000002e-309

   1. Initial program 61.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   2. Taylor expanded in B around -inf 37.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -1.000000000000002e-309 < B

   1. Initial program 48.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   2. Taylor expanded in B around inf 40.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-309}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 23: 20.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ 180 \cdot \frac{\tan^{-1} -1}{\pi} \end{array} \]

FPCore

(FPCore (A B C) :precision binary64 (* 180.0 (/ (atan -1.0) PI)))

C

double code(double A, double B, double C) {
	return 180.0 * (atan(-1.0) / ((double) M_PI));
}

Java

public static double code(double A, double B, double C) {
	return 180.0 * (Math.atan(-1.0) / Math.PI);
}

Python

def code(A, B, C):
	return 180.0 * (math.atan(-1.0) / math.pi)

Julia

function code(A, B, C)
	return Float64(180.0 * Float64(atan(-1.0) / pi))
end

MATLAB

function tmp = code(A, B, C)
	tmp = 180.0 * (atan(-1.0) / pi);
end

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 55.1%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

2. Taylor expanded in B around inf 20.2%

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

3. Final simplification 20.2%

   \[\leadsto 180 \cdot \frac{\tan^{-1} -1}{\pi} \]

Reproduce

herbie shell --seed 2023310 
(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)))