ABCF->ab-angle angle

Percentage Accurate: 53.9% → 81.3%

Time: 22.1s

Alternatives: 21

Speedup: 3.6×

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: 53.9% 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: 81.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ t_1 := \tan^{-1} \left(\frac{A - A}{B} + -0.5 \cdot \frac{B}{C}\right)\\ \mathbf{if}\;C \leq 5.4 \cdot 10^{+154}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{+199}:\\ \;\;\;\;180 \cdot \frac{t\_1}{\pi}\\ \mathbf{elif}\;C \leq 5.6 \cdot 10^{+234}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{t\_1}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI)))
        (t_1 (atan (+ (/ (- A A) B) (* -0.5 (/ B C))))))
   (if (<= C 5.4e+154)
     t_0
     (if (<= C 3.5e+199)
       (* 180.0 (/ t_1 PI))
       (if (<= C 5.6e+234) t_0 (/ 180.0 (/ PI t_1)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	double t_1 = atan((((A - A) / B) + (-0.5 * (B / C))));
	double tmp;
	if (C <= 5.4e+154) {
		tmp = t_0;
	} else if (C <= 3.5e+199) {
		tmp = 180.0 * (t_1 / ((double) M_PI));
	} else if (C <= 5.6e+234) {
		tmp = t_0;
	} else {
		tmp = 180.0 / (((double) M_PI) / t_1);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	double t_1 = Math.atan((((A - A) / B) + (-0.5 * (B / C))));
	double tmp;
	if (C <= 5.4e+154) {
		tmp = t_0;
	} else if (C <= 3.5e+199) {
		tmp = 180.0 * (t_1 / Math.PI);
	} else if (C <= 5.6e+234) {
		tmp = t_0;
	} else {
		tmp = 180.0 / (Math.PI / t_1);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	t_1 = math.atan((((A - A) / B) + (-0.5 * (B / C))))
	tmp = 0
	if C <= 5.4e+154:
		tmp = t_0
	elif C <= 3.5e+199:
		tmp = 180.0 * (t_1 / math.pi)
	elif C <= 5.6e+234:
		tmp = t_0
	else:
		tmp = 180.0 / (math.pi / t_1)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi))
	t_1 = atan(Float64(Float64(Float64(A - A) / B) + Float64(-0.5 * Float64(B / C))))
	tmp = 0.0
	if (C <= 5.4e+154)
		tmp = t_0;
	elseif (C <= 3.5e+199)
		tmp = Float64(180.0 * Float64(t_1 / pi));
	elseif (C <= 5.6e+234)
		tmp = t_0;
	else
		tmp = Float64(180.0 / Float64(pi / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	t_1 = atan((((A - A) / B) + (-0.5 * (B / C))));
	tmp = 0.0;
	if (C <= 5.4e+154)
		tmp = t_0;
	elseif (C <= 3.5e+199)
		tmp = 180.0 * (t_1 / pi);
	elseif (C <= 5.6e+234)
		tmp = t_0;
	else
		tmp = 180.0 / (pi / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, Block[{t$95$1 = N[ArcTan[N[(N[(N[(A - A), $MachinePrecision] / B), $MachinePrecision] + N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[C, 5.4e+154], t$95$0, If[LessEqual[C, 3.5e+199], N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 5.6e+234], t$95$0, N[(180.0 / N[(Pi / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if C < 5.40000000000000011e154 or 3.49999999999999981e199 < C < 5.5999999999999997e234

   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. Step-by-step derivation

      1. associate-*l/ 60.5%

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

      2. *-lft-identity 60.5%

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

      3. +-commutative 60.5%

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

      4. unpow2 60.5%

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

      5. unpow2 60.5%

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

      6. hypot-define 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. Add Preprocessing

   if 5.40000000000000011e154 < C < 3.49999999999999981e199

   1. Initial program 6.2%

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

   3. Taylor expanded in C around inf 86.9%

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

   if 5.5999999999999997e234 < C

   1. Initial program 4.5%

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

   4. Applied egg-rr 45.5%

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

   5. Taylor expanded in C around inf 99.7%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 5.4 \cdot 10^{+154}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{+199}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A - A}{B} + -0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.6 \cdot 10^{+234}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{A - A}{B} + -0.5 \cdot \frac{B}{C}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -0.02 \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{-A}\right)}}\\ \end{array} \end{array} \]

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 (or (<= t_0 -0.02) (not (<= t_0 0.0)))
     (/ 180.0 (/ PI (atan (/ (- (- C A) (hypot (- A C) B)) B))))
     (/ 180.0 (/ PI (atan (/ (* -0.5 (+ B (* B (/ C A)))) (- A))))))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -0.02) || !(t_0 <= 0.0)) {
		tmp = 180.0 / (((double) M_PI) / atan((((C - A) - hypot((A - C), B)) / B)));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((-0.5 * (B + (B * (C / A)))) / -A)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -0.02) || !(t_0 <= 0.0)) {
		tmp = 180.0 / (Math.PI / Math.atan((((C - A) - Math.hypot((A - C), B)) / B)));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((-0.5 * (B + (B * (C / A)))) / -A)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if (t_0 <= -0.02) or not (t_0 <= 0.0):
		tmp = 180.0 / (math.pi / math.atan((((C - A) - math.hypot((A - C), B)) / B)))
	else:
		tmp = 180.0 / (math.pi / math.atan(((-0.5 * (B + (B * (C / A)))) / -A)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if ((t_0 <= -0.02) || !(t_0 <= 0.0))
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(-0.5 * Float64(B + Float64(B * Float64(C / A)))) / Float64(-A)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if ((t_0 <= -0.02) || ~((t_0 <= 0.0)))
		tmp = 180.0 / (pi / atan((((C - A) - hypot((A - C), B)) / B)));
	else
		tmp = 180.0 / (pi / atan(((-0.5 * (B + (B * (C / A)))) / -A)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -0.02], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(-0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-A)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -0.0200000000000000004 or -0.0 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 60.3%

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

   4. Applied egg-rr 88.8%

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

   if -0.0200000000000000004 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -0.0

   1. Initial program 17.7%

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

   4. Applied egg-rr 17.7%

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

   5. Taylor expanded in A around -inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. distribute-neg-frac2 55.9%

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

      3. distribute-lft-out 55.9%

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

      4. associate-/l* 56.8%

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

   7. Simplified 56.8%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.02 \lor \neg \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0\right):\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{-A}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -5.2 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -2.7 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{t\_0}{\pi}\\ \mathbf{elif}\;A \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq 8 \cdot 10^{+84}:\\ \;\;\;\;\frac{180}{\frac{\pi}{t\_0}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (/ (- C (hypot B C)) B)))
        (t_1 (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))))
   (if (<= A -5.2e+166)
     t_1
     (if (<= A -2.7e-20)
       (* 180.0 (/ t_0 PI))
       (if (<= A -2.25e-61)
         t_1
         (if (<= A 8e+84)
           (/ 180.0 (/ PI t_0))
           (* 180.0 (/ (atan (/ (+ A (hypot B A)) (- B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((C - hypot(B, C)) / B));
	double t_1 = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	double tmp;
	if (A <= -5.2e+166) {
		tmp = t_1;
	} else if (A <= -2.7e-20) {
		tmp = 180.0 * (t_0 / ((double) M_PI));
	} else if (A <= -2.25e-61) {
		tmp = t_1;
	} else if (A <= 8e+84) {
		tmp = 180.0 / (((double) M_PI) / 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 = Math.atan(((C - Math.hypot(B, C)) / B));
	double t_1 = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	double tmp;
	if (A <= -5.2e+166) {
		tmp = t_1;
	} else if (A <= -2.7e-20) {
		tmp = 180.0 * (t_0 / Math.PI);
	} else if (A <= -2.25e-61) {
		tmp = t_1;
	} else if (A <= 8e+84) {
		tmp = 180.0 / (Math.PI / 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 = math.atan(((C - math.hypot(B, C)) / B))
	t_1 = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	tmp = 0
	if A <= -5.2e+166:
		tmp = t_1
	elif A <= -2.7e-20:
		tmp = 180.0 * (t_0 / math.pi)
	elif A <= -2.25e-61:
		tmp = t_1
	elif A <= 8e+84:
		tmp = 180.0 / (math.pi / 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 = atan(Float64(Float64(C - hypot(B, C)) / B))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi))
	tmp = 0.0
	if (A <= -5.2e+166)
		tmp = t_1;
	elseif (A <= -2.7e-20)
		tmp = Float64(180.0 * Float64(t_0 / pi));
	elseif (A <= -2.25e-61)
		tmp = t_1;
	elseif (A <= 8e+84)
		tmp = Float64(180.0 / Float64(pi / t_0));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((C - hypot(B, C)) / B));
	t_1 = 180.0 * (atan(((B * 0.5) / A)) / pi);
	tmp = 0.0;
	if (A <= -5.2e+166)
		tmp = t_1;
	elseif (A <= -2.7e-20)
		tmp = 180.0 * (t_0 / pi);
	elseif (A <= -2.25e-61)
		tmp = t_1;
	elseif (A <= 8e+84)
		tmp = 180.0 / (pi / 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[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -5.2e+166], t$95$1, If[LessEqual[A, -2.7e-20], N[(180.0 * N[(t$95$0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.25e-61], t$95$1, If[LessEqual[A, 8e+84], N[(180.0 / N[(Pi / t$95$0), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -5.1999999999999999e166 or -2.7e-20 < A < -2.25e-61

   1. Initial program 13.8%

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

   3. Taylor expanded in A around -inf 80.9%

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

      1. associate-*r/ 80.9%

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

   5. Simplified 80.9%

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

   if -5.1999999999999999e166 < A < -2.7e-20

   1. Initial program 47.2%

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

   3. Taylor expanded in A around 0 39.0%

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

      1. unpow2 39.0%

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

      2. unpow2 39.0%

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

      3. hypot-define 72.3%

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

   5. Simplified 72.3%

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

   if -2.25e-61 < A < 8.00000000000000046e84

   1. Initial program 60.3%

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

   4. Applied egg-rr 84.8%

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

   5. Taylor expanded in A around 0 57.0%

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

      1. unpow2 57.0%

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

      2. unpow2 57.0%

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

      3. hypot-define 81.6%

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

   7. Simplified 81.6%

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

   if 8.00000000000000046e84 < A

   1. Initial program 75.5%

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

   3. Taylor expanded in C around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. distribute-neg-frac2 75.5%

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

      3. +-commutative 75.5%

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

      4. unpow2 75.5%

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

      5. unpow2 75.5%

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

      6. hypot-define 92.6%

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

   5. Simplified 92.6%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.7 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 8 \cdot 10^{+84}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -1.8 \cdot 10^{+167}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -2.7 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{t\_0}{\pi}\\ \mathbf{elif}\;A \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq 8 \cdot 10^{+84}:\\ \;\;\;\;\frac{180}{\frac{\pi}{t\_0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (/ (- C (hypot B C)) B)))
        (t_1 (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))))
   (if (<= A -1.8e+167)
     t_1
     (if (<= A -2.7e-20)
       (* 180.0 (/ t_0 PI))
       (if (<= A -2.25e-61)
         t_1
         (if (<= A 8e+84)
           (/ 180.0 (/ PI t_0))
           (/ 180.0 (/ PI (atan (/ (- (- A) (hypot A B)) B))))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((C - hypot(B, C)) / B));
	double t_1 = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	double tmp;
	if (A <= -1.8e+167) {
		tmp = t_1;
	} else if (A <= -2.7e-20) {
		tmp = 180.0 * (t_0 / ((double) M_PI));
	} else if (A <= -2.25e-61) {
		tmp = t_1;
	} else if (A <= 8e+84) {
		tmp = 180.0 / (((double) M_PI) / 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 = Math.atan(((C - Math.hypot(B, C)) / B));
	double t_1 = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	double tmp;
	if (A <= -1.8e+167) {
		tmp = t_1;
	} else if (A <= -2.7e-20) {
		tmp = 180.0 * (t_0 / Math.PI);
	} else if (A <= -2.25e-61) {
		tmp = t_1;
	} else if (A <= 8e+84) {
		tmp = 180.0 / (Math.PI / 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 = math.atan(((C - math.hypot(B, C)) / B))
	t_1 = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	tmp = 0
	if A <= -1.8e+167:
		tmp = t_1
	elif A <= -2.7e-20:
		tmp = 180.0 * (t_0 / math.pi)
	elif A <= -2.25e-61:
		tmp = t_1
	elif A <= 8e+84:
		tmp = 180.0 / (math.pi / 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 = atan(Float64(Float64(C - hypot(B, C)) / B))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi))
	tmp = 0.0
	if (A <= -1.8e+167)
		tmp = t_1;
	elseif (A <= -2.7e-20)
		tmp = Float64(180.0 * Float64(t_0 / pi));
	elseif (A <= -2.25e-61)
		tmp = t_1;
	elseif (A <= 8e+84)
		tmp = Float64(180.0 / Float64(pi / 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 = atan(((C - hypot(B, C)) / B));
	t_1 = 180.0 * (atan(((B * 0.5) / A)) / pi);
	tmp = 0.0;
	if (A <= -1.8e+167)
		tmp = t_1;
	elseif (A <= -2.7e-20)
		tmp = 180.0 * (t_0 / pi);
	elseif (A <= -2.25e-61)
		tmp = t_1;
	elseif (A <= 8e+84)
		tmp = 180.0 / (pi / 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[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.8e+167], t$95$1, If[LessEqual[A, -2.7e-20], N[(180.0 * N[(t$95$0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.25e-61], t$95$1, If[LessEqual[A, 8e+84], N[(180.0 / N[(Pi / t$95$0), $MachinePrecision]), $MachinePrecision], 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 < -1.80000000000000012e167 or -2.7e-20 < A < -2.25e-61

   1. Initial program 13.8%

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

   3. Taylor expanded in A around -inf 80.9%

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

      1. associate-*r/ 80.9%

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

   5. Simplified 80.9%

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

   if -1.80000000000000012e167 < A < -2.7e-20

   1. Initial program 47.2%

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

   3. Taylor expanded in A around 0 39.0%

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

      1. unpow2 39.0%

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

      2. unpow2 39.0%

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

      3. hypot-define 72.3%

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

   5. Simplified 72.3%

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

   if -2.25e-61 < A < 8.00000000000000046e84

   1. Initial program 60.3%

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

   4. Applied egg-rr 84.8%

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

   5. Taylor expanded in A around 0 57.0%

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

      1. unpow2 57.0%

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

      2. unpow2 57.0%

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

      3. hypot-define 81.6%

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

   7. Simplified 81.6%

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

   if 8.00000000000000046e84 < A

   1. Initial program 75.5%

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

   4. Applied egg-rr 92.6%

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

   5. Taylor expanded in C around 0 75.5%

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

      1. distribute-lft-in 75.5%

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

      2. +-commutative 75.5%

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

      3. unpow2 75.5%

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

      4. unpow2 75.5%

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

      5. hypot-undefine 92.7%

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

      6. neg-mul-1 92.7%

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

      7. unsub-neg 92.7%

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

      8. neg-mul-1 92.7%

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

      9. hypot-undefine 75.5%

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

      10. unpow2 75.5%

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

      11. unpow2 75.5%

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

      12. +-commutative 75.5%

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

      13. unpow2 75.5%

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

      14. unpow2 75.5%

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

      15. hypot-define 92.7%

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

   7. Simplified 92.7%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+167}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.7 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 8 \cdot 10^{+84}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -9.5 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -2.7 \cdot 10^{-20}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{+85}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + A}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI)))
        (t_1 (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))))
   (if (<= A -9.5e+166)
     t_1
     (if (<= A -2.7e-20)
       t_0
       (if (<= A -2.25e-61)
         t_1
         (if (<= A 1.05e+85)
           t_0
           (* 180.0 (/ (atan (/ (+ B A) (- B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	double tmp;
	if (A <= -9.5e+166) {
		tmp = t_1;
	} else if (A <= -2.7e-20) {
		tmp = t_0;
	} else if (A <= -2.25e-61) {
		tmp = t_1;
	} else if (A <= 1.05e+85) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((B + A) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	double tmp;
	if (A <= -9.5e+166) {
		tmp = t_1;
	} else if (A <= -2.7e-20) {
		tmp = t_0;
	} else if (A <= -2.25e-61) {
		tmp = t_1;
	} else if (A <= 1.05e+85) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((B + A) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	t_1 = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	tmp = 0
	if A <= -9.5e+166:
		tmp = t_1
	elif A <= -2.7e-20:
		tmp = t_0
	elif A <= -2.25e-61:
		tmp = t_1
	elif A <= 1.05e+85:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((B + A) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi))
	tmp = 0.0
	if (A <= -9.5e+166)
		tmp = t_1;
	elseif (A <= -2.7e-20)
		tmp = t_0;
	elseif (A <= -2.25e-61)
		tmp = t_1;
	elseif (A <= 1.05e+85)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + A) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	t_1 = 180.0 * (atan(((B * 0.5) / A)) / pi);
	tmp = 0.0;
	if (A <= -9.5e+166)
		tmp = t_1;
	elseif (A <= -2.7e-20)
		tmp = t_0;
	elseif (A <= -2.25e-61)
		tmp = t_1;
	elseif (A <= 1.05e+85)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((B + A) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -9.5e+166], t$95$1, If[LessEqual[A, -2.7e-20], t$95$0, If[LessEqual[A, -2.25e-61], t$95$1, If[LessEqual[A, 1.05e+85], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(B + A), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if A < -9.49999999999999984e166 or -2.7e-20 < A < -2.25e-61

   1. Initial program 13.8%

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

   3. Taylor expanded in A around -inf 80.9%

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

      1. associate-*r/ 80.9%

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

   5. Simplified 80.9%

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

   if -9.49999999999999984e166 < A < -2.7e-20 or -2.25e-61 < A < 1.05000000000000005e85

   1. Initial program 57.2%

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

   3. Taylor expanded in A around 0 52.8%

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

      1. unpow2 52.8%

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

      2. unpow2 52.8%

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

      3. hypot-define 79.4%

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

   5. Simplified 79.4%

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

   if 1.05000000000000005e85 < A

   1. Initial program 75.5%

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

   3. Taylor expanded in C around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. distribute-neg-frac2 75.5%

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

      3. +-commutative 75.5%

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

      4. unpow2 75.5%

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

      5. unpow2 75.5%

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

      6. hypot-define 92.6%

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

   5. Simplified 92.6%

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

   6. Taylor expanded in A around 0 81.7%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{+166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.7 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{+85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + A}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -9.5 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -2.7 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{t\_0}{\pi}\\ \mathbf{elif}\;A \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq 5.8 \cdot 10^{+85}:\\ \;\;\;\;\frac{180}{\frac{\pi}{t\_0}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + A}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (/ (- C (hypot B C)) B)))
        (t_1 (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))))
   (if (<= A -9.5e+166)
     t_1
     (if (<= A -2.7e-20)
       (* 180.0 (/ t_0 PI))
       (if (<= A -2.25e-61)
         t_1
         (if (<= A 5.8e+85)
           (/ 180.0 (/ PI t_0))
           (* 180.0 (/ (atan (/ (+ B A) (- B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((C - hypot(B, C)) / B));
	double t_1 = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	double tmp;
	if (A <= -9.5e+166) {
		tmp = t_1;
	} else if (A <= -2.7e-20) {
		tmp = 180.0 * (t_0 / ((double) M_PI));
	} else if (A <= -2.25e-61) {
		tmp = t_1;
	} else if (A <= 5.8e+85) {
		tmp = 180.0 / (((double) M_PI) / t_0);
	} else {
		tmp = 180.0 * (atan(((B + A) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((C - Math.hypot(B, C)) / B));
	double t_1 = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	double tmp;
	if (A <= -9.5e+166) {
		tmp = t_1;
	} else if (A <= -2.7e-20) {
		tmp = 180.0 * (t_0 / Math.PI);
	} else if (A <= -2.25e-61) {
		tmp = t_1;
	} else if (A <= 5.8e+85) {
		tmp = 180.0 / (Math.PI / t_0);
	} else {
		tmp = 180.0 * (Math.atan(((B + A) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((C - math.hypot(B, C)) / B))
	t_1 = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	tmp = 0
	if A <= -9.5e+166:
		tmp = t_1
	elif A <= -2.7e-20:
		tmp = 180.0 * (t_0 / math.pi)
	elif A <= -2.25e-61:
		tmp = t_1
	elif A <= 5.8e+85:
		tmp = 180.0 / (math.pi / t_0)
	else:
		tmp = 180.0 * (math.atan(((B + A) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(Float64(C - hypot(B, C)) / B))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi))
	tmp = 0.0
	if (A <= -9.5e+166)
		tmp = t_1;
	elseif (A <= -2.7e-20)
		tmp = Float64(180.0 * Float64(t_0 / pi));
	elseif (A <= -2.25e-61)
		tmp = t_1;
	elseif (A <= 5.8e+85)
		tmp = Float64(180.0 / Float64(pi / t_0));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + A) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((C - hypot(B, C)) / B));
	t_1 = 180.0 * (atan(((B * 0.5) / A)) / pi);
	tmp = 0.0;
	if (A <= -9.5e+166)
		tmp = t_1;
	elseif (A <= -2.7e-20)
		tmp = 180.0 * (t_0 / pi);
	elseif (A <= -2.25e-61)
		tmp = t_1;
	elseif (A <= 5.8e+85)
		tmp = 180.0 / (pi / t_0);
	else
		tmp = 180.0 * (atan(((B + A) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -9.5e+166], t$95$1, If[LessEqual[A, -2.7e-20], N[(180.0 * N[(t$95$0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.25e-61], t$95$1, If[LessEqual[A, 5.8e+85], N[(180.0 / N[(Pi / t$95$0), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B + A), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -9.49999999999999984e166 or -2.7e-20 < A < -2.25e-61

   1. Initial program 13.8%

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

   3. Taylor expanded in A around -inf 80.9%

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

      1. associate-*r/ 80.9%

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

   5. Simplified 80.9%

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

   if -9.49999999999999984e166 < A < -2.7e-20

   1. Initial program 47.2%

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

   3. Taylor expanded in A around 0 39.0%

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

      1. unpow2 39.0%

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

      2. unpow2 39.0%

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

      3. hypot-define 72.3%

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

   5. Simplified 72.3%

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

   if -2.25e-61 < A < 5.79999999999999995e85

   1. Initial program 60.3%

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

   4. Applied egg-rr 84.8%

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

   5. Taylor expanded in A around 0 57.0%

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

      1. unpow2 57.0%

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

      2. unpow2 57.0%

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

      3. hypot-define 81.6%

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

   7. Simplified 81.6%

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

   if 5.79999999999999995e85 < A

   1. Initial program 75.5%

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

   3. Taylor expanded in C around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. distribute-neg-frac2 75.5%

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

      3. +-commutative 75.5%

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

      4. unpow2 75.5%

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

      5. unpow2 75.5%

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

      6. hypot-define 92.6%

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

   5. Simplified 92.6%

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

   6. Taylor expanded in A around 0 81.7%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{+166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.7 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.8 \cdot 10^{+85}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + A}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+166} \lor \neg \left(A \leq -2.7 \cdot 10^{-20}\right) \land A \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (or (<= A -5.2e+166) (and (not (<= A -2.7e-20)) (<= A -2.25e-61)))
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if ((A <= -5.2e+166) || (!(A <= -2.7e-20) && (A <= -2.25e-61))) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if ((A <= -5.2e+166) || (!(A <= -2.7e-20) && (A <= -2.25e-61))) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if (A <= -5.2e+166) or (not (A <= -2.7e-20) and (A <= -2.25e-61)):
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if ((A <= -5.2e+166) || (!(A <= -2.7e-20) && (A <= -2.25e-61)))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if ((A <= -5.2e+166) || (~((A <= -2.7e-20)) && (A <= -2.25e-61)))
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[Or[LessEqual[A, -5.2e+166], And[N[Not[LessEqual[A, -2.7e-20]], $MachinePrecision], LessEqual[A, -2.25e-61]]], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -5.1999999999999999e166 or -2.7e-20 < A < -2.25e-61

   1. Initial program 13.8%

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

   3. Taylor expanded in A around -inf 80.9%

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

      1. associate-*r/ 80.9%

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

   5. Simplified 80.9%

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

   if -5.1999999999999999e166 < A < -2.7e-20 or -2.25e-61 < A

   1. Initial program 61.5%

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

   3. Simplified 85.3%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+166} \lor \neg \left(A \leq -2.7 \cdot 10^{-20}\right) \land A \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{if}\;B \leq -4.8 \cdot 10^{-53}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-245}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;B \leq -9.6 \cdot 10^{-273}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-293}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-221}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + A}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ 180.0 (/ PI (atan 0.0)))))
   (if (<= B -4.8e-53)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (if (<= B -2.4e-245)
       (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
       (if (<= B -9.6e-273)
         (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
         (if (<= B 7.2e-293)
           t_0
           (if (<= B 1.8e-252)
             (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
             (if (<= B 2.2e-221)
               t_0
               (* 180.0 (/ (atan (/ (+ B A) (- B))) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 / (((double) M_PI) / atan(0.0));
	double tmp;
	if (B <= -4.8e-53) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (B <= -2.4e-245) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (B <= -9.6e-273) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (B <= 7.2e-293) {
		tmp = t_0;
	} else if (B <= 1.8e-252) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 2.2e-221) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((B + A) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 / (Math.PI / Math.atan(0.0));
	double tmp;
	if (B <= -4.8e-53) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (B <= -2.4e-245) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (B <= -9.6e-273) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (B <= 7.2e-293) {
		tmp = t_0;
	} else if (B <= 1.8e-252) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 2.2e-221) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((B + A) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 / (math.pi / math.atan(0.0))
	tmp = 0
	if B <= -4.8e-53:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif B <= -2.4e-245:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif B <= -9.6e-273:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif B <= 7.2e-293:
		tmp = t_0
	elif B <= 1.8e-252:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 2.2e-221:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((B + A) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 / Float64(pi / atan(0.0)))
	tmp = 0.0
	if (B <= -4.8e-53)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (B <= -2.4e-245)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (B <= -9.6e-273)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (B <= 7.2e-293)
		tmp = t_0;
	elseif (B <= 1.8e-252)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 2.2e-221)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + A) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 / (pi / atan(0.0));
	tmp = 0.0;
	if (B <= -4.8e-53)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (B <= -2.4e-245)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (B <= -9.6e-273)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (B <= 7.2e-293)
		tmp = t_0;
	elseif (B <= 1.8e-252)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 2.2e-221)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((B + A) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 / N[(Pi / N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -4.8e-53], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.4e-245], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -9.6e-273], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.2e-293], t$95$0, If[LessEqual[B, 1.8e-252], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.2e-221], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(B + A), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -4.80000000000000015e-53

   1. Initial program 55.0%

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

   3. Taylor expanded in B around -inf 82.5%

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

      1. associate--l+ 82.5%

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

      2. div-sub 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in C around inf 76.3%

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

   if -4.80000000000000015e-53 < B < -2.4e-245

   1. Initial program 46.7%

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

   4. Applied egg-rr 69.9%

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

   5. Taylor expanded in A around -inf 43.8%

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

   if -2.4e-245 < B < -9.59999999999999926e-273

   1. Initial program 100.0%

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

   3. Taylor expanded in C around -inf 100.0%

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

   if -9.59999999999999926e-273 < B < 7.1999999999999997e-293 or 1.80000000000000011e-252 < B < 2.20000000000000001e-221

   1. Initial program 40.6%

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

   4. Applied egg-rr 75.3%

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

      1. div-sub 23.3%

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

      2. sub-neg 23.3%

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

   6. Applied egg-rr 23.3%

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

      1. sub-neg 23.3%

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

   8. Simplified 23.3%

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

   9. Taylor expanded in C around inf 32.7%

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

       1. distribute-lft1-in 32.7%

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

       2. metadata-eval 32.7%

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

       3. mul0-lft 54.6%

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

       4. metadata-eval 54.6%

          \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{0}}} \]

   11. Simplified 54.6%

       \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{0}}} \]

   if 7.1999999999999997e-293 < B < 1.80000000000000011e-252

   1. Initial program 57.6%

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

   3. Taylor expanded in A around inf 57.0%

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

   if 2.20000000000000001e-221 < B

   1. Initial program 58.9%

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

   3. Taylor expanded in C around 0 51.2%

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

      1. mul-1-neg 51.2%

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

      2. distribute-neg-frac2 51.2%

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

      3. +-commutative 51.2%

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

      4. unpow2 51.2%

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

      5. unpow2 51.2%

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

      6. hypot-define 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in A around 0 64.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{A + B}}{-B}\right)}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.8 \cdot 10^{-53}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.4 \cdot 10^{-245}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;B \leq -9.6 \cdot 10^{-273}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-293}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-221}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + A}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{if}\;B \leq -6.5 \cdot 10^{-273}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-295}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-217}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-41}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ 180.0 (/ PI (atan 0.0))))
        (t_1 (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))))
   (if (<= B -6.5e-273)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (if (<= B 2.7e-295)
       t_0
       (if (<= B 1.35e-249)
         t_1
         (if (<= B 1.4e-217)
           t_0
           (if (<= B 1.1e-175)
             t_1
             (if (<= B 1.35e-41)
               (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
               (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 / (((double) M_PI) / atan(0.0));
	double t_1 = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	double tmp;
	if (B <= -6.5e-273) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (B <= 2.7e-295) {
		tmp = t_0;
	} else if (B <= 1.35e-249) {
		tmp = t_1;
	} else if (B <= 1.4e-217) {
		tmp = t_0;
	} else if (B <= 1.1e-175) {
		tmp = t_1;
	} else if (B <= 1.35e-41) {
		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 t_0 = 180.0 / (Math.PI / Math.atan(0.0));
	double t_1 = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	double tmp;
	if (B <= -6.5e-273) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (B <= 2.7e-295) {
		tmp = t_0;
	} else if (B <= 1.35e-249) {
		tmp = t_1;
	} else if (B <= 1.4e-217) {
		tmp = t_0;
	} else if (B <= 1.1e-175) {
		tmp = t_1;
	} else if (B <= 1.35e-41) {
		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):
	t_0 = 180.0 / (math.pi / math.atan(0.0))
	t_1 = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	tmp = 0
	if B <= -6.5e-273:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif B <= 2.7e-295:
		tmp = t_0
	elif B <= 1.35e-249:
		tmp = t_1
	elif B <= 1.4e-217:
		tmp = t_0
	elif B <= 1.1e-175:
		tmp = t_1
	elif B <= 1.35e-41:
		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)
	t_0 = Float64(180.0 / Float64(pi / atan(0.0)))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi))
	tmp = 0.0
	if (B <= -6.5e-273)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (B <= 2.7e-295)
		tmp = t_0;
	elseif (B <= 1.35e-249)
		tmp = t_1;
	elseif (B <= 1.4e-217)
		tmp = t_0;
	elseif (B <= 1.1e-175)
		tmp = t_1;
	elseif (B <= 1.35e-41)
		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)
	t_0 = 180.0 / (pi / atan(0.0));
	t_1 = 180.0 * (atan(((A / B) * -2.0)) / pi);
	tmp = 0.0;
	if (B <= -6.5e-273)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (B <= 2.7e-295)
		tmp = t_0;
	elseif (B <= 1.35e-249)
		tmp = t_1;
	elseif (B <= 1.4e-217)
		tmp = t_0;
	elseif (B <= 1.1e-175)
		tmp = t_1;
	elseif (B <= 1.35e-41)
		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_] := Block[{t$95$0 = N[(180.0 / N[(Pi / N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -6.5e-273], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.7e-295], t$95$0, If[LessEqual[B, 1.35e-249], t$95$1, If[LessEqual[B, 1.4e-217], t$95$0, If[LessEqual[B, 1.1e-175], t$95$1, If[LessEqual[B, 1.35e-41], 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 5 regimes

2. if B < -6.49999999999999979e-273

   1. Initial program 53.9%

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

   3. Taylor expanded in B around -inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. div-sub 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in C around inf 63.1%

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

   if -6.49999999999999979e-273 < B < 2.7000000000000001e-295 or 1.35e-249 < B < 1.4e-217

   1. Initial program 33.7%

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

   4. Applied egg-rr 75.3%

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

      1. div-sub 16.1%

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

      2. sub-neg 16.1%

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

   6. Applied egg-rr 16.1%

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

      1. sub-neg 16.1%

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

   8. Simplified 16.1%

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

   9. Taylor expanded in C around inf 32.7%

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

       1. distribute-lft1-in 32.7%

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

       2. metadata-eval 32.7%

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

       3. mul0-lft 61.5%

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

       4. metadata-eval 61.5%

          \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{0}}} \]

   11. Simplified 61.5%

       \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{0}}} \]

   if 2.7000000000000001e-295 < B < 1.35e-249 or 1.4e-217 < B < 1.1e-175

   1. Initial program 61.8%

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

   3. Taylor expanded in A around inf 61.2%

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

   if 1.1e-175 < B < 1.35e-41

   1. Initial program 77.5%

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

   3. Taylor expanded in C around -inf 56.2%

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

   if 1.35e-41 < B

   1. Initial program 53.6%

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

   3. Taylor expanded in B around inf 60.7%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.5 \cdot 10^{-273}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-295}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-249}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-217}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-175}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-41}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.2% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -5.1 \cdot 10^{-52}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -6.3 \cdot 10^{-273}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-295}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-175}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 10^{-40}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))))
   (if (<= B -5.1e-52)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -6.3e-273)
       t_0
       (if (<= B 4e-295)
         (/ 180.0 (/ PI (atan 0.0)))
         (if (<= B 1.5e-175)
           (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
           (if (<= B 1e-40) 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 <= -5.1e-52) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -6.3e-273) {
		tmp = t_0;
	} else if (B <= 4e-295) {
		tmp = 180.0 / (((double) M_PI) / atan(0.0));
	} else if (B <= 1.5e-175) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (B <= 1e-40) {
		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 <= -5.1e-52) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -6.3e-273) {
		tmp = t_0;
	} else if (B <= 4e-295) {
		tmp = 180.0 / (Math.PI / Math.atan(0.0));
	} else if (B <= 1.5e-175) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (B <= 1e-40) {
		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 <= -5.1e-52:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -6.3e-273:
		tmp = t_0
	elif B <= 4e-295:
		tmp = 180.0 / (math.pi / math.atan(0.0))
	elif B <= 1.5e-175:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif B <= 1e-40:
		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 <= -5.1e-52)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -6.3e-273)
		tmp = t_0;
	elseif (B <= 4e-295)
		tmp = Float64(180.0 / Float64(pi / atan(0.0)));
	elseif (B <= 1.5e-175)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (B <= 1e-40)
		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 <= -5.1e-52)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -6.3e-273)
		tmp = t_0;
	elseif (B <= 4e-295)
		tmp = 180.0 / (pi / atan(0.0));
	elseif (B <= 1.5e-175)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (B <= 1e-40)
		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, -5.1e-52], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6.3e-273], t$95$0, If[LessEqual[B, 4e-295], N[(180.0 / N[(Pi / N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.5e-175], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1e-40], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -5.09999999999999989e-52

   1. Initial program 54.4%

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

   3. Taylor expanded in B around -inf 68.3%

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

   if -5.09999999999999989e-52 < B < -6.29999999999999977e-273 or 1.5e-175 < B < 9.9999999999999993e-41

   1. Initial program 61.2%

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

   3. Taylor expanded in C around -inf 43.6%

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

   if -6.29999999999999977e-273 < B < 4.00000000000000024e-295

   1. Initial program 35.8%

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

   4. Applied egg-rr 77.3%

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

      1. div-sub 16.0%

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

      2. sub-neg 16.0%

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

   6. Applied egg-rr 16.0%

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

      1. sub-neg 16.0%

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

   8. Simplified 16.0%

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

   9. Taylor expanded in C around inf 20.1%

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

       1. distribute-lft1-in 20.1%

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

       2. metadata-eval 20.1%

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

       3. mul0-lft 63.4%

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

       4. metadata-eval 63.4%

          \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{0}}} \]

   11. Simplified 63.4%

       \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{0}}} \]

   if 4.00000000000000024e-295 < B < 1.5e-175

   1. Initial program 54.0%

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

   3. Taylor expanded in A around inf 49.9%

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

   if 9.9999999999999993e-41 < B

   1. Initial program 53.6%

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

   3. Taylor expanded in B around inf 60.7%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.1 \cdot 10^{-52}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -6.3 \cdot 10^{-273}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-295}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-175}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 10^{-40}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -5.2 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -4.5 \cdot 10^{+103}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq 8.2 \cdot 10^{-176}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI)))
        (t_1 (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))))
   (if (<= A -5.2e+166)
     t_1
     (if (<= A -4.5e+103)
       t_0
       (if (<= A -2.4e-62)
         t_1
         (if (<= A 8.2e-176) 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 + (C / B))) / ((double) M_PI));
	double t_1 = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	double tmp;
	if (A <= -5.2e+166) {
		tmp = t_1;
	} else if (A <= -4.5e+103) {
		tmp = t_0;
	} else if (A <= -2.4e-62) {
		tmp = t_1;
	} else if (A <= 8.2e-176) {
		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 + (C / B))) / Math.PI);
	double t_1 = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	double tmp;
	if (A <= -5.2e+166) {
		tmp = t_1;
	} else if (A <= -4.5e+103) {
		tmp = t_0;
	} else if (A <= -2.4e-62) {
		tmp = t_1;
	} else if (A <= 8.2e-176) {
		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 + (C / B))) / math.pi)
	t_1 = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	tmp = 0
	if A <= -5.2e+166:
		tmp = t_1
	elif A <= -4.5e+103:
		tmp = t_0
	elif A <= -2.4e-62:
		tmp = t_1
	elif A <= 8.2e-176:
		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(C / B))) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi))
	tmp = 0.0
	if (A <= -5.2e+166)
		tmp = t_1;
	elseif (A <= -4.5e+103)
		tmp = t_0;
	elseif (A <= -2.4e-62)
		tmp = t_1;
	elseif (A <= 8.2e-176)
		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 + (C / B))) / pi);
	t_1 = 180.0 * (atan(((B * 0.5) / A)) / pi);
	tmp = 0.0;
	if (A <= -5.2e+166)
		tmp = t_1;
	elseif (A <= -4.5e+103)
		tmp = t_0;
	elseif (A <= -2.4e-62)
		tmp = t_1;
	elseif (A <= 8.2e-176)
		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[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -5.2e+166], t$95$1, If[LessEqual[A, -4.5e+103], t$95$0, If[LessEqual[A, -2.4e-62], t$95$1, If[LessEqual[A, 8.2e-176], 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 < -5.1999999999999999e166 or -4.50000000000000001e103 < A < -2.39999999999999984e-62

   1. Initial program 29.7%

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

   3. Taylor expanded in A around -inf 62.0%

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

      1. associate-*r/ 62.0%

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

   5. Simplified 62.0%

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

   if -5.1999999999999999e166 < A < -4.50000000000000001e103 or -2.39999999999999984e-62 < A < 8.2000000000000005e-176

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf 54.0%

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

      1. associate--l+ 54.0%

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

      2. div-sub 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in C around inf 55.0%

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

   if 8.2000000000000005e-176 < A

   1. Initial program 70.3%

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

   3. Taylor expanded in C around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. distribute-neg-frac2 68.3%

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

      3. +-commutative 68.3%

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

      4. unpow2 68.3%

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

      5. unpow2 68.3%

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

      6. hypot-define 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in B around -inf 67.0%

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

      1. neg-mul-1 67.0%

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

      2. unsub-neg 67.0%

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

   8. Simplified 67.0%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.5 \cdot 10^{+103}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{-62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 8.2 \cdot 10^{-176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.5 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-7}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.5e-61)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.85e-7)
     (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.5e-61) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.85e-7) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.5e-61) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.85e-7) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -6.5e-61:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.85e-7:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -6.5e-61)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.85e-7)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -6.5e-61)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.85e-7)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -6.5e-61], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.85e-7], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -6.4999999999999994e-61

   1. Initial program 53.8%

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

   3. Taylor expanded in B around -inf 66.4%

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

   if -6.4999999999999994e-61 < B < 1.85000000000000002e-7

   1. Initial program 58.8%

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

   3. Taylor expanded in A around inf 36.1%

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

   if 1.85000000000000002e-7 < B

   1. Initial program 52.2%

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

   3. Taylor expanded in B around inf 62.1%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.5 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-7}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.5 \cdot 10^{+167}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{elif}\;A \leq 1.22 \cdot 10^{-176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.5e+167)
   (/ 180.0 (/ PI (atan 0.0)))
   (if (<= A 1.22e-176)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.5e+167) {
		tmp = 180.0 / (((double) M_PI) / atan(0.0));
	} else if (A <= 1.22e-176) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.5e+167) {
		tmp = 180.0 / (Math.PI / Math.atan(0.0));
	} else if (A <= 1.22e-176) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.5e+167:
		tmp = 180.0 / (math.pi / math.atan(0.0))
	elif A <= 1.22e-176:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.5e+167)
		tmp = Float64(180.0 / Float64(pi / atan(0.0)));
	elseif (A <= 1.22e-176)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.5e+167)
		tmp = 180.0 / (pi / atan(0.0));
	elseif (A <= 1.22e-176)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.5e+167], N[(180.0 / N[(Pi / N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.22e-176], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.49999999999999987e167

   1. Initial program 13.1%

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

   4. Applied egg-rr 52.8%

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

      1. div-sub 16.7%

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

      2. sub-neg 16.7%

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

   6. Applied egg-rr 16.7%

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

      1. sub-neg 16.7%

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

   8. Simplified 16.7%

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

   9. Taylor expanded in C around inf 2.8%

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

       1. distribute-lft1-in 2.8%

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

       2. metadata-eval 2.8%

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

       3. mul0-lft 39.0%

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

       4. metadata-eval 39.0%

          \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{0}}} \]

   11. Simplified 39.0%

       \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{0}}} \]

   if -3.49999999999999987e167 < A < 1.2200000000000001e-176

   1. Initial program 52.0%

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

   3. Taylor expanded in B around -inf 47.2%

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

      1. associate--l+ 47.2%

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

      2. div-sub 48.0%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in C around inf 48.1%

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

   if 1.2200000000000001e-176 < A

   1. Initial program 70.3%

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

   3. Taylor expanded in C around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. distribute-neg-frac2 68.3%

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

      3. +-commutative 68.3%

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

      4. unpow2 68.3%

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

      5. unpow2 68.3%

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

      6. hypot-define 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in B around -inf 67.0%

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

      1. neg-mul-1 67.0%

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

      2. unsub-neg 67.0%

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

   8. Simplified 67.0%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.5 \cdot 10^{+167}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{elif}\;A \leq 1.22 \cdot 10^{-176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - B\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8.4e-53)
   (/ (* 180.0 (atan (- 1.0 (/ (- A C) B)))) PI)
   (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.4e-53) {
		tmp = (180.0 * atan((1.0 - ((A - C) / B)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.4e-53) {
		tmp = (180.0 * Math.atan((1.0 - ((A - C) / B)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -8.4e-53:
		tmp = (180.0 * math.atan((1.0 - ((A - C) / B)))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C - A) - B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -8.4e-53)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 - Float64(Float64(A - C) / B)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -8.4e-53)
		tmp = (180.0 * atan((1.0 - ((A - C) / B)))) / pi;
	else
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -8.4e-53], N[(N[(180.0 * N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -8.3999999999999991e-53

   1. Initial program 54.4%

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

      1. associate-*r/ 54.4%

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

      2. associate-*l/ 54.4%

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

      3. *-un-lft-identity 54.4%

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

      4. unpow2 54.4%

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

      5. unpow2 54.4%

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

      6. hypot-define 84.2%

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

   4. Applied egg-rr 84.2%

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

   5. Taylor expanded in B around -inf 82.3%

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

      1. associate--l+ 82.3%

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

      2. div-sub 82.3%

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

   7. Simplified 82.3%

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

   if -8.3999999999999991e-53 < B

   1. Initial program 55.8%

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

   3. Taylor expanded in B around inf 62.7%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - B\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 63.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 7.5 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + A}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 7.5e-95)
   (* 180.0 (/ (atan (- 1.0 (/ (- A C) B))) PI))
   (* 180.0 (/ (atan (/ (+ B A) (- B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 7.5e-95) {
		tmp = 180.0 * (atan((1.0 - ((A - C) / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B + A) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 7.5e-95) {
		tmp = 180.0 * (Math.atan((1.0 - ((A - C) / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B + A) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 7.5e-95:
		tmp = 180.0 * (math.atan((1.0 - ((A - C) / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B + A) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 7.5e-95)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(Float64(A - C) / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + A) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 7.5e-95)
		tmp = 180.0 * (atan((1.0 - ((A - C) / B))) / pi);
	else
		tmp = 180.0 * (atan(((B + A) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 7.5e-95], 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[(B + A), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 7.5000000000000003e-95

   1. Initial program 55.4%

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

   3. Taylor expanded in B around -inf 63.8%

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

      1. associate--l+ 63.8%

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

      2. div-sub 65.5%

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

   5. Simplified 65.5%

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

   if 7.5000000000000003e-95 < B

   1. Initial program 55.3%

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

   3. Taylor expanded in C around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. distribute-neg-frac2 51.7%

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

      3. +-commutative 51.7%

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

      4. unpow2 51.7%

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

      5. unpow2 51.7%

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

      6. hypot-define 74.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in A around 0 71.2%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 7.5 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + A}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 63.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.8 \cdot 10^{-97}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.8e-97)
   (* 180.0 (/ (atan (- 1.0 (/ (- A C) B))) PI))
   (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.8e-97) {
		tmp = 180.0 * (atan((1.0 - ((A - C) / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.8e-97) {
		tmp = 180.0 * (Math.atan((1.0 - ((A - C) / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 1.8e-97:
		tmp = 180.0 * (math.atan((1.0 - ((A - C) / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 1.8e-97)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(Float64(A - C) / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 1.8e-97)
		tmp = 180.0 * (atan((1.0 - ((A - C) / B))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 1.8e-97], 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[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 1.79999999999999999e-97

   1. Initial program 55.4%

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

   3. Taylor expanded in B around -inf 63.8%

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

      1. associate--l+ 63.8%

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

      2. div-sub 65.5%

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

   5. Simplified 65.5%

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

   if 1.79999999999999999e-97 < B

   1. Initial program 55.3%

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

   3. Taylor expanded in C around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. distribute-neg-frac2 51.7%

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

      3. +-commutative 51.7%

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

      4. unpow2 51.7%

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

      5. unpow2 51.7%

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

      6. hypot-define 74.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in A around 0 71.2%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.8 \cdot 10^{-97}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 65.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8.4 \cdot 10^{-53}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 + \frac{C - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8.4e-53)
   (* 180.0 (/ (atan (- 1.0 (/ (- A C) B))) PI))
   (/ 180.0 (/ PI (atan (+ -1.0 (/ (- C A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.4e-53) {
		tmp = 180.0 * (atan((1.0 - ((A - C) / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((-1.0 + ((C - A) / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.4e-53) {
		tmp = 180.0 * (Math.atan((1.0 - ((A - C) / B))) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((-1.0 + ((C - A) / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -8.4e-53:
		tmp = 180.0 * (math.atan((1.0 - ((A - C) / B))) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((-1.0 + ((C - A) / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -8.4e-53)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(Float64(A - C) / B))) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-1.0 + Float64(Float64(C - A) / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -8.4e-53)
		tmp = 180.0 * (atan((1.0 - ((A - C) / B))) / pi);
	else
		tmp = 180.0 / (pi / atan((-1.0 + ((C - A) / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -8.4e-53], 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[(Pi / N[ArcTan[N[(-1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -8.3999999999999991e-53

   1. Initial program 54.4%

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

   3. Taylor expanded in B around -inf 82.3%

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

      1. associate--l+ 82.3%

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

      2. div-sub 82.3%

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

   5. Simplified 82.3%

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

   if -8.3999999999999991e-53 < B

   1. Initial program 55.8%

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

   4. Applied egg-rr 78.6%

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

      1. div-sub 65.1%

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

      2. sub-neg 65.1%

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

   6. Applied egg-rr 65.1%

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

      1. sub-neg 65.1%

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

   8. Simplified 65.1%

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

   9. Taylor expanded in B around inf 60.9%

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

       1. +-commutative 60.9%

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

       2. associate--r+ 60.9%

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

       3. div-sub 62.7%

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

   11. Simplified 62.7%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.4 \cdot 10^{-53}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 + \frac{C - A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 65.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 + \frac{C - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8.4e-53)
   (/ (* 180.0 (atan (- 1.0 (/ (- A C) B)))) PI)
   (/ 180.0 (/ PI (atan (+ -1.0 (/ (- C A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.4e-53) {
		tmp = (180.0 * atan((1.0 - ((A - C) / B)))) / ((double) M_PI);
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((-1.0 + ((C - A) / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.4e-53) {
		tmp = (180.0 * Math.atan((1.0 - ((A - C) / B)))) / Math.PI;
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((-1.0 + ((C - A) / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -8.4e-53:
		tmp = (180.0 * math.atan((1.0 - ((A - C) / B)))) / math.pi
	else:
		tmp = 180.0 / (math.pi / math.atan((-1.0 + ((C - A) / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -8.4e-53)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 - Float64(Float64(A - C) / B)))) / pi);
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-1.0 + Float64(Float64(C - A) / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -8.4e-53)
		tmp = (180.0 * atan((1.0 - ((A - C) / B)))) / pi;
	else
		tmp = 180.0 / (pi / atan((-1.0 + ((C - A) / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -8.4e-53], N[(N[(180.0 * N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(-1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -8.3999999999999991e-53

   1. Initial program 54.4%

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

      1. associate-*r/ 54.4%

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

      2. associate-*l/ 54.4%

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

      3. *-un-lft-identity 54.4%

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

      4. unpow2 54.4%

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

      5. unpow2 54.4%

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

      6. hypot-define 84.2%

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

   4. Applied egg-rr 84.2%

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

   5. Taylor expanded in B around -inf 82.3%

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

      1. associate--l+ 82.3%

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

      2. div-sub 82.3%

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

   7. Simplified 82.3%

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

   if -8.3999999999999991e-53 < B

   1. Initial program 55.8%

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

   4. Applied egg-rr 78.6%

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

      1. div-sub 65.1%

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

      2. sub-neg 65.1%

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

   6. Applied egg-rr 65.1%

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

      1. sub-neg 65.1%

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

   8. Simplified 65.1%

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

   9. Taylor expanded in B around inf 60.9%

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

       1. +-commutative 60.9%

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

       2. associate--r+ 60.9%

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

       3. div-sub 62.7%

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

   11. Simplified 62.7%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 + \frac{C - A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 45.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.46 \cdot 10^{-74}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.45 \cdot 10^{-174}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.46e-74)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.45e-174)
     (/ 180.0 (/ PI (atan 0.0)))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.46e-74) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.45e-174) {
		tmp = 180.0 / (((double) M_PI) / atan(0.0));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.46e-74) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.45e-174) {
		tmp = 180.0 / (Math.PI / Math.atan(0.0));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.46e-74:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.45e-174:
		tmp = 180.0 / (math.pi / math.atan(0.0))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.46e-74)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.45e-174)
		tmp = Float64(180.0 / Float64(pi / atan(0.0)));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.46e-74)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.45e-174)
		tmp = 180.0 / (pi / atan(0.0));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.46e-74], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.45e-174], N[(180.0 / N[(Pi / N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.46e-74

   1. Initial program 54.3%

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

   3. Taylor expanded in B around -inf 65.8%

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

   if -1.46e-74 < B < 2.45000000000000005e-174

   1. Initial program 52.8%

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

   4. Applied egg-rr 76.2%

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

      1. div-sub 46.8%

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

      2. sub-neg 46.8%

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

   6. Applied egg-rr 46.8%

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

      1. sub-neg 46.8%

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

   8. Simplified 46.8%

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

   9. Taylor expanded in C around inf 16.9%

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

       1. distribute-lft1-in 16.9%

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

       2. metadata-eval 16.9%

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

       3. mul0-lft 32.3%

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

       4. metadata-eval 32.3%

          \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{0}}} \]

   11. Simplified 32.3%

       \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{0}}} \]

   if 2.45000000000000005e-174 < B

   1. Initial program 58.4%

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

   3. Taylor expanded in B around inf 52.6%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.46 \cdot 10^{-74}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.45 \cdot 10^{-174}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 41.3% accurate, 3.8× 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 53.3%

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

   3. Taylor expanded in B around -inf 47.2%

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

   if -1.000000000000002e-309 < B

   1. Initial program 57.5%

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

   3. Taylor expanded in B around inf 42.3%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-309}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 21.7% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 55.3%

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

3. Taylor expanded in B around inf 21.1%

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

4. Final simplification 21.1%

   \[\leadsto 180 \cdot \frac{\tan^{-1} -1}{\pi} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024130 
(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)))