ABCF->ab-angle angle

Percentage Accurate: 53.9% → 81.9%

Time: 15.8s

Alternatives: 17

Speedup: 2.4×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.9% 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: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{-27} \lor \neg \left(t_0 \leq 10^{-6}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

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 -5e-27) (not (<= t_0 1e-6)))
     (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))
     (/ (* 180.0 (atan (* -0.5 (/ B C)))) PI))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -5e-27) || !(t_0 <= 1e-6)) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((-0.5 * (B / C)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -5e-27) || !(t_0 <= 1e-6)) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((-0.5 * (B / C)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if (t_0 <= -5e-27) or not (t_0 <= 1e-6):
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan((-0.5 * (B / C)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if ((t_0 <= -5e-27) || !(t_0 <= 1e-6))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / C)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if ((t_0 <= -5e-27) || ~((t_0 <= 1e-6)))
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	else
		tmp = (180.0 * atan((-0.5 * (B / C)))) / pi;
	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, -5e-27], N[Not[LessEqual[t$95$0, 1e-6]], $MachinePrecision]], 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], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -5.0000000000000002e-27 or 9.99999999999999955e-7 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 60.8%

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

      1. associate-*l/ 60.8%

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

      2. *-lft-identity 60.8%

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

      3. +-commutative 60.8%

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

      4. unpow2 60.8%

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

      5. unpow2 60.8%

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

      6. hypot-def 87.2%

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

   3. Simplified 87.2%

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

   if -5.0000000000000002e-27 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 9.99999999999999955e-7

   1. Initial program 15.3%

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

      1. associate-*l/ 15.3%

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

      2. *-lft-identity 15.3%

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

      3. +-commutative 15.3%

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

      4. unpow2 15.3%

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

      5. unpow2 15.3%

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

      6. hypot-def 15.4%

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

   3. Simplified 15.4%

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

   4. Taylor expanded in C around -inf 8.1%

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

   5. Taylor expanded in C around inf 24.6%

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

      1. +-commutative 24.6%

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

      2. associate-+l+ 29.3%

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

   7. Simplified 42.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{\frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{\frac{C}{0.5}} + 0}}{B}\right)}{\pi} \]

   8. Taylor expanded in B around 0 59.6%

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

      1. associate-*r/ 59.7%

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

      2. associate-*r* 59.7%

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

      3. metadata-eval 59.7%

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

   10. Applied egg-rr 59.7%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -5 \cdot 10^{-27} \lor \neg \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 10^{-6}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 2: 78.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.14 \cdot 10^{+83}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 260:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.14e+83)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (if (<= A 260.0)
     (/ 180.0 (/ PI (atan (/ (- C (hypot B C)) B))))
     (* 180.0 (/ (atan (/ (- (- A) (hypot A B)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.14e+83) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= 260.0) {
		tmp = 180.0 / (((double) M_PI) / atan(((C - hypot(B, C)) / B)));
	} else {
		tmp = 180.0 * (atan(((-A - hypot(A, B)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.14e+83) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= 260.0) {
		tmp = 180.0 / (Math.PI / Math.atan(((C - Math.hypot(B, C)) / B)));
	} else {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(A, B)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.14e+83:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= 260.0:
		tmp = 180.0 / (math.pi / math.atan(((C - math.hypot(B, C)) / B)))
	else:
		tmp = 180.0 * (math.atan(((-A - math.hypot(A, B)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.14e+83)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= 260.0)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - hypot(B, C)) / B))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(A, B)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.14e+83)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= 260.0)
		tmp = 180.0 / (pi / atan(((C - hypot(B, C)) / B)));
	else
		tmp = 180.0 * (atan(((-A - hypot(A, B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.14e+83], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 260.0], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.14000000000000003e83

   1. Initial program 15.3%

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

      1. associate-*r/ 15.3%

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

      2. unpow2 15.3%

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

   3. Simplified 15.3%

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

   4. Taylor expanded in B around 0 11.6%

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

      1. div-sub 11.4%

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

      2. +-commutative 11.4%

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

   6. Simplified 46.3%

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

   7. Taylor expanded in A around -inf 81.2%

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

   if -1.14000000000000003e83 < A < 260

   1. Initial program 53.5%

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

      1. associate-*l/ 53.5%

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

      2. *-lft-identity 53.5%

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

      3. +-commutative 53.5%

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

      4. unpow2 53.5%

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

      5. unpow2 53.5%

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

      6. hypot-def 74.7%

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

   3. Simplified 74.7%

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

      1. clear-num 74.7%

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

      2. un-div-inv 74.7%

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

      3. associate--r+ 74.6%

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

   5. Applied egg-rr 74.6%

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

   6. Taylor expanded in A around 0 50.7%

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

      1. unpow2 50.7%

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

      2. unpow2 50.7%

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

      3. hypot-def 71.8%

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

   8. Simplified 71.8%

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

   if 260 < A

   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. Step-by-step derivation

      1. associate-*l/ 77.5%

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

      2. *-lft-identity 77.5%

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

      3. +-commutative 77.5%

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

      4. unpow2 77.5%

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

      5. unpow2 77.5%

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

      6. hypot-def 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in C around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. +-commutative 75.7%

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

      3. unpow2 75.7%

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

      4. unpow2 75.7%

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

      5. hypot-def 84.5%

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

   6. Simplified 84.5%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.14 \cdot 10^{+83}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 260:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3: 76.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9.4 \cdot 10^{+81}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.12 \cdot 10^{+74}:\\ \;\;\;\;\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9.4e+81)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (if (<= A 1.12e+74)
     (* (atan (/ (- C (hypot B C)) B)) (/ 180.0 PI))
     (/ 180.0 (/ PI (atan (/ (- (+ B C) A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.4e+81) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= 1.12e+74) {
		tmp = atan(((C - hypot(B, C)) / B)) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((B + C) - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.4e+81) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= 1.12e+74) {
		tmp = Math.atan(((C - Math.hypot(B, C)) / B)) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((B + C) - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -9.4e+81:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= 1.12e+74:
		tmp = math.atan(((C - math.hypot(B, C)) / B)) * (180.0 / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((((B + C) - A) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -9.4e+81)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= 1.12e+74)
		tmp = Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(B + C) - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -9.4e+81)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= 1.12e+74)
		tmp = atan(((C - hypot(B, C)) / B)) * (180.0 / pi);
	else
		tmp = 180.0 / (pi / atan((((B + C) - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -9.4e+81], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.12e+74], N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -9.4000000000000004e81

   1. Initial program 15.3%

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

      1. associate-*r/ 15.3%

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

      2. unpow2 15.3%

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

   3. Simplified 15.3%

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

   4. Taylor expanded in B around 0 11.6%

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

      1. div-sub 11.4%

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

      2. +-commutative 11.4%

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

   6. Simplified 46.3%

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

   7. Taylor expanded in A around -inf 81.2%

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

   if -9.4000000000000004e81 < A < 1.12000000000000003e74

   1. Initial program 56.8%

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

      1. associate-*r/ 56.8%

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

      2. associate-*l/ 56.8%

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

      3. associate-*l/ 56.8%

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

      4. *-lft-identity 56.8%

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

      5. sub-neg 56.8%

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

      6. associate-+l- 56.7%

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

      7. sub-neg 56.7%

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

      8. remove-double-neg 56.7%

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

      9. +-commutative 56.7%

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

      10. unpow2 56.7%

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

      11. unpow2 56.7%

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

      12. hypot-def 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in A around 0 52.4%

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

      1. unpow2 52.4%

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

      2. unpow2 52.4%

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

      3. hypot-def 72.3%

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

   6. Simplified 72.3%

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

   if 1.12000000000000003e74 < A

   1. Initial program 71.8%

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

      1. associate-*l/ 71.8%

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

      2. *-lft-identity 71.8%

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

      3. +-commutative 71.8%

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

      4. unpow2 71.8%

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

      5. unpow2 71.8%

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

      6. hypot-def 93.1%

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

   3. Simplified 93.1%

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

      1. clear-num 93.1%

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

      2. un-div-inv 93.1%

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

      3. associate--r+ 93.1%

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

   5. Applied egg-rr 93.1%

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

   6. Taylor expanded in B around -inf 81.5%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9.4 \cdot 10^{+81}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.12 \cdot 10^{+74}:\\ \;\;\;\;\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \end{array} \]

Alternative 4: 76.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{+82}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{+80}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.9e+82)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (if (<= A 1.9e+80)
     (/ 180.0 (/ PI (atan (/ (- C (hypot B C)) B))))
     (/ 180.0 (/ PI (atan (/ (- (+ B C) A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e+82) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= 1.9e+80) {
		tmp = 180.0 / (((double) M_PI) / atan(((C - hypot(B, C)) / B)));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((B + C) - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e+82) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= 1.9e+80) {
		tmp = 180.0 / (Math.PI / Math.atan(((C - Math.hypot(B, C)) / B)));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((B + C) - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.9e+82:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= 1.9e+80:
		tmp = 180.0 / (math.pi / math.atan(((C - math.hypot(B, C)) / B)))
	else:
		tmp = 180.0 / (math.pi / math.atan((((B + C) - A) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.9e+82)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= 1.9e+80)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - hypot(B, C)) / B))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(B + C) - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.9e+82)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= 1.9e+80)
		tmp = 180.0 / (pi / atan(((C - hypot(B, C)) / B)));
	else
		tmp = 180.0 / (pi / atan((((B + C) - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.9e+82], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.9e+80], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.90000000000000017e82

   1. Initial program 15.3%

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

      1. associate-*r/ 15.3%

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

      2. unpow2 15.3%

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

   3. Simplified 15.3%

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

   4. Taylor expanded in B around 0 11.6%

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

      1. div-sub 11.4%

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

      2. +-commutative 11.4%

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

   6. Simplified 46.3%

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

   7. Taylor expanded in A around -inf 81.2%

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

   if -1.90000000000000017e82 < A < 1.89999999999999999e80

   1. Initial program 56.8%

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

      1. associate-*l/ 56.8%

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

      2. *-lft-identity 56.8%

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

      3. +-commutative 56.8%

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

      4. unpow2 56.8%

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

      5. unpow2 56.8%

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

      6. hypot-def 76.7%

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

   3. Simplified 76.7%

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

      1. clear-num 76.7%

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

      2. un-div-inv 76.7%

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

      3. associate--r+ 76.6%

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

   5. Applied egg-rr 76.6%

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

   6. Taylor expanded in A around 0 52.4%

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

      1. unpow2 52.4%

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

      2. unpow2 52.4%

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

      3. hypot-def 72.3%

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

   8. Simplified 72.3%

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

   if 1.89999999999999999e80 < A

   1. Initial program 71.8%

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

      1. associate-*l/ 71.8%

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

      2. *-lft-identity 71.8%

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

      3. +-commutative 71.8%

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

      4. unpow2 71.8%

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

      5. unpow2 71.8%

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

      6. hypot-def 93.1%

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

   3. Simplified 93.1%

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

      1. clear-num 93.1%

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

      2. un-div-inv 93.1%

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

      3. associate--r+ 93.1%

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

   5. Applied egg-rr 93.1%

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

   6. Taylor expanded in B around -inf 81.5%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{+82}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{+80}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \end{array} \]

Alternative 5: 63.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.8 \cdot 10^{-175}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \mathbf{elif}\;B \leq -2.7 \cdot 10^{-240}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\frac{B}{\frac{A}{B}} \cdot \left(--0.5\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-215} \lor \neg \left(B \leq 3.6 \cdot 10^{-144}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.8e-175)
   (/ 180.0 (/ PI (atan (/ (- (+ B C) A) B))))
   (if (<= B -2.7e-240)
     (* 180.0 (/ (atan (/ (* (/ B (/ A B)) (- -0.5)) B)) PI))
     (if (or (<= B 1.1e-215) (not (<= B 3.6e-144)))
       (* (/ 180.0 PI) (atan (/ (- C (+ B A)) B)))
       (* (/ 180.0 PI) (atan (/ B (/ C -0.5))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.8e-175) {
		tmp = 180.0 / (((double) M_PI) / atan((((B + C) - A) / B)));
	} else if (B <= -2.7e-240) {
		tmp = 180.0 * (atan((((B / (A / B)) * -(-0.5)) / B)) / ((double) M_PI));
	} else if ((B <= 1.1e-215) || !(B <= 3.6e-144)) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (B + A)) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((B / (C / -0.5)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.8e-175) {
		tmp = 180.0 / (Math.PI / Math.atan((((B + C) - A) / B)));
	} else if (B <= -2.7e-240) {
		tmp = 180.0 * (Math.atan((((B / (A / B)) * -(-0.5)) / B)) / Math.PI);
	} else if ((B <= 1.1e-215) || !(B <= 3.6e-144)) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (B + A)) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((B / (C / -0.5)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.8e-175:
		tmp = 180.0 / (math.pi / math.atan((((B + C) - A) / B)))
	elif B <= -2.7e-240:
		tmp = 180.0 * (math.atan((((B / (A / B)) * -(-0.5)) / B)) / math.pi)
	elif (B <= 1.1e-215) or not (B <= 3.6e-144):
		tmp = (180.0 / math.pi) * math.atan(((C - (B + A)) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan((B / (C / -0.5)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.8e-175)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(B + C) - A) / B))));
	elseif (B <= -2.7e-240)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(B / Float64(A / B)) * Float64(-(-0.5))) / B)) / pi));
	elseif ((B <= 1.1e-215) || !(B <= 3.6e-144))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(B + A)) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B / Float64(C / -0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.8e-175)
		tmp = 180.0 / (pi / atan((((B + C) - A) / B)));
	elseif (B <= -2.7e-240)
		tmp = 180.0 * (atan((((B / (A / B)) * -(-0.5)) / B)) / pi);
	elseif ((B <= 1.1e-215) || ~((B <= 3.6e-144)))
		tmp = (180.0 / pi) * atan(((C - (B + A)) / B));
	else
		tmp = (180.0 / pi) * atan((B / (C / -0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.8e-175], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.7e-240], N[(180.0 * N[(N[ArcTan[N[(N[(N[(B / N[(A / B), $MachinePrecision]), $MachinePrecision] * (--0.5)), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 1.1e-215], N[Not[LessEqual[B, 3.6e-144]], $MachinePrecision]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -3.8e-175

   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. Step-by-step derivation

      1. associate-*l/ 53.9%

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

      2. *-lft-identity 53.9%

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

      3. +-commutative 53.9%

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

      4. unpow2 53.9%

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

      5. unpow2 53.9%

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

      6. hypot-def 74.2%

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

   3. Simplified 74.2%

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

      1. clear-num 74.2%

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

      2. un-div-inv 74.2%

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

      3. associate--r+ 73.1%

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

   5. Applied egg-rr 73.1%

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

   6. Taylor expanded in B around -inf 70.1%

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

   if -3.8e-175 < B < -2.70000000000000018e-240

   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. Step-by-step derivation

      1. associate-*l/ 53.6%

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

      2. *-lft-identity 53.6%

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

      3. +-commutative 53.6%

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

      4. unpow2 53.6%

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

      5. unpow2 53.6%

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

      6. hypot-def 71.2%

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

   3. Simplified 71.2%

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

   4. Taylor expanded in C around -inf 47.5%

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

   5. Taylor expanded in A around -inf 44.7%

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

      1. associate-+r+ 44.7%

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

      2. distribute-lft1-in 44.7%

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

      3. metadata-eval 44.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot C + -0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}{\pi} \]

      4. mul0-lft 44.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} + -0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}{\pi} \]

      5. +-commutative 44.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{-0.5 \cdot \frac{{B}^{2}}{A} + 0}}{B}\right)}{\pi} \]

      6. unpow2 44.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{-0.5 \cdot \frac{\color{blue}{B \cdot B}}{A} + 0}{B}\right)}{\pi} \]

      7. associate-/l* 70.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{-0.5 \cdot \color{blue}{\frac{B}{\frac{A}{B}}} + 0}{B}\right)}{\pi} \]

   7. Simplified 70.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{-0.5 \cdot \frac{B}{\frac{A}{B}} + 0}}{B}\right)}{\pi} \]

   if -2.70000000000000018e-240 < B < 1.09999999999999998e-215 or 3.6e-144 < B

   1. Initial program 56.5%

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

      1. associate-*r/ 56.5%

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

      2. associate-*l/ 56.5%

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

      3. associate-*l/ 56.5%

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

      4. *-lft-identity 56.5%

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

      5. sub-neg 56.5%

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

      6. associate-+l- 56.4%

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

      7. sub-neg 56.4%

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

      8. remove-double-neg 56.4%

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

      9. +-commutative 56.4%

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

      10. unpow2 56.4%

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

      11. unpow2 56.4%

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

      12. hypot-def 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in B around inf 71.4%

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

   if 1.09999999999999998e-215 < B < 3.6e-144

   1. Initial program 24.1%

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

      1. associate-*l/ 24.1%

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

      2. *-lft-identity 24.1%

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

      3. +-commutative 24.1%

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

      4. unpow2 24.1%

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

      5. unpow2 24.1%

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

      6. hypot-def 56.2%

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

   3. Simplified 56.2%

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

   4. Taylor expanded in C around -inf 33.0%

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

   5. Taylor expanded in C around inf 23.2%

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

      1. +-commutative 23.2%

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

      2. associate-+l+ 23.2%

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

   7. Simplified 49.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{\frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{\frac{C}{0.5}} + 0}}{B}\right)}{\pi} \]

   8. Taylor expanded in B around 0 53.1%

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

   9. Taylor expanded in B around 0 53.1%

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

       1. associate-*r/ 53.4%

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

       2. associate-/l* 49.8%

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

       3. associate-/r/ 53.5%

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

       4. associate-*r/ 53.5%

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

       5. *-commutative 53.5%

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

       6. associate-/l* 53.5%

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

   11. Simplified 53.5%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.8 \cdot 10^{-175}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \mathbf{elif}\;B \leq -2.7 \cdot 10^{-240}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\frac{B}{\frac{A}{B}} \cdot \left(--0.5\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-215} \lor \neg \left(B \leq 3.6 \cdot 10^{-144}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)\\ \end{array} \]

Alternative 6: 56.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C}{B}\right)}}\\ \mathbf{if}\;A \leq -7.6 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-295}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{-233}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 5.18 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ 180.0 (/ PI (atan (+ 1.0 (/ C B)))))))
   (if (<= A -7.6e-78)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (if (<= A 1.9e-295)
       t_0
       (if (<= A 4.2e-233)
         (* 180.0 (/ (atan -1.0) PI))
         (if (<= A 5.18e-8) t_0 (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 / (((double) M_PI) / atan((1.0 + (C / B))));
	double tmp;
	if (A <= -7.6e-78) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 1.9e-295) {
		tmp = t_0;
	} else if (A <= 4.2e-233) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 5.18e-8) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / 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((1.0 + (C / B))));
	double tmp;
	if (A <= -7.6e-78) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 1.9e-295) {
		tmp = t_0;
	} else if (A <= 4.2e-233) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 5.18e-8) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 / (math.pi / math.atan((1.0 + (C / B))))
	tmp = 0
	if A <= -7.6e-78:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 1.9e-295:
		tmp = t_0
	elif A <= 4.2e-233:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 5.18e-8:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 / Float64(pi / atan(Float64(1.0 + Float64(C / B)))))
	tmp = 0.0
	if (A <= -7.6e-78)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 1.9e-295)
		tmp = t_0;
	elseif (A <= 4.2e-233)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 5.18e-8)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 / (pi / atan((1.0 + (C / B))));
	tmp = 0.0;
	if (A <= -7.6e-78)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 1.9e-295)
		tmp = t_0;
	elseif (A <= 4.2e-233)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 5.18e-8)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 / N[(Pi / N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -7.6e-78], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.9e-295], t$95$0, If[LessEqual[A, 4.2e-233], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.18e-8], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -7.5999999999999998e-78

   1. Initial program 29.8%

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

      1. associate-*l/ 29.8%

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

      2. *-lft-identity 29.8%

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

      3. +-commutative 29.8%

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

      4. unpow2 29.8%

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

      5. unpow2 29.8%

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

      6. hypot-def 52.7%

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

   3. Simplified 52.7%

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

   4. Taylor expanded in A around -inf 62.9%

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

   if -7.5999999999999998e-78 < A < 1.90000000000000009e-295 or 4.1999999999999997e-233 < A < 5.1800000000000001e-8

   1. Initial program 56.5%

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

      1. associate-*l/ 56.5%

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

      2. *-lft-identity 56.5%

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

      3. +-commutative 56.5%

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

      4. unpow2 56.5%

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

      5. unpow2 56.5%

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

      6. hypot-def 78.6%

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

   3. Simplified 78.6%

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

      1. clear-num 78.6%

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

      2. un-div-inv 78.6%

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

      3. associate--r+ 78.6%

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

   5. Applied egg-rr 78.6%

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

   6. Taylor expanded in A around 0 53.1%

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

      1. unpow2 53.1%

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

      2. unpow2 53.1%

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

      3. hypot-def 75.0%

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

   8. Simplified 75.0%

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

   9. Taylor expanded in B around -inf 57.0%

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

   if 1.90000000000000009e-295 < A < 4.1999999999999997e-233

   1. Initial program 53.0%

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

      1. associate-*l/ 53.0%

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

      2. *-lft-identity 53.0%

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

      3. +-commutative 53.0%

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

      4. unpow2 53.0%

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

      5. unpow2 53.0%

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

      6. hypot-def 82.8%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in B around inf 55.8%

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

   if 5.1800000000000001e-8 < A

   1. Initial program 75.6%

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

      1. associate-*l/ 75.6%

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

      2. *-lft-identity 75.6%

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

      3. +-commutative 75.6%

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

      4. unpow2 75.6%

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

      5. unpow2 75.6%

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

      6. hypot-def 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in A around inf 68.9%

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

      1. *-commutative 68.9%

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

   6. Simplified 68.9%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7.6 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-295}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C}{B}\right)}}\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{-233}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 5.18 \cdot 10^{-8}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 56.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C}{B}\right)}}\\ \mathbf{if}\;A \leq -1.7 \cdot 10^{-78}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-295}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{-233}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 5.18 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ 180.0 (/ PI (atan (+ 1.0 (/ C B)))))))
   (if (<= A -1.7e-78)
     (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
     (if (<= A 1.9e-295)
       t_0
       (if (<= A 4.2e-233)
         (* 180.0 (/ (atan -1.0) PI))
         (if (<= A 5.18e-8) t_0 (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 / (((double) M_PI) / atan((1.0 + (C / B))));
	double tmp;
	if (A <= -1.7e-78) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= 1.9e-295) {
		tmp = t_0;
	} else if (A <= 4.2e-233) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 5.18e-8) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / 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((1.0 + (C / B))));
	double tmp;
	if (A <= -1.7e-78) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= 1.9e-295) {
		tmp = t_0;
	} else if (A <= 4.2e-233) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 5.18e-8) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 / (math.pi / math.atan((1.0 + (C / B))))
	tmp = 0
	if A <= -1.7e-78:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= 1.9e-295:
		tmp = t_0
	elif A <= 4.2e-233:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 5.18e-8:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 / Float64(pi / atan(Float64(1.0 + Float64(C / B)))))
	tmp = 0.0
	if (A <= -1.7e-78)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= 1.9e-295)
		tmp = t_0;
	elseif (A <= 4.2e-233)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 5.18e-8)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 / (pi / atan((1.0 + (C / B))));
	tmp = 0.0;
	if (A <= -1.7e-78)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= 1.9e-295)
		tmp = t_0;
	elseif (A <= 4.2e-233)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 5.18e-8)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 / N[(Pi / N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.7e-78], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.9e-295], t$95$0, If[LessEqual[A, 4.2e-233], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.18e-8], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.70000000000000006e-78

   1. Initial program 29.8%

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

      1. associate-*r/ 29.8%

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

      2. unpow2 29.8%

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

   3. Simplified 29.8%

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

   4. Taylor expanded in B around 0 27.6%

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

      1. div-sub 26.5%

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

      2. +-commutative 26.5%

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

   6. Simplified 52.7%

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

   7. Taylor expanded in A around -inf 62.9%

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

   if -1.70000000000000006e-78 < A < 1.90000000000000009e-295 or 4.1999999999999997e-233 < A < 5.1800000000000001e-8

   1. Initial program 56.5%

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

      1. associate-*l/ 56.5%

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

      2. *-lft-identity 56.5%

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

      3. +-commutative 56.5%

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

      4. unpow2 56.5%

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

      5. unpow2 56.5%

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

      6. hypot-def 78.6%

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

   3. Simplified 78.6%

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

      1. clear-num 78.6%

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

      2. un-div-inv 78.6%

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

      3. associate--r+ 78.6%

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

   5. Applied egg-rr 78.6%

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

   6. Taylor expanded in A around 0 53.1%

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

      1. unpow2 53.1%

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

      2. unpow2 53.1%

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

      3. hypot-def 75.0%

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

   8. Simplified 75.0%

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

   9. Taylor expanded in B around -inf 57.0%

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

   if 1.90000000000000009e-295 < A < 4.1999999999999997e-233

   1. Initial program 53.0%

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

      1. associate-*l/ 53.0%

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

      2. *-lft-identity 53.0%

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

      3. +-commutative 53.0%

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

      4. unpow2 53.0%

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

      5. unpow2 53.0%

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

      6. hypot-def 82.8%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in B around inf 55.8%

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

   if 5.1800000000000001e-8 < A

   1. Initial program 75.6%

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

      1. associate-*l/ 75.6%

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

      2. *-lft-identity 75.6%

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

      3. +-commutative 75.6%

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

      4. unpow2 75.6%

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

      5. unpow2 75.6%

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

      6. hypot-def 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in A around inf 68.9%

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

      1. *-commutative 68.9%

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

   6. Simplified 68.9%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.7 \cdot 10^{-78}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-295}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C}{B}\right)}}\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{-233}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 5.18 \cdot 10^{-8}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 61.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.04 \cdot 10^{-215}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-144}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-64}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) \cdot 2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.04e-215)
   (* 180.0 (/ (atan (/ (- (+ B C) A) B)) PI))
   (if (<= B 3.6e-144)
     (* (/ 180.0 PI) (atan (/ B (/ C -0.5))))
     (if (<= B 1.95e-64)
       (* 180.0 (/ (atan (/ (* (- C A) 2.0) B)) PI))
       (/ (* 180.0 (atan (/ (- (- A) B) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.04e-215) {
		tmp = 180.0 * (atan((((B + C) - A) / B)) / ((double) M_PI));
	} else if (B <= 3.6e-144) {
		tmp = (180.0 / ((double) M_PI)) * atan((B / (C / -0.5)));
	} else if (B <= 1.95e-64) {
		tmp = 180.0 * (atan((((C - A) * 2.0) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((-A - B) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.04e-215) {
		tmp = 180.0 * (Math.atan((((B + C) - A) / B)) / Math.PI);
	} else if (B <= 3.6e-144) {
		tmp = (180.0 / Math.PI) * Math.atan((B / (C / -0.5)));
	} else if (B <= 1.95e-64) {
		tmp = 180.0 * (Math.atan((((C - A) * 2.0) / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((-A - B) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 1.04e-215:
		tmp = 180.0 * (math.atan((((B + C) - A) / B)) / math.pi)
	elif B <= 3.6e-144:
		tmp = (180.0 / math.pi) * math.atan((B / (C / -0.5)))
	elif B <= 1.95e-64:
		tmp = 180.0 * (math.atan((((C - A) * 2.0) / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan(((-A - B) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 1.04e-215)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(B + C) - A) / B)) / pi));
	elseif (B <= 3.6e-144)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B / Float64(C / -0.5))));
	elseif (B <= 1.95e-64)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) * 2.0) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(-A) - B) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 1.04e-215)
		tmp = 180.0 * (atan((((B + C) - A) / B)) / pi);
	elseif (B <= 3.6e-144)
		tmp = (180.0 / pi) * atan((B / (C / -0.5)));
	elseif (B <= 1.95e-64)
		tmp = 180.0 * (atan((((C - A) * 2.0) / B)) / pi);
	else
		tmp = (180.0 * atan(((-A - B) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 1.04e-215], N[(180.0 * N[(N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.6e-144], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.95e-64], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[((-A) - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < 1.0399999999999999e-215

   1. Initial program 57.0%

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

      1. associate-*l/ 57.0%

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

      2. *-lft-identity 57.0%

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

      3. +-commutative 57.0%

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

      4. unpow2 57.0%

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

      5. unpow2 57.0%

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

      6. hypot-def 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in B around -inf 65.7%

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

   if 1.0399999999999999e-215 < B < 3.6e-144

   1. Initial program 24.1%

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

      1. associate-*l/ 24.1%

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

      2. *-lft-identity 24.1%

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

      3. +-commutative 24.1%

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

      4. unpow2 24.1%

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

      5. unpow2 24.1%

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

      6. hypot-def 56.2%

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

   3. Simplified 56.2%

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

   4. Taylor expanded in C around -inf 33.0%

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

   5. Taylor expanded in C around inf 23.2%

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

      1. +-commutative 23.2%

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

      2. associate-+l+ 23.2%

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

   7. Simplified 49.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{\frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{\frac{C}{0.5}} + 0}}{B}\right)}{\pi} \]

   8. Taylor expanded in B around 0 53.1%

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

   9. Taylor expanded in B around 0 53.1%

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

       1. associate-*r/ 53.4%

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

       2. associate-/l* 49.8%

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

       3. associate-/r/ 53.5%

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

       4. associate-*r/ 53.5%

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

       5. *-commutative 53.5%

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

       6. associate-/l* 53.5%

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

   11. Simplified 53.5%

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

   if 3.6e-144 < B < 1.9499999999999998e-64

   1. Initial program 69.6%

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

      1. associate-*l/ 69.6%

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

      2. *-lft-identity 69.6%

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

      3. +-commutative 69.6%

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

      4. unpow2 69.6%

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

      5. unpow2 69.6%

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

      6. hypot-def 79.8%

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

   3. Simplified 79.8%

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

   4. Taylor expanded in C around -inf 69.1%

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

      1. +-commutative 69.1%

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

      2. metadata-eval 69.1%

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

      3. cancel-sign-sub-inv 69.1%

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

      4. distribute-lft-out-- 69.1%

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

   6. Simplified 69.1%

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

   if 1.9499999999999998e-64 < B

   1. Initial program 46.8%

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

      1. associate-*l/ 46.8%

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

      2. *-lft-identity 46.8%

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

      3. +-commutative 46.8%

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

      4. unpow2 46.8%

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

      5. unpow2 46.8%

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

      6. hypot-def 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in C around -inf 76.6%

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

   5. Taylor expanded in B around inf 67.0%

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

      1. associate-*r/ 67.0%

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

      2. mul-1-neg 67.0%

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

   7. Applied egg-rr 67.0%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.04 \cdot 10^{-215}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-144}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-64}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) \cdot 2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9: 64.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 6.6 \cdot 10^{-215}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-144}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 6.6e-215)
   (* 180.0 (/ (atan (/ (- (+ B C) A) B)) PI))
   (if (<= B 3.6e-144)
     (* (/ 180.0 PI) (atan (/ B (/ C -0.5))))
     (* (/ 180.0 PI) (atan (/ (- C (+ B A)) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 6.6e-215) {
		tmp = 180.0 * (atan((((B + C) - A) / B)) / ((double) M_PI));
	} else if (B <= 3.6e-144) {
		tmp = (180.0 / ((double) M_PI)) * atan((B / (C / -0.5)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (B + A)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 6.6e-215) {
		tmp = 180.0 * (Math.atan((((B + C) - A) / B)) / Math.PI);
	} else if (B <= 3.6e-144) {
		tmp = (180.0 / Math.PI) * Math.atan((B / (C / -0.5)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (B + A)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 6.6e-215:
		tmp = 180.0 * (math.atan((((B + C) - A) / B)) / math.pi)
	elif B <= 3.6e-144:
		tmp = (180.0 / math.pi) * math.atan((B / (C / -0.5)))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (B + A)) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 6.6e-215)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(B + C) - A) / B)) / pi));
	elseif (B <= 3.6e-144)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B / Float64(C / -0.5))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(B + A)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 6.6e-215)
		tmp = 180.0 * (atan((((B + C) - A) / B)) / pi);
	elseif (B <= 3.6e-144)
		tmp = (180.0 / pi) * atan((B / (C / -0.5)));
	else
		tmp = (180.0 / pi) * atan(((C - (B + A)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 6.6e-215], N[(180.0 * N[(N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.6e-144], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 6.5999999999999996e-215

   1. Initial program 57.0%

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

      1. associate-*l/ 57.0%

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

      2. *-lft-identity 57.0%

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

      3. +-commutative 57.0%

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

      4. unpow2 57.0%

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

      5. unpow2 57.0%

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

      6. hypot-def 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in B around -inf 65.7%

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

   if 6.5999999999999996e-215 < B < 3.6e-144

   1. Initial program 24.1%

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

      1. associate-*l/ 24.1%

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

      2. *-lft-identity 24.1%

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

      3. +-commutative 24.1%

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

      4. unpow2 24.1%

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

      5. unpow2 24.1%

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

      6. hypot-def 56.2%

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

   3. Simplified 56.2%

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

   4. Taylor expanded in C around -inf 33.0%

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

   5. Taylor expanded in C around inf 23.2%

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

      1. +-commutative 23.2%

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

      2. associate-+l+ 23.2%

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

   7. Simplified 49.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{\frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{\frac{C}{0.5}} + 0}}{B}\right)}{\pi} \]

   8. Taylor expanded in B around 0 53.1%

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

   9. Taylor expanded in B around 0 53.1%

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

       1. associate-*r/ 53.4%

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

       2. associate-/l* 49.8%

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

       3. associate-/r/ 53.5%

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

       4. associate-*r/ 53.5%

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

       5. *-commutative 53.5%

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

       6. associate-/l* 53.5%

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

   11. Simplified 53.5%

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

   if 3.6e-144 < B

   1. Initial program 51.9%

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

      1. associate-*r/ 51.9%

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

      2. associate-*l/ 51.9%

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

      3. associate-*l/ 51.9%

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

      4. *-lft-identity 51.9%

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

      5. sub-neg 51.9%

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

      6. associate-+l- 52.0%

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

      7. sub-neg 52.0%

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

      8. remove-double-neg 52.0%

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

      9. +-commutative 52.0%

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

      10. unpow2 52.0%

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

      11. unpow2 52.0%

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

      12. hypot-def 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in B around inf 73.4%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 6.6 \cdot 10^{-215}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-144}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \]

Alternative 10: 64.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 7.1 \cdot 10^{-215}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-144}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 7.1e-215)
   (/ 180.0 (/ PI (atan (/ (- (+ B C) A) B))))
   (if (<= B 3.8e-144)
     (* (/ 180.0 PI) (atan (/ B (/ C -0.5))))
     (* (/ 180.0 PI) (atan (/ (- C (+ B A)) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 7.1e-215) {
		tmp = 180.0 / (((double) M_PI) / atan((((B + C) - A) / B)));
	} else if (B <= 3.8e-144) {
		tmp = (180.0 / ((double) M_PI)) * atan((B / (C / -0.5)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (B + A)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 7.1e-215) {
		tmp = 180.0 / (Math.PI / Math.atan((((B + C) - A) / B)));
	} else if (B <= 3.8e-144) {
		tmp = (180.0 / Math.PI) * Math.atan((B / (C / -0.5)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (B + A)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 7.1e-215:
		tmp = 180.0 / (math.pi / math.atan((((B + C) - A) / B)))
	elif B <= 3.8e-144:
		tmp = (180.0 / math.pi) * math.atan((B / (C / -0.5)))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (B + A)) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 7.1e-215)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(B + C) - A) / B))));
	elseif (B <= 3.8e-144)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B / Float64(C / -0.5))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(B + A)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 7.1e-215)
		tmp = 180.0 / (pi / atan((((B + C) - A) / B)));
	elseif (B <= 3.8e-144)
		tmp = (180.0 / pi) * atan((B / (C / -0.5)));
	else
		tmp = (180.0 / pi) * atan(((C - (B + A)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 7.1e-215], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(B + C), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.8e-144], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 7.1000000000000001e-215

   1. Initial program 57.0%

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

      1. associate-*l/ 57.0%

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

      2. *-lft-identity 57.0%

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

      3. +-commutative 57.0%

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

      4. unpow2 57.0%

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

      5. unpow2 57.0%

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

      6. hypot-def 75.6%

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

   3. Simplified 75.6%

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

      1. clear-num 75.6%

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

      2. un-div-inv 75.6%

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

      3. associate--r+ 72.9%

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

   5. Applied egg-rr 72.9%

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

   6. Taylor expanded in B around -inf 65.7%

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

   if 7.1000000000000001e-215 < B < 3.79999999999999993e-144

   1. Initial program 24.1%

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

      1. associate-*l/ 24.1%

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

      2. *-lft-identity 24.1%

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

      3. +-commutative 24.1%

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

      4. unpow2 24.1%

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

      5. unpow2 24.1%

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

      6. hypot-def 56.2%

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

   3. Simplified 56.2%

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

   4. Taylor expanded in C around -inf 33.0%

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

   5. Taylor expanded in C around inf 23.2%

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

      1. +-commutative 23.2%

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

      2. associate-+l+ 23.2%

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

   7. Simplified 49.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{\frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{\frac{C}{0.5}} + 0}}{B}\right)}{\pi} \]

   8. Taylor expanded in B around 0 53.1%

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

   9. Taylor expanded in B around 0 53.1%

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

       1. associate-*r/ 53.4%

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

       2. associate-/l* 49.8%

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

       3. associate-/r/ 53.5%

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

       4. associate-*r/ 53.5%

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

       5. *-commutative 53.5%

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

       6. associate-/l* 53.5%

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

   11. Simplified 53.5%

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

   if 3.79999999999999993e-144 < B

   1. Initial program 51.9%

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

      1. associate-*r/ 51.9%

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

      2. associate-*l/ 51.9%

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

      3. associate-*l/ 51.9%

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

      4. *-lft-identity 51.9%

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

      5. sub-neg 51.9%

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

      6. associate-+l- 52.0%

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

      7. sub-neg 52.0%

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

      8. remove-double-neg 52.0%

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

      9. +-commutative 52.0%

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

      10. unpow2 52.0%

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

      11. unpow2 52.0%

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

      12. hypot-def 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in B around inf 73.4%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 7.1 \cdot 10^{-215}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-144}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \]

Alternative 11: 59.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -4.1 \cdot 10^{-157}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C}{B}\right)}}\\ \mathbf{elif}\;C \leq 9 \cdot 10^{-86}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -4.1e-157)
   (/ 180.0 (/ PI (atan (+ 1.0 (/ C B)))))
   (if (<= C 9e-86)
     (/ (* 180.0 (atan (/ (- (- A) B) B))) PI)
     (* (/ 180.0 PI) (atan (/ B (/ C -0.5)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.1e-157) {
		tmp = 180.0 / (((double) M_PI) / atan((1.0 + (C / B))));
	} else if (C <= 9e-86) {
		tmp = (180.0 * atan(((-A - B) / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((B / (C / -0.5)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.1e-157) {
		tmp = 180.0 / (Math.PI / Math.atan((1.0 + (C / B))));
	} else if (C <= 9e-86) {
		tmp = (180.0 * Math.atan(((-A - B) / B))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((B / (C / -0.5)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -4.1e-157:
		tmp = 180.0 / (math.pi / math.atan((1.0 + (C / B))))
	elif C <= 9e-86:
		tmp = (180.0 * math.atan(((-A - B) / B))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan((B / (C / -0.5)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -4.1e-157)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(1.0 + Float64(C / B)))));
	elseif (C <= 9e-86)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(-A) - B) / B))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B / Float64(C / -0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -4.1e-157)
		tmp = 180.0 / (pi / atan((1.0 + (C / B))));
	elseif (C <= 9e-86)
		tmp = (180.0 * atan(((-A - B) / B))) / pi;
	else
		tmp = (180.0 / pi) * atan((B / (C / -0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -4.1e-157], N[(180.0 / N[(Pi / N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 9e-86], N[(N[(180.0 * N[ArcTan[N[(N[((-A) - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B / N[(C / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -4.1000000000000002e-157

   1. Initial program 68.3%

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

      1. associate-*l/ 68.3%

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

      2. *-lft-identity 68.3%

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

      3. +-commutative 68.3%

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

      4. unpow2 68.3%

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

      5. unpow2 68.3%

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

      6. hypot-def 86.9%

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

   3. Simplified 86.9%

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

      1. clear-num 86.9%

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

      2. un-div-inv 86.9%

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

      3. associate--r+ 85.3%

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

   5. Applied egg-rr 85.3%

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

   6. Taylor expanded in A around 0 66.1%

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

      1. unpow2 66.1%

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

      2. unpow2 66.1%

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

      3. hypot-def 82.6%

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

   8. Simplified 82.6%

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

   9. Taylor expanded in B around -inf 70.1%

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

   if -4.1000000000000002e-157 < C < 8.9999999999999995e-86

   1. Initial program 61.6%

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

      1. associate-*l/ 61.6%

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

      2. *-lft-identity 61.6%

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

      3. +-commutative 61.6%

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

      4. unpow2 61.6%

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

      5. unpow2 61.6%

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

      6. hypot-def 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in C around -inf 79.7%

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

   5. Taylor expanded in B around inf 52.3%

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

      1. associate-*r/ 52.3%

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

      2. mul-1-neg 52.3%

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

   7. Applied egg-rr 52.3%

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

   if 8.9999999999999995e-86 < C

   1. Initial program 26.9%

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

      1. associate-*l/ 26.9%

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

      2. *-lft-identity 26.9%

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

      3. +-commutative 26.9%

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

      4. unpow2 26.9%

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

      5. unpow2 26.9%

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

      6. hypot-def 56.4%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in C around -inf 39.9%

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

   5. Taylor expanded in C around inf 23.6%

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

      1. +-commutative 23.6%

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

      2. associate-+l+ 29.1%

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

   7. Simplified 52.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{\frac{\mathsf{fma}\left(B, B, 0 \cdot \left(A - \left(-A\right)\right)\right)}{\frac{C}{0.5}} + 0}}{B}\right)}{\pi} \]

   8. Taylor expanded in B around 0 62.5%

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

   9. Taylor expanded in B around 0 62.5%

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

       1. associate-*r/ 62.6%

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

       2. associate-/l* 59.6%

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

       3. associate-/r/ 62.6%

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

       4. associate-*r/ 62.6%

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

       5. *-commutative 62.6%

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

       6. associate-/l* 62.6%

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

   11. Simplified 62.6%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -4.1 \cdot 10^{-157}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C}{B}\right)}}\\ \mathbf{elif}\;C \leq 9 \cdot 10^{-86}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{\frac{C}{-0.5}}\right)\\ \end{array} \]

Alternative 12: 46.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-217}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7.2e-24)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.4e-217)
     (* 180.0 (/ (atan (/ (- A) B)) PI))
     (if (<= B 8.2e-126)
       (* 180.0 (/ (atan (/ 0.0 B)) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.2e-24) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.4e-217) {
		tmp = 180.0 * (atan((-A / B)) / ((double) M_PI));
	} else if (B <= 8.2e-126) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.2e-24) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.4e-217) {
		tmp = 180.0 * (Math.atan((-A / B)) / Math.PI);
	} else if (B <= 8.2e-126) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7.2e-24:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.4e-217:
		tmp = 180.0 * (math.atan((-A / B)) / math.pi)
	elif B <= 8.2e-126:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -7.2e-24)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.4e-217)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi));
	elseif (B <= 8.2e-126)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -7.2e-24)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.4e-217)
		tmp = 180.0 * (atan((-A / B)) / pi);
	elseif (B <= 8.2e-126)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7.2e-24], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.4e-217], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.2e-126], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -7.2000000000000002e-24

   1. Initial program 54.9%

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

      1. associate-*l/ 54.9%

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

      2. *-lft-identity 54.9%

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

      3. +-commutative 54.9%

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

      4. unpow2 54.9%

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

      5. unpow2 54.9%

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

      6. hypot-def 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in B around -inf 63.7%

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

   if -7.2000000000000002e-24 < B < 2.3999999999999999e-217

   1. Initial program 59.3%

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

      1. associate-*l/ 59.3%

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

      2. *-lft-identity 59.3%

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

      3. +-commutative 59.3%

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

      4. unpow2 59.3%

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

      5. unpow2 59.3%

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

      6. hypot-def 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in C around -inf 60.2%

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

   5. Taylor expanded in B around inf 36.3%

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

   6. Taylor expanded in A around inf 36.5%

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

   if 2.3999999999999999e-217 < B < 8.1999999999999995e-126

   1. Initial program 32.8%

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

      1. associate-*l/ 32.8%

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

      2. *-lft-identity 32.8%

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

      3. +-commutative 32.8%

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

      4. unpow2 32.8%

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

      5. unpow2 32.8%

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

      6. hypot-def 66.0%

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

   3. Simplified 66.0%

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

   4. Taylor expanded in C around inf 36.2%

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

      1. distribute-rgt1-in 36.2%

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

      2. metadata-eval 36.2%

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

      3. mul0-lft 36.2%

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

      4. metadata-eval 36.2%

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

   6. Simplified 36.2%

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

   if 8.1999999999999995e-126 < B

   1. Initial program 51.3%

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

      1. associate-*l/ 51.3%

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

      2. *-lft-identity 51.3%

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

      3. +-commutative 51.3%

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

      4. unpow2 51.3%

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

      5. unpow2 51.3%

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

      6. hypot-def 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in B around inf 51.7%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-217}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-126}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 13: 49.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{-242}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9.5e-242)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 2e-176)
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.5e-242) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 2e-176) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.5e-242) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 2e-176) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -9.5e-242:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 2e-176:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -9.5e-242)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 2e-176)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -9.5e-242)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 2e-176)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -9.5e-242], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2e-176], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -9.4999999999999997e-242

   1. Initial program 39.4%

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

      1. associate-*l/ 39.4%

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

      2. *-lft-identity 39.4%

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

      3. +-commutative 39.4%

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

      4. unpow2 39.4%

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

      5. unpow2 39.4%

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

      6. hypot-def 60.7%

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

   3. Simplified 60.7%

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

   4. Taylor expanded in A around -inf 54.2%

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

   if -9.4999999999999997e-242 < A < 2e-176

   1. Initial program 56.0%

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

      1. associate-*l/ 56.0%

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

      2. *-lft-identity 56.0%

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

      3. +-commutative 56.0%

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

      4. unpow2 56.0%

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

      5. unpow2 56.0%

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

      6. hypot-def 84.2%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in B around inf 38.3%

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

   if 2e-176 < A

   1. Initial program 68.0%

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

      1. associate-*l/ 68.0%

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

      2. *-lft-identity 68.0%

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

      3. +-commutative 68.0%

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

      4. unpow2 68.0%

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

      5. unpow2 68.0%

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

      6. hypot-def 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in A around inf 54.7%

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

      1. *-commutative 54.7%

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

   6. Simplified 54.7%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{-242}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 14: 49.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{-242}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-191}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9e-242)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 2.6e-191)
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (/ (- A) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9e-242) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 2.6e-191) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-A / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -9e-242) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 2.6e-191) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-A / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -9e-242:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 2.6e-191:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-A / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -9e-242)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 2.6e-191)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -9e-242)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 2.6e-191)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-A / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -9e-242], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.6e-191], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.9999999999999997e-242

   1. Initial program 39.4%

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

      1. associate-*l/ 39.4%

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

      2. *-lft-identity 39.4%

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

      3. +-commutative 39.4%

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

      4. unpow2 39.4%

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

      5. unpow2 39.4%

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

      6. hypot-def 60.7%

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

   3. Simplified 60.7%

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

   4. Taylor expanded in A around -inf 54.2%

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

   if -8.9999999999999997e-242 < A < 2.59999999999999986e-191

   1. Initial program 56.0%

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

      1. associate-*l/ 56.0%

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

      2. *-lft-identity 56.0%

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

      3. +-commutative 56.0%

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

      4. unpow2 56.0%

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

      5. unpow2 56.0%

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

      6. hypot-def 84.2%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in B around inf 38.3%

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

   if 2.59999999999999986e-191 < A

   1. Initial program 68.0%

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

      1. associate-*l/ 68.0%

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

      2. *-lft-identity 68.0%

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

      3. +-commutative 68.0%

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

      4. unpow2 68.0%

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

      5. unpow2 68.0%

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

      6. hypot-def 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in C around -inf 80.0%

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

   5. Taylor expanded in B around inf 58.0%

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

   6. Taylor expanded in A around inf 53.7%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{-242}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-191}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 15: 45.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.6 \cdot 10^{-152}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-124}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.6e-152)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.7e-124)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.6e-152) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.7e-124) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.6e-152) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.7e-124) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.6e-152:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.7e-124:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.6e-152)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.7e-124)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.6e-152)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.7e-124)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.6e-152], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.7e-124], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.60000000000000006e-152

   1. Initial program 54.0%

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

      1. associate-*l/ 54.0%

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

      2. *-lft-identity 54.0%

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

      3. +-commutative 54.0%

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

      4. unpow2 54.0%

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

      5. unpow2 54.0%

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

      6. hypot-def 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in B around -inf 49.4%

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

   if -1.60000000000000006e-152 < B < 1.7e-124

   1. Initial program 53.4%

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

      1. associate-*l/ 53.4%

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

      2. *-lft-identity 53.4%

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

      3. +-commutative 53.4%

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

      4. unpow2 53.4%

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

      5. unpow2 53.4%

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

      6. hypot-def 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in C around inf 28.5%

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

      1. distribute-rgt1-in 28.5%

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

      2. metadata-eval 28.5%

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

      3. mul0-lft 28.5%

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

      4. metadata-eval 28.5%

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

   6. Simplified 28.5%

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

   if 1.7e-124 < B

   1. Initial program 51.3%

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

      1. associate-*l/ 51.3%

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

      2. *-lft-identity 51.3%

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

      3. +-commutative 51.3%

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

      4. unpow2 51.3%

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

      5. unpow2 51.3%

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

      6. hypot-def 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in B around inf 51.7%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.6 \cdot 10^{-152}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-124}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 16: 39.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.999999999999994e-310

   1. Initial program 55.5%

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

      1. associate-*l/ 55.5%

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

      2. *-lft-identity 55.5%

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

      3. +-commutative 55.5%

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

      4. unpow2 55.5%

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

      5. unpow2 55.5%

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

      6. hypot-def 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in B around -inf 40.3%

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

   if -1.999999999999994e-310 < B

   1. Initial program 50.2%

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

      1. associate-*l/ 50.2%

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

      2. *-lft-identity 50.2%

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

      3. +-commutative 50.2%

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

      4. unpow2 50.2%

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

      5. unpow2 50.2%

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

      6. hypot-def 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in B around inf 37.7%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 17: 21.6% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 53.0%

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

   1. associate-*l/ 53.0%

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

   2. *-lft-identity 53.0%

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

   3. +-commutative 53.0%

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

   4. unpow2 53.0%

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

   5. unpow2 53.0%

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

   6. hypot-def 74.8%

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

3. Simplified 74.8%

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

4. Taylor expanded in B around inf 18.6%

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

5. Final simplification 18.6%

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

Reproduce

herbie shell --seed 2023240 
(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)))