ABCF->ab-angle angle

Percentage Accurate: 53.4% → 89.1%

Time: 15.5s

Alternatives: 21

Speedup: 3.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.1% accurate, 0.5× speedup

Math

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

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 -0.5) (not (<= t_0 0.0)))
     (/ 180.0 (/ PI (atan (/ (- (- C A) (hypot (- A C) B)) B))))
     (* (atan (* -0.5 (/ B (- C A)))) (/ 180.0 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 <= -0.5) || !(t_0 <= 0.0)) {
		tmp = 180.0 / (((double) M_PI) / atan((((C - A) - hypot((A - C), B)) / B)));
	} else {
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / ((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 <= -0.5) || !(t_0 <= 0.0)) {
		tmp = 180.0 / (Math.PI / Math.atan((((C - A) - Math.hypot((A - C), B)) / B)));
	} else {
		tmp = Math.atan((-0.5 * (B / (C - A)))) * (180.0 / 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 <= -0.5) or not (t_0 <= 0.0):
		tmp = 180.0 / (math.pi / math.atan((((C - A) - math.hypot((A - C), B)) / B)))
	else:
		tmp = math.atan((-0.5 * (B / (C - A)))) * (180.0 / 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 <= -0.5) || !(t_0 <= 0.0))
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B))));
	else
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) * Float64(180.0 / 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 <= -0.5) || ~((t_0 <= 0.0)))
		tmp = 180.0 / (pi / atan((((C - A) - hypot((A - C), B)) / B)));
	else
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / 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, -0.5], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -0.5 or 0.0 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 66.2%

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

      1. clear-num 66.2%

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

      2. un-div-inv 66.2%

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

      3. associate-*l/ 66.2%

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

      4. *-un-lft-identity 66.2%

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

      5. unpow2 66.2%

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

      6. unpow2 66.2%

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

      7. hypot-define 90.7%

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

   4. Applied egg-rr 90.7%

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

   if -0.5 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 0.0

   1. Initial program 24.8%

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

   3. Simplified 11.2%

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

   5. Taylor expanded in B around 0 99.6%

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

4. Final simplification 92.2%

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

Alternative 2: 76.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.8 \cdot 10^{-76}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.8e-76)
   (/ (* 180.0 (atan (* -0.5 (/ B (- C A))))) PI)
   (if (<= A 2.8e-22)
     (/ 180.0 (/ PI (atan (/ (- C (hypot B C)) B))))
     (* 180.0 (/ (atan (/ (+ A (hypot B A)) (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.8e-76) {
		tmp = (180.0 * atan((-0.5 * (B / (C - A))))) / ((double) M_PI);
	} else if (A <= 2.8e-22) {
		tmp = 180.0 / (((double) M_PI) / atan(((C - hypot(B, C)) / B)));
	} else {
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.8e-76) {
		tmp = (180.0 * Math.atan((-0.5 * (B / (C - A))))) / Math.PI;
	} else if (A <= 2.8e-22) {
		tmp = 180.0 / (Math.PI / Math.atan(((C - Math.hypot(B, C)) / B)));
	} else {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(B, A)) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.8e-76:
		tmp = (180.0 * math.atan((-0.5 * (B / (C - A))))) / math.pi
	elif A <= 2.8e-22:
		tmp = 180.0 / (math.pi / math.atan(((C - math.hypot(B, C)) / B)))
	else:
		tmp = 180.0 * (math.atan(((A + math.hypot(B, A)) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.8e-76)
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / Float64(C - A))))) / pi);
	elseif (A <= 2.8e-22)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - hypot(B, C)) / B))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.8e-76)
		tmp = (180.0 * atan((-0.5 * (B / (C - A))))) / pi;
	elseif (A <= 2.8e-22)
		tmp = 180.0 / (pi / atan(((C - hypot(B, C)) / B)));
	else
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.8e-76], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 2.8e-22], 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[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.8000000000000001e-76

   1. Initial program 27.9%

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

   3. Simplified 38.1%

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

      1. associate-*r/ 38.2%

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

   6. Applied egg-rr 38.2%

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

   7. Taylor expanded in B around 0 71.6%

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

   if -2.8000000000000001e-76 < A < 2.79999999999999995e-22

   1. Initial program 67.1%

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

      1. clear-num 67.1%

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

      2. un-div-inv 67.1%

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

      3. associate-*l/ 67.1%

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

      4. *-un-lft-identity 67.1%

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

      5. unpow2 67.1%

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

      6. unpow2 67.1%

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

      7. hypot-define 85.0%

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

   4. Applied egg-rr 85.0%

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

   5. Taylor expanded in A around 0 63.1%

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

      1. unpow2 63.1%

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

      2. unpow2 63.1%

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

      3. hypot-define 81.2%

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

   7. Simplified 81.2%

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

   if 2.79999999999999995e-22 < A

   1. Initial program 79.5%

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

   3. Taylor expanded in C around 0 79.3%

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

      1. associate-*r/ 79.3%

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

      2. mul-1-neg 79.3%

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

      3. +-commutative 79.3%

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

      4. unpow2 79.3%

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

      5. unpow2 79.3%

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

      6. hypot-define 87.6%

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

   5. Simplified 87.6%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.8 \cdot 10^{-76}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.4 \cdot 10^{-76}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.2 \cdot 10^{-18}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + B \cdot \left(-1 - \frac{A}{B}\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.4e-76)
   (/ (* 180.0 (atan (* -0.5 (/ B (- C A))))) PI)
   (if (<= A 3.2e-18)
     (/ 180.0 (/ PI (atan (/ (- C (hypot B C)) B))))
     (* (/ 180.0 PI) (atan (/ (+ C (* B (- -1.0 (/ A B)))) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.4e-76) {
		tmp = (180.0 * atan((-0.5 * (B / (C - A))))) / ((double) M_PI);
	} else if (A <= 3.2e-18) {
		tmp = 180.0 / (((double) M_PI) / atan(((C - hypot(B, C)) / B)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C + (B * (-1.0 - (A / B)))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.4e-76) {
		tmp = (180.0 * Math.atan((-0.5 * (B / (C - A))))) / Math.PI;
	} else if (A <= 3.2e-18) {
		tmp = 180.0 / (Math.PI / Math.atan(((C - Math.hypot(B, C)) / B)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C + (B * (-1.0 - (A / B)))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.4e-76:
		tmp = (180.0 * math.atan((-0.5 * (B / (C - A))))) / math.pi
	elif A <= 3.2e-18:
		tmp = 180.0 / (math.pi / math.atan(((C - math.hypot(B, C)) / B)))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C + (B * (-1.0 - (A / B)))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.4e-76)
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / Float64(C - A))))) / pi);
	elseif (A <= 3.2e-18)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - hypot(B, C)) / B))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + Float64(B * Float64(-1.0 - Float64(A / B)))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.4e-76)
		tmp = (180.0 * atan((-0.5 * (B / (C - A))))) / pi;
	elseif (A <= 3.2e-18)
		tmp = 180.0 / (pi / atan(((C - hypot(B, C)) / B)));
	else
		tmp = (180.0 / pi) * atan(((C + (B * (-1.0 - (A / B)))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.4e-76], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 3.2e-18], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C + N[(B * N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.3999999999999999e-76

   1. Initial program 27.9%

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

   3. Simplified 38.1%

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

      1. associate-*r/ 38.2%

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

   6. Applied egg-rr 38.2%

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

   7. Taylor expanded in B around 0 71.6%

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

   if -3.3999999999999999e-76 < A < 3.1999999999999999e-18

   1. Initial program 67.0%

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

      1. clear-num 67.0%

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

      2. un-div-inv 67.0%

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

      3. associate-*l/ 67.0%

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

      4. *-un-lft-identity 67.0%

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

      5. unpow2 67.0%

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

      6. unpow2 67.0%

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

      7. hypot-define 85.2%

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

   4. Applied egg-rr 85.2%

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

   5. Taylor expanded in A around 0 63.0%

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

      1. unpow2 63.0%

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

      2. unpow2 63.0%

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

      3. hypot-define 81.6%

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

   7. Simplified 81.6%

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

   if 3.1999999999999999e-18 < A

   1. Initial program 80.1%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in B around inf 80.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.4 \cdot 10^{-76}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.2 \cdot 10^{-18}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + B \cdot \left(-1 - \frac{A}{B}\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.2 \cdot 10^{-77}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.4 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + B \cdot \left(-1 - \frac{A}{B}\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.2e-77)
   (/ (* 180.0 (atan (* -0.5 (/ B (- C A))))) PI)
   (if (<= A 5.4e-17)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* (/ 180.0 PI) (atan (/ (+ C (* B (- -1.0 (/ A B)))) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.2e-77) {
		tmp = (180.0 * atan((-0.5 * (B / (C - A))))) / ((double) M_PI);
	} else if (A <= 5.4e-17) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C + (B * (-1.0 - (A / B)))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.2e-77) {
		tmp = (180.0 * Math.atan((-0.5 * (B / (C - A))))) / Math.PI;
	} else if (A <= 5.4e-17) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C + (B * (-1.0 - (A / B)))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.2e-77:
		tmp = (180.0 * math.atan((-0.5 * (B / (C - A))))) / math.pi
	elif A <= 5.4e-17:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C + (B * (-1.0 - (A / B)))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.2e-77)
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / Float64(C - A))))) / pi);
	elseif (A <= 5.4e-17)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + Float64(B * Float64(-1.0 - Float64(A / B)))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.2e-77)
		tmp = (180.0 * atan((-0.5 * (B / (C - A))))) / pi;
	elseif (A <= 5.4e-17)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = (180.0 / pi) * atan(((C + (B * (-1.0 - (A / B)))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.2e-77], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 5.4e-17], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C + N[(B * N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -4.20000000000000031e-77

   1. Initial program 27.9%

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

   3. Simplified 38.1%

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

      1. associate-*r/ 38.2%

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

   6. Applied egg-rr 38.2%

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

   7. Taylor expanded in B around 0 71.6%

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

   if -4.20000000000000031e-77 < A < 5.4000000000000002e-17

   1. Initial program 67.0%

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

   3. Taylor expanded in A around 0 63.0%

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

      1. unpow2 63.0%

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

      2. unpow2 63.0%

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

      3. hypot-define 81.6%

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

   5. Simplified 81.6%

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

   if 5.4000000000000002e-17 < A

   1. Initial program 80.1%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in B around inf 80.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.2 \cdot 10^{-77}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.4 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + B \cdot \left(-1 - \frac{A}{B}\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.25 \cdot 10^{-76}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.25e-76)
   (/ (* 180.0 (atan (* -0.5 (/ B (- C A))))) PI)
   (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B (- C A)))) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.25e-76) {
		tmp = (180.0 * atan((-0.5 * (B / (C - A))))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(B, (C - A)))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.25e-76) {
		tmp = (180.0 * Math.atan((-0.5 * (B / (C - A))))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, (C - A)))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.25e-76:
		tmp = (180.0 * math.atan((-0.5 * (B / (C - A))))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(B, (C - A)))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.25e-76)
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / Float64(C - A))))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(B, Float64(C - A)))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.25e-76)
		tmp = (180.0 * atan((-0.5 * (B / (C - A))))) / pi;
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(B, (C - A)))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.25e-76], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.2499999999999999e-76

   1. Initial program 27.9%

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

   3. Simplified 38.1%

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

      1. associate-*r/ 38.2%

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

   6. Applied egg-rr 38.2%

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

   7. Taylor expanded in B around 0 71.6%

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

   if -1.2499999999999999e-76 < A

   1. Initial program 71.7%

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

   3. Simplified 88.5%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.25 \cdot 10^{-76}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ t_1 := t\_0 \cdot \frac{180}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -6 \cdot 10^{-87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;B \leq -1.7 \cdot 10^{-185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-274}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-32} \lor \neg \left(B \leq 950\right):\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - B}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot t\_0}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (atan (* -0.5 (/ B (- C A)))))
        (t_1 (* t_0 (/ 180.0 PI)))
        (t_2 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B -6e-87)
     t_2
     (if (<= B -1.7e-185)
       t_1
       (if (<= B 9.5e-274)
         t_2
         (if (<= B 3.6e-119)
           t_1
           (if (or (<= B 1.95e-32) (not (<= B 950.0)))
             (/ 180.0 (/ PI (atan (/ (- C B) B))))
             (/ (* 180.0 t_0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan((-0.5 * (B / (C - A))));
	double t_1 = t_0 * (180.0 / ((double) M_PI));
	double t_2 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (B <= -6e-87) {
		tmp = t_2;
	} else if (B <= -1.7e-185) {
		tmp = t_1;
	} else if (B <= 9.5e-274) {
		tmp = t_2;
	} else if (B <= 3.6e-119) {
		tmp = t_1;
	} else if ((B <= 1.95e-32) || !(B <= 950.0)) {
		tmp = 180.0 / (((double) M_PI) / atan(((C - B) / B)));
	} else {
		tmp = (180.0 * t_0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan((-0.5 * (B / (C - A))));
	double t_1 = t_0 * (180.0 / Math.PI);
	double t_2 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= -6e-87) {
		tmp = t_2;
	} else if (B <= -1.7e-185) {
		tmp = t_1;
	} else if (B <= 9.5e-274) {
		tmp = t_2;
	} else if (B <= 3.6e-119) {
		tmp = t_1;
	} else if ((B <= 1.95e-32) || !(B <= 950.0)) {
		tmp = 180.0 / (Math.PI / Math.atan(((C - B) / B)));
	} else {
		tmp = (180.0 * t_0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan((-0.5 * (B / (C - A))))
	t_1 = t_0 * (180.0 / math.pi)
	t_2 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= -6e-87:
		tmp = t_2
	elif B <= -1.7e-185:
		tmp = t_1
	elif B <= 9.5e-274:
		tmp = t_2
	elif B <= 3.6e-119:
		tmp = t_1
	elif (B <= 1.95e-32) or not (B <= 950.0):
		tmp = 180.0 / (math.pi / math.atan(((C - B) / B)))
	else:
		tmp = (180.0 * t_0) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = atan(Float64(-0.5 * Float64(B / Float64(C - A))))
	t_1 = Float64(t_0 * Float64(180.0 / pi))
	t_2 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= -6e-87)
		tmp = t_2;
	elseif (B <= -1.7e-185)
		tmp = t_1;
	elseif (B <= 9.5e-274)
		tmp = t_2;
	elseif (B <= 3.6e-119)
		tmp = t_1;
	elseif ((B <= 1.95e-32) || !(B <= 950.0))
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - B) / B))));
	else
		tmp = Float64(Float64(180.0 * t_0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan((-0.5 * (B / (C - A))));
	t_1 = t_0 * (180.0 / pi);
	t_2 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= -6e-87)
		tmp = t_2;
	elseif (B <= -1.7e-185)
		tmp = t_1;
	elseif (B <= 9.5e-274)
		tmp = t_2;
	elseif (B <= 3.6e-119)
		tmp = t_1;
	elseif ((B <= 1.95e-32) || ~((B <= 950.0)))
		tmp = 180.0 / (pi / atan(((C - B) / B)));
	else
		tmp = (180.0 * t_0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -6e-87], t$95$2, If[LessEqual[B, -1.7e-185], t$95$1, If[LessEqual[B, 9.5e-274], t$95$2, If[LessEqual[B, 3.6e-119], t$95$1, If[Or[LessEqual[B, 1.95e-32], N[Not[LessEqual[B, 950.0]], $MachinePrecision]], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * t$95$0), $MachinePrecision] / Pi), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -6.00000000000000033e-87 or -1.6999999999999999e-185 < B < 9.5000000000000009e-274

   1. Initial program 69.0%

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

   3. Taylor expanded in B around -inf 79.7%

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

      1. associate--l+ 79.7%

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

      2. div-sub 79.7%

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

   5. Simplified 79.7%

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

   if -6.00000000000000033e-87 < B < -1.6999999999999999e-185 or 9.5000000000000009e-274 < B < 3.6e-119

   1. Initial program 41.1%

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

   3. Simplified 50.2%

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

   5. Taylor expanded in B around 0 68.4%

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

   if 3.6e-119 < B < 1.9500000000000001e-32 or 950 < B

   1. Initial program 62.1%

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

      1. clear-num 62.1%

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

      2. un-div-inv 62.1%

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

      3. associate-*l/ 62.1%

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

      4. *-un-lft-identity 62.1%

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

      5. unpow2 62.1%

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

      6. unpow2 62.1%

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

      7. hypot-define 81.9%

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

   4. Applied egg-rr 81.9%

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

   5. Taylor expanded in A around 0 54.9%

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

      1. unpow2 54.9%

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

      2. unpow2 54.9%

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

      3. hypot-define 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in C around 0 69.7%

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

   if 1.9500000000000001e-32 < B < 950

   1. Initial program 19.7%

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

   3. Simplified 20.1%

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

      1. associate-*r/ 20.1%

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

   6. Applied egg-rr 20.1%

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

   7. Taylor expanded in B around 0 83.2%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6 \cdot 10^{-87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.7 \cdot 10^{-185}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-274}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-119}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-32} \lor \neg \left(B \leq 950\right):\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - B}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -6.6 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{-183}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.02 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-117} \lor \neg \left(B \leq 4.9 \cdot 10^{-33}\right) \land B \leq 700:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - B}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (atan (* -0.5 (/ B (- C A)))) (/ 180.0 PI)))
        (t_1 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B -6.6e-88)
     t_1
     (if (<= B -1.3e-183)
       t_0
       (if (<= B 1.02e-273)
         t_1
         (if (or (<= B 2.1e-117) (and (not (<= B 4.9e-33)) (<= B 700.0)))
           t_0
           (/ 180.0 (/ PI (atan (/ (- C B) B))))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan((-0.5 * (B / (C - A)))) * (180.0 / ((double) M_PI));
	double t_1 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (B <= -6.6e-88) {
		tmp = t_1;
	} else if (B <= -1.3e-183) {
		tmp = t_0;
	} else if (B <= 1.02e-273) {
		tmp = t_1;
	} else if ((B <= 2.1e-117) || (!(B <= 4.9e-33) && (B <= 700.0))) {
		tmp = t_0;
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((C - B) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan((-0.5 * (B / (C - A)))) * (180.0 / Math.PI);
	double t_1 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= -6.6e-88) {
		tmp = t_1;
	} else if (B <= -1.3e-183) {
		tmp = t_0;
	} else if (B <= 1.02e-273) {
		tmp = t_1;
	} else if ((B <= 2.1e-117) || (!(B <= 4.9e-33) && (B <= 700.0))) {
		tmp = t_0;
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((C - B) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan((-0.5 * (B / (C - A)))) * (180.0 / math.pi)
	t_1 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= -6.6e-88:
		tmp = t_1
	elif B <= -1.3e-183:
		tmp = t_0
	elif B <= 1.02e-273:
		tmp = t_1
	elif (B <= 2.1e-117) or (not (B <= 4.9e-33) and (B <= 700.0)):
		tmp = t_0
	else:
		tmp = 180.0 / (math.pi / math.atan(((C - B) / B)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) * Float64(180.0 / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= -6.6e-88)
		tmp = t_1;
	elseif (B <= -1.3e-183)
		tmp = t_0;
	elseif (B <= 1.02e-273)
		tmp = t_1;
	elseif ((B <= 2.1e-117) || (!(B <= 4.9e-33) && (B <= 700.0)))
		tmp = t_0;
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - B) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan((-0.5 * (B / (C - A)))) * (180.0 / pi);
	t_1 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= -6.6e-88)
		tmp = t_1;
	elseif (B <= -1.3e-183)
		tmp = t_0;
	elseif (B <= 1.02e-273)
		tmp = t_1;
	elseif ((B <= 2.1e-117) || (~((B <= 4.9e-33)) && (B <= 700.0)))
		tmp = t_0;
	else
		tmp = 180.0 / (pi / atan(((C - B) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -6.6e-88], t$95$1, If[LessEqual[B, -1.3e-183], t$95$0, If[LessEqual[B, 1.02e-273], t$95$1, If[Or[LessEqual[B, 2.1e-117], And[N[Not[LessEqual[B, 4.9e-33]], $MachinePrecision], LessEqual[B, 700.0]]], t$95$0, N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -6.59999999999999987e-88 or -1.2999999999999999e-183 < B < 1.0200000000000001e-273

   1. Initial program 69.0%

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

   3. Taylor expanded in B around -inf 79.7%

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

      1. associate--l+ 79.7%

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

      2. div-sub 79.7%

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

   5. Simplified 79.7%

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

   if -6.59999999999999987e-88 < B < -1.2999999999999999e-183 or 1.0200000000000001e-273 < B < 2.0999999999999999e-117 or 4.8999999999999998e-33 < B < 700

   1. Initial program 39.2%

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

   3. Simplified 47.5%

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

   5. Taylor expanded in B around 0 69.7%

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

   if 2.0999999999999999e-117 < B < 4.8999999999999998e-33 or 700 < B

   1. Initial program 62.1%

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

      1. clear-num 62.1%

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

      2. un-div-inv 62.1%

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

      3. associate-*l/ 62.1%

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

      4. *-un-lft-identity 62.1%

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

      5. unpow2 62.1%

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

      6. unpow2 62.1%

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

      7. hypot-define 81.9%

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

   4. Applied egg-rr 81.9%

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

   5. Taylor expanded in A around 0 54.9%

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

      1. unpow2 54.9%

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

      2. unpow2 54.9%

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

      3. hypot-define 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in C around 0 69.7%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.6 \cdot 10^{-88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{-183}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 1.02 \cdot 10^{-273}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.1 \cdot 10^{-117} \lor \neg \left(B \leq 4.9 \cdot 10^{-33}\right) \land B \leq 700:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - B}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.1 \cdot 10^{-33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.45 \cdot 10^{-93}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -2.05 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-238}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 28500:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))
        (t_1 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= B -1.1e-33)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -1.45e-93)
       t_0
       (if (<= B -2.05e-137)
         t_1
         (if (<= B -4.5e-238)
           t_0
           (if (<= B 2.3e-51)
             t_1
             (if (<= B 28500.0) t_0 (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	double t_1 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (B <= -1.1e-33) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -1.45e-93) {
		tmp = t_0;
	} else if (B <= -2.05e-137) {
		tmp = t_1;
	} else if (B <= -4.5e-238) {
		tmp = t_0;
	} else if (B <= 2.3e-51) {
		tmp = t_1;
	} else if (B <= 28500.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (B <= -1.1e-33) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -1.45e-93) {
		tmp = t_0;
	} else if (B <= -2.05e-137) {
		tmp = t_1;
	} else if (B <= -4.5e-238) {
		tmp = t_0;
	} else if (B <= 2.3e-51) {
		tmp = t_1;
	} else if (B <= 28500.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	t_1 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	tmp = 0
	if B <= -1.1e-33:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -1.45e-93:
		tmp = t_0
	elif B <= -2.05e-137:
		tmp = t_1
	elif B <= -4.5e-238:
		tmp = t_0
	elif B <= 2.3e-51:
		tmp = t_1
	elif B <= 28500.0:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (B <= -1.1e-33)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -1.45e-93)
		tmp = t_0;
	elseif (B <= -2.05e-137)
		tmp = t_1;
	elseif (B <= -4.5e-238)
		tmp = t_0;
	elseif (B <= 2.3e-51)
		tmp = t_1;
	elseif (B <= 28500.0)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((-0.5 * (B / C))) / pi);
	t_1 = 180.0 * (atan((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (B <= -1.1e-33)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -1.45e-93)
		tmp = t_0;
	elseif (B <= -2.05e-137)
		tmp = t_1;
	elseif (B <= -4.5e-238)
		tmp = t_0;
	elseif (B <= 2.3e-51)
		tmp = t_1;
	elseif (B <= 28500.0)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.1e-33], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.45e-93], t$95$0, If[LessEqual[B, -2.05e-137], t$95$1, If[LessEqual[B, -4.5e-238], t$95$0, If[LessEqual[B, 2.3e-51], t$95$1, If[LessEqual[B, 28500.0], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.10000000000000003e-33

   1. Initial program 61.9%

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

   3. Taylor expanded in B around -inf 66.2%

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

   if -1.10000000000000003e-33 < B < -1.4499999999999999e-93 or -2.0499999999999999e-137 < B < -4.49999999999999996e-238 or 2.30000000000000002e-51 < B < 28500

   1. Initial program 51.0%

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

   3. Taylor expanded in C around inf 52.6%

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

      1. +-commutative 52.6%

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

      2. associate-*r/ 52.6%

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

      3. mul-1-neg 52.6%

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

      4. distribute-rgt1-in 52.6%

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

      5. metadata-eval 52.6%

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

      6. mul0-lft 52.6%

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

      7. metadata-eval 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in B around 0 52.6%

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

   if -1.4499999999999999e-93 < B < -2.0499999999999999e-137 or -4.49999999999999996e-238 < B < 2.30000000000000002e-51

   1. Initial program 62.0%

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

   3. Taylor expanded in A around -inf 39.6%

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

   if 28500 < B

   1. Initial program 59.0%

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

   3. Taylor expanded in B around inf 58.8%

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

Alternative 9: 65.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.1 \cdot 10^{-88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.8 \cdot 10^{-187} \lor \neg \left(B \leq 1.05 \cdot 10^{-273}\right) \land B \leq 1.45 \cdot 10^{-140}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + B \cdot \left(-1 - \frac{A}{B}\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.1e-88)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (or (<= B -7.8e-187) (and (not (<= B 1.05e-273)) (<= B 1.45e-140)))
     (* (atan (* -0.5 (/ B (- C A)))) (/ 180.0 PI))
     (* (/ 180.0 PI) (atan (/ (+ C (* B (- -1.0 (/ A B)))) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.1e-88) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if ((B <= -7.8e-187) || (!(B <= 1.05e-273) && (B <= 1.45e-140))) {
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C + (B * (-1.0 - (A / B)))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.1e-88) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if ((B <= -7.8e-187) || (!(B <= 1.05e-273) && (B <= 1.45e-140))) {
		tmp = Math.atan((-0.5 * (B / (C - A)))) * (180.0 / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C + (B * (-1.0 - (A / B)))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.1e-88:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif (B <= -7.8e-187) or (not (B <= 1.05e-273) and (B <= 1.45e-140)):
		tmp = math.atan((-0.5 * (B / (C - A)))) * (180.0 / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C + (B * (-1.0 - (A / B)))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.1e-88)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif ((B <= -7.8e-187) || (!(B <= 1.05e-273) && (B <= 1.45e-140)))
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + Float64(B * Float64(-1.0 - Float64(A / B)))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.1e-88)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif ((B <= -7.8e-187) || (~((B <= 1.05e-273)) && (B <= 1.45e-140)))
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / pi);
	else
		tmp = (180.0 / pi) * atan(((C + (B * (-1.0 - (A / B)))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.1e-88], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, -7.8e-187], And[N[Not[LessEqual[B, 1.05e-273]], $MachinePrecision], LessEqual[B, 1.45e-140]]], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C + N[(B * N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.10000000000000002e-88

   1. Initial program 63.2%

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

   3. Taylor expanded in B around -inf 86.6%

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

      1. associate--l+ 86.6%

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

      2. div-sub 86.6%

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

   5. Simplified 86.6%

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

   if -1.10000000000000002e-88 < B < -7.7999999999999998e-187 or 1.0500000000000001e-273 < B < 1.44999999999999999e-140

   1. Initial program 40.3%

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

   3. Simplified 49.9%

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

   5. Taylor expanded in B around 0 69.6%

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

   if -7.7999999999999998e-187 < B < 1.0500000000000001e-273 or 1.44999999999999999e-140 < B

   1. Initial program 65.1%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in B around inf 71.7%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.1 \cdot 10^{-88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -7.8 \cdot 10^{-187} \lor \neg \left(B \leq 1.05 \cdot 10^{-273}\right) \land B \leq 1.45 \cdot 10^{-140}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + B \cdot \left(-1 - \frac{A}{B}\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.2 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq -2.05 \cdot 10^{-184}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-140}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (atan (* -0.5 (/ B (- C A)))) (/ 180.0 PI)))
        (t_1 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B -2.2e-88)
     t_1
     (if (<= B -2.05e-184)
       t_0
       (if (<= B 9e-274)
         t_1
         (if (<= B 1.45e-140)
           t_0
           (/ 180.0 (/ PI (atan (+ (/ C B) (- -1.0 (/ A B))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan((-0.5 * (B / (C - A)))) * (180.0 / ((double) M_PI));
	double t_1 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (B <= -2.2e-88) {
		tmp = t_1;
	} else if (B <= -2.05e-184) {
		tmp = t_0;
	} else if (B <= 9e-274) {
		tmp = t_1;
	} else if (B <= 1.45e-140) {
		tmp = t_0;
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((C / B) + (-1.0 - (A / B)))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan((-0.5 * (B / (C - A)))) * (180.0 / Math.PI);
	double t_1 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= -2.2e-88) {
		tmp = t_1;
	} else if (B <= -2.05e-184) {
		tmp = t_0;
	} else if (B <= 9e-274) {
		tmp = t_1;
	} else if (B <= 1.45e-140) {
		tmp = t_0;
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((C / B) + (-1.0 - (A / B)))));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan((-0.5 * (B / (C - A)))) * (180.0 / math.pi)
	t_1 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= -2.2e-88:
		tmp = t_1
	elif B <= -2.05e-184:
		tmp = t_0
	elif B <= 9e-274:
		tmp = t_1
	elif B <= 1.45e-140:
		tmp = t_0
	else:
		tmp = 180.0 / (math.pi / math.atan(((C / B) + (-1.0 - (A / B)))))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) * Float64(180.0 / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= -2.2e-88)
		tmp = t_1;
	elseif (B <= -2.05e-184)
		tmp = t_0;
	elseif (B <= 9e-274)
		tmp = t_1;
	elseif (B <= 1.45e-140)
		tmp = t_0;
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan((-0.5 * (B / (C - A)))) * (180.0 / pi);
	t_1 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= -2.2e-88)
		tmp = t_1;
	elseif (B <= -2.05e-184)
		tmp = t_0;
	elseif (B <= 9e-274)
		tmp = t_1;
	elseif (B <= 1.45e-140)
		tmp = t_0;
	else
		tmp = 180.0 / (pi / atan(((C / B) + (-1.0 - (A / B)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.2e-88], t$95$1, If[LessEqual[B, -2.05e-184], t$95$0, If[LessEqual[B, 9e-274], t$95$1, If[LessEqual[B, 1.45e-140], t$95$0, N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.20000000000000005e-88 or -2.05e-184 < B < 8.99999999999999982e-274

   1. Initial program 69.0%

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

   3. Taylor expanded in B around -inf 79.7%

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

      1. associate--l+ 79.7%

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

      2. div-sub 79.7%

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

   5. Simplified 79.7%

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

   if -2.20000000000000005e-88 < B < -2.05e-184 or 8.99999999999999982e-274 < B < 1.44999999999999999e-140

   1. Initial program 40.3%

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

   3. Simplified 49.9%

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

   5. Taylor expanded in B around 0 69.6%

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

   if 1.44999999999999999e-140 < B

   1. Initial program 58.8%

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

      1. clear-num 58.8%

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

      2. un-div-inv 58.8%

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

      3. associate-*l/ 58.8%

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

      4. *-un-lft-identity 58.8%

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

      5. unpow2 58.8%

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

      6. unpow2 58.8%

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

      7. hypot-define 76.6%

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

   4. Applied egg-rr 76.6%

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

   5. Taylor expanded in B around inf 73.8%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.2 \cdot 10^{-88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.05 \cdot 10^{-184}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-274}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-140}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.8 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq -1.92 \cdot 10^{-184}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.18 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-141}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (atan (* -0.5 (/ B (- C A)))) (/ 180.0 PI)))
        (t_1 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B -2.8e-87)
     t_1
     (if (<= B -1.92e-184)
       t_0
       (if (<= B 1.18e-273)
         t_1
         (if (<= B 9.5e-141)
           t_0
           (* 180.0 (/ (atan (+ (/ C B) (- -1.0 (/ A B)))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan((-0.5 * (B / (C - A)))) * (180.0 / ((double) M_PI));
	double t_1 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (B <= -2.8e-87) {
		tmp = t_1;
	} else if (B <= -1.92e-184) {
		tmp = t_0;
	} else if (B <= 1.18e-273) {
		tmp = t_1;
	} else if (B <= 9.5e-141) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan((-0.5 * (B / (C - A)))) * (180.0 / Math.PI);
	double t_1 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= -2.8e-87) {
		tmp = t_1;
	} else if (B <= -1.92e-184) {
		tmp = t_0;
	} else if (B <= 1.18e-273) {
		tmp = t_1;
	} else if (B <= 9.5e-141) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((C / B) + (-1.0 - (A / B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan((-0.5 * (B / (C - A)))) * (180.0 / math.pi)
	t_1 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= -2.8e-87:
		tmp = t_1
	elif B <= -1.92e-184:
		tmp = t_0
	elif B <= 1.18e-273:
		tmp = t_1
	elif B <= 9.5e-141:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((C / B) + (-1.0 - (A / B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) * Float64(180.0 / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= -2.8e-87)
		tmp = t_1;
	elseif (B <= -1.92e-184)
		tmp = t_0;
	elseif (B <= 1.18e-273)
		tmp = t_1;
	elseif (B <= 9.5e-141)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan((-0.5 * (B / (C - A)))) * (180.0 / pi);
	t_1 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= -2.8e-87)
		tmp = t_1;
	elseif (B <= -1.92e-184)
		tmp = t_0;
	elseif (B <= 1.18e-273)
		tmp = t_1;
	elseif (B <= 9.5e-141)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.8e-87], t$95$1, If[LessEqual[B, -1.92e-184], t$95$0, If[LessEqual[B, 1.18e-273], t$95$1, If[LessEqual[B, 9.5e-141], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.8000000000000001e-87 or -1.9200000000000001e-184 < B < 1.17999999999999991e-273

   1. Initial program 69.0%

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

   3. Taylor expanded in B around -inf 79.7%

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

      1. associate--l+ 79.7%

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

      2. div-sub 79.7%

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

   5. Simplified 79.7%

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

   if -2.8000000000000001e-87 < B < -1.9200000000000001e-184 or 1.17999999999999991e-273 < B < 9.49999999999999996e-141

   1. Initial program 40.3%

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

   3. Simplified 49.9%

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

   5. Taylor expanded in B around 0 69.6%

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

   if 9.49999999999999996e-141 < B

   1. Initial program 58.8%

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

   3. Taylor expanded in B around inf 73.8%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.8 \cdot 10^{-87}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.92 \cdot 10^{-184}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 1.18 \cdot 10^{-273}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-141}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.6 \cdot 10^{-37}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.35 \cdot 10^{-236}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.04 \cdot 10^{-193}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4700:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))
   (if (<= B -2.6e-37)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -2.35e-236)
       t_0
       (if (<= B 1.04e-193)
         (* 180.0 (/ (atan (/ 0.0 B)) PI))
         (if (<= B 4700.0) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	double tmp;
	if (B <= -2.6e-37) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2.35e-236) {
		tmp = t_0;
	} else if (B <= 1.04e-193) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 4700.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	double tmp;
	if (B <= -2.6e-37) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2.35e-236) {
		tmp = t_0;
	} else if (B <= 1.04e-193) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 4700.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	tmp = 0
	if B <= -2.6e-37:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2.35e-236:
		tmp = t_0
	elif B <= 1.04e-193:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 4700.0:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi))
	tmp = 0.0
	if (B <= -2.6e-37)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2.35e-236)
		tmp = t_0;
	elseif (B <= 1.04e-193)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 4700.0)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((-0.5 * (B / C))) / pi);
	tmp = 0.0;
	if (B <= -2.6e-37)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2.35e-236)
		tmp = t_0;
	elseif (B <= 1.04e-193)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 4700.0)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.6e-37], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.35e-236], t$95$0, If[LessEqual[B, 1.04e-193], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4700.0], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.5999999999999998e-37

   1. Initial program 61.9%

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

   3. Taylor expanded in B around -inf 66.2%

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

   if -2.5999999999999998e-37 < B < -2.35000000000000013e-236 or 1.04000000000000001e-193 < B < 4700

   1. Initial program 50.5%

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

   3. Taylor expanded in C around inf 40.1%

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

      1. +-commutative 40.1%

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

      2. associate-*r/ 40.1%

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

      3. mul-1-neg 40.1%

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

      4. distribute-rgt1-in 40.1%

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

      5. metadata-eval 40.1%

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

      6. mul0-lft 40.1%

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

      7. metadata-eval 40.1%

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

   5. Simplified 40.1%

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

   6. Taylor expanded in B around 0 40.1%

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

   if -2.35000000000000013e-236 < B < 1.04000000000000001e-193

   1. Initial program 72.2%

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

   3. Taylor expanded in C around inf 40.0%

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

      1. associate-*r/ 40.0%

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

      2. mul-1-neg 40.0%

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

      3. distribute-rgt1-in 40.0%

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

      4. metadata-eval 40.0%

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

      5. mul0-lft 40.0%

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

      6. metadata-eval 40.0%

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

   5. Simplified 40.0%

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

   if 4700 < B

   1. Initial program 59.0%

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

   3. Taylor expanded in B around inf 58.8%

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

Alternative 13: 59.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.75 \cdot 10^{-32}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - B}{B}\right)}}\\ \mathbf{elif}\;C \leq 1.15 \cdot 10^{+31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.75e-32)
   (/ 180.0 (/ PI (atan (/ (- C B) B))))
   (if (<= C 1.15e+31)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (/ 180.0 (/ PI (atan (* -0.5 (/ B C))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.75e-32) {
		tmp = 180.0 / (((double) M_PI) / atan(((C - B) / B)));
	} else if (C <= 1.15e+31) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((-0.5 * (B / C))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.75e-32) {
		tmp = 180.0 / (Math.PI / Math.atan(((C - B) / B)));
	} else if (C <= 1.15e+31) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((-0.5 * (B / C))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.75e-32:
		tmp = 180.0 / (math.pi / math.atan(((C - B) / B)))
	elif C <= 1.15e+31:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((-0.5 * (B / C))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.75e-32)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - B) / B))));
	elseif (C <= 1.15e+31)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-0.5 * Float64(B / C)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.75e-32)
		tmp = 180.0 / (pi / atan(((C - B) / B)));
	elseif (C <= 1.15e+31)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 / (pi / atan((-0.5 * (B / C))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.75e-32], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.15e+31], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.7499999999999999e-32

   1. Initial program 80.3%

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

      1. clear-num 80.3%

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

      2. un-div-inv 80.4%

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

      3. associate-*l/ 80.4%

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

      4. *-un-lft-identity 80.4%

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

      5. unpow2 80.4%

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

      6. unpow2 80.4%

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

      7. hypot-define 92.3%

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

   4. Applied egg-rr 92.3%

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

   5. Taylor expanded in A around 0 80.4%

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

      1. unpow2 80.4%

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

      2. unpow2 80.4%

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

      3. hypot-define 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in C around 0 79.8%

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

   if -1.7499999999999999e-32 < C < 1.15e31

   1. Initial program 63.2%

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

   3. Taylor expanded in C around 0 59.2%

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

      1. associate-*r/ 59.2%

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

      2. mul-1-neg 59.2%

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

      3. +-commutative 59.2%

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

      4. unpow2 59.2%

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

      5. unpow2 59.2%

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

      6. hypot-define 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in B around -inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. unsub-neg 51.1%

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

   8. Simplified 51.1%

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

   if 1.15e31 < C

   1. Initial program 24.7%

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

      1. clear-num 24.7%

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

      2. un-div-inv 24.7%

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

      3. associate-*l/ 24.7%

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

      4. *-un-lft-identity 24.7%

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

      5. unpow2 24.7%

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

      6. unpow2 24.7%

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

      7. hypot-define 59.4%

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

   4. Applied egg-rr 59.4%

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

   5. Taylor expanded in A around 0 23.3%

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

      1. unpow2 23.3%

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

      2. unpow2 23.3%

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

      3. hypot-define 52.0%

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

   7. Simplified 52.0%

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

   8. Taylor expanded in C around inf 70.9%

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

Alternative 14: 59.1% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -2.3 \cdot 10^{-165}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(1 + \frac{C}{B}\right)}}\\ \mathbf{elif}\;C \leq 1.2 \cdot 10^{+31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -2.3e-165)
   (/ 180.0 (/ PI (atan (+ 1.0 (/ C B)))))
   (if (<= C 1.2e+31)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (/ 180.0 (/ PI (atan (* -0.5 (/ B C))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.3e-165) {
		tmp = 180.0 / (((double) M_PI) / atan((1.0 + (C / B))));
	} else if (C <= 1.2e+31) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((-0.5 * (B / C))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.3e-165) {
		tmp = 180.0 / (Math.PI / Math.atan((1.0 + (C / B))));
	} else if (C <= 1.2e+31) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((-0.5 * (B / C))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -2.3e-165:
		tmp = 180.0 / (math.pi / math.atan((1.0 + (C / B))))
	elif C <= 1.2e+31:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((-0.5 * (B / C))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -2.3e-165)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(1.0 + Float64(C / B)))));
	elseif (C <= 1.2e+31)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-0.5 * Float64(B / C)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -2.3e-165)
		tmp = 180.0 / (pi / atan((1.0 + (C / B))));
	elseif (C <= 1.2e+31)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 / (pi / atan((-0.5 * (B / C))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -2.3e-165], N[(180.0 / N[(Pi / N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.2e+31], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -2.3e-165

   1. Initial program 78.4%

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

      1. clear-num 78.4%

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

      2. un-div-inv 78.5%

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

      3. associate-*l/ 78.5%

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

      4. *-un-lft-identity 78.5%

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

      5. unpow2 78.5%

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

      6. unpow2 78.5%

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

      7. hypot-define 91.2%

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

   4. Applied egg-rr 91.2%

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

   5. Taylor expanded in B around -inf 74.5%

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

      1. associate--l+ 74.5%

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

      2. div-sub 74.5%

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

   7. Simplified 74.5%

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

   8. Taylor expanded in C around inf 70.7%

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

   if -2.3e-165 < C < 1.19999999999999991e31

   1. Initial program 61.1%

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

   3. Taylor expanded in C around 0 60.1%

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

      1. associate-*r/ 60.1%

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

      2. mul-1-neg 60.1%

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

      3. +-commutative 60.1%

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

      4. unpow2 60.1%

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

      5. unpow2 60.1%

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

      6. hypot-define 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in B around -inf 51.5%

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

      1. mul-1-neg 51.5%

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

      2. unsub-neg 51.5%

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

   8. Simplified 51.5%

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

   if 1.19999999999999991e31 < C

   1. Initial program 24.7%

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

      1. clear-num 24.7%

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

      2. un-div-inv 24.7%

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

      3. associate-*l/ 24.7%

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

      4. *-un-lft-identity 24.7%

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

      5. unpow2 24.7%

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

      6. unpow2 24.7%

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

      7. hypot-define 59.4%

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

   4. Applied egg-rr 59.4%

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

   5. Taylor expanded in A around 0 23.3%

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

      1. unpow2 23.3%

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

      2. unpow2 23.3%

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

      3. hypot-define 52.0%

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

   7. Simplified 52.0%

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

   8. Taylor expanded in C around inf 70.9%

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

Alternative 15: 56.8% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.5 \cdot 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 7.5 \cdot 10^{+31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.5e+80)
   (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
   (if (<= C 7.5e+31)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (/ 180.0 (/ PI (atan (* -0.5 (/ B C))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.5e+80) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= 7.5e+31) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((-0.5 * (B / C))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.5e+80) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= 7.5e+31) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((-0.5 * (B / C))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.5e+80:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= 7.5e+31:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((-0.5 * (B / C))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.5e+80)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= 7.5e+31)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-0.5 * Float64(B / C)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.5e+80)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= 7.5e+31)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 / (pi / atan((-0.5 * (B / C))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.5e+80], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 7.5e+31], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.49999999999999993e80

   1. Initial program 86.0%

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

   3. Taylor expanded in C around -inf 81.6%

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

   if -1.49999999999999993e80 < C < 7.5e31

   1. Initial program 63.8%

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

   3. Taylor expanded in C around 0 58.8%

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

      1. associate-*r/ 58.8%

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

      2. mul-1-neg 58.8%

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

      3. +-commutative 58.8%

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

      4. unpow2 58.8%

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

      5. unpow2 58.8%

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

      6. hypot-define 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in B around -inf 50.7%

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

      1. mul-1-neg 50.7%

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

      2. unsub-neg 50.7%

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

   8. Simplified 50.7%

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

   if 7.5e31 < C

   1. Initial program 24.7%

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

      1. clear-num 24.7%

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

      2. un-div-inv 24.7%

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

      3. associate-*l/ 24.7%

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

      4. *-un-lft-identity 24.7%

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

      5. unpow2 24.7%

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

      6. unpow2 24.7%

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

      7. hypot-define 59.4%

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

   4. Applied egg-rr 59.4%

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

   5. Taylor expanded in A around 0 23.3%

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

      1. unpow2 23.3%

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

      2. unpow2 23.3%

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

      3. hypot-define 52.0%

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

   7. Simplified 52.0%

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

   8. Taylor expanded in C around inf 70.9%

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

Alternative 16: 57.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.2 \cdot 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.75 \cdot 10^{+31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.2e+80)
   (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
   (if (<= C 1.75e+31)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.2e+80) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= 1.75e+31) {
		tmp = 180.0 * (atan((1.0 - (A / 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 tmp;
	if (C <= -1.2e+80) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= 1.75e+31) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.2e+80:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= 1.75e+31:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.2e+80)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= 1.75e+31)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.2e+80)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= 1.75e+31)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.2e+80], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.75e+31], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.1999999999999999e80

   1. Initial program 86.0%

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

   3. Taylor expanded in C around -inf 81.6%

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

   if -1.1999999999999999e80 < C < 1.75e31

   1. Initial program 63.8%

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

   3. Taylor expanded in C around 0 58.8%

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

      1. associate-*r/ 58.8%

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

      2. mul-1-neg 58.8%

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

      3. +-commutative 58.8%

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

      4. unpow2 58.8%

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

      5. unpow2 58.8%

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

      6. hypot-define 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in B around -inf 50.7%

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

      1. mul-1-neg 50.7%

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

      2. unsub-neg 50.7%

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

   8. Simplified 50.7%

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

   if 1.75e31 < C

   1. Initial program 24.7%

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

   3. Taylor expanded in C around inf 70.8%

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

      1. +-commutative 70.8%

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

      2. associate-*r/ 70.8%

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

      3. mul-1-neg 70.8%

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

      4. distribute-rgt1-in 70.8%

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

      5. metadata-eval 70.8%

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

      6. mul0-lft 70.8%

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

      7. metadata-eval 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in B around 0 70.8%

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

Alternative 17: 48.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -7 \cdot 10^{-153}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 7.8 \cdot 10^{-207}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -7e-153)
   (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
   (if (<= C 7.8e-207)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -7e-153) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= 7.8e-207) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((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 tmp;
	if (C <= -7e-153) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= 7.8e-207) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -7e-153:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= 7.8e-207:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -7e-153)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= 7.8e-207)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -7e-153)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= 7.8e-207)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -7e-153], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 7.8e-207], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -6.99999999999999961e-153

   1. Initial program 79.8%

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

   3. Taylor expanded in C around -inf 62.3%

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

   if -6.99999999999999961e-153 < C < 7.80000000000000042e-207

   1. Initial program 55.6%

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

   3. Taylor expanded in A around -inf 37.7%

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

   if 7.80000000000000042e-207 < C

   1. Initial program 42.6%

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

   3. Taylor expanded in C around inf 57.1%

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

      1. +-commutative 57.1%

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

      2. associate-*r/ 57.1%

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

      3. mul-1-neg 57.1%

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

      4. distribute-rgt1-in 57.1%

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

      5. metadata-eval 57.1%

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

      6. mul0-lft 57.1%

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

      7. metadata-eval 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in B around 0 57.1%

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

Alternative 18: 45.3% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -9 \cdot 10^{-84}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-189}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -9e-84)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.8e-189)
     (* 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 <= -9e-84) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.8e-189) {
		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 <= -9e-84) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.8e-189) {
		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 <= -9e-84:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.8e-189:
		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 <= -9e-84)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.8e-189)
		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 <= -9e-84)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.8e-189)
		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, -9e-84], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.8e-189], 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 < -9.00000000000000031e-84

   1. Initial program 63.2%

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

   3. Taylor expanded in B around -inf 61.3%

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

   if -9.00000000000000031e-84 < B < 1.80000000000000008e-189

   1. Initial program 58.1%

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

   3. Taylor expanded in C around inf 34.3%

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

      1. associate-*r/ 34.3%

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

      2. mul-1-neg 34.3%

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

      3. distribute-rgt1-in 34.3%

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

      4. metadata-eval 34.3%

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

      5. mul0-lft 34.3%

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

      6. metadata-eval 34.3%

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

   5. Simplified 34.3%

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

   if 1.80000000000000008e-189 < B

   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. Add Preprocessing

   3. Taylor expanded in B around inf 43.4%

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

Alternative 19: 60.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 1.6 \cdot 10^{+31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 1.6e+31)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (/ 180.0 (/ PI (atan (* -0.5 (/ B C)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.6e+31) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((-0.5 * (B / C))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.6e+31) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((-0.5 * (B / C))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 1.6e+31:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((-0.5 * (B / C))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 1.6e+31)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-0.5 * Float64(B / C)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 1.6e+31)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	else
		tmp = 180.0 / (pi / atan((-0.5 * (B / C))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 1.6e+31], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 1.6e31

   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. Add Preprocessing

   3. Taylor expanded in B around -inf 62.7%

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

      1. associate--l+ 62.7%

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

      2. div-sub 62.7%

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

   5. Simplified 62.7%

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

   if 1.6e31 < C

   1. Initial program 24.7%

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

      1. clear-num 24.7%

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

      2. un-div-inv 24.7%

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

      3. associate-*l/ 24.7%

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

      4. *-un-lft-identity 24.7%

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

      5. unpow2 24.7%

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

      6. unpow2 24.7%

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

      7. hypot-define 59.4%

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

   4. Applied egg-rr 59.4%

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

   5. Taylor expanded in A around 0 23.3%

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

      1. unpow2 23.3%

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

      2. unpow2 23.3%

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

      3. hypot-define 52.0%

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

   7. Simplified 52.0%

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

   8. Taylor expanded in C around inf 70.9%

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

Alternative 20: 40.7% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-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 <= -5e-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 <= -5e-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 <= -5e-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 <= -5e-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 <= -5e-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, -5e-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 < -4.999999999999985e-310

   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. Add Preprocessing

   3. Taylor expanded in B around -inf 39.5%

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

   if -4.999999999999985e-310 < B

   1. Initial program 58.8%

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

   3. Taylor expanded in B around inf 36.0%

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

Alternative 21: 20.7% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.1%

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

3. Taylor expanded in B around inf 18.7%

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

Reproduce

herbie shell --seed 2024096 
(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)))