ABCF->ab-angle angle

Percentage Accurate: 54.1% → 82.6%

Time: 27.3s

Alternatives: 26

Speedup: 3.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-35} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (or (<= t_0 -2e-35) (not (<= t_0 0.0)))
     (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))
     (* (/ 180.0 PI) (atan (* B (/ 0.5 A)))))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -2e-35) || !(t_0 <= 0.0)) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / A)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -2e-35) || !(t_0 <= 0.0)) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / A)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if (t_0 <= -2e-35) or not (t_0 <= 0.0):
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / A)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if ((t_0 <= -2e-35) || !(t_0 <= 0.0))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / A))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if ((t_0 <= -2e-35) || ~((t_0 <= 0.0)))
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	else
		tmp = (180.0 / pi) * atan((B * (0.5 / A)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-35], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -2.00000000000000002e-35 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 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. Step-by-step derivation

      1. associate-*l/ 62.0%

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

      2. *-lft-identity 62.0%

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

      3. +-commutative 62.0%

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

      4. unpow2 62.0%

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

      5. unpow2 62.0%

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

      6. hypot-define 90.5%

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

   3. Simplified 90.5%

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

   if -2.00000000000000002e-35 < (*.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 20.6%

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

   3. Taylor expanded in B around 0 7.0%

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

   5. Simplified 7.0%

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

   6. Taylor expanded in A around -inf 46.0%

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

   7. Taylor expanded in B around 0 54.7%

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

      1. associate-*r/ 54.8%

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

      2. *-rgt-identity 54.8%

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

      3. times-frac 54.8%

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

      4. /-rgt-identity 54.8%

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

   9. Simplified 54.8%

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

       1. *-un-lft-identity 54.8%

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

   11. Applied egg-rr 54.8%

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

       1. *-lft-identity 54.8%

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

       2. metadata-eval 54.8%

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

       3. times-frac 54.8%

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

       4. *-commutative 54.8%

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

       5. times-frac 54.8%

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

       6. /-rgt-identity 54.8%

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

   13. Simplified 54.8%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -2 \cdot 10^{-35} \lor \neg \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := A + \mathsf{hypot}\left(B, A\right)\\ \mathbf{if}\;C \leq -1.25 \cdot 10^{-117}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - t\_0}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.6 \cdot 10^{+151}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{t\_0}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (+ A (hypot B A))))
   (if (<= C -1.25e-117)
     (* 180.0 (/ (atan (/ (- C t_0) B)) PI))
     (if (<= C 6.6e+151)
       (* 180.0 (/ (atan (/ t_0 (- B))) PI))
       (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))))))

C

double code(double A, double B, double C) {
	double t_0 = A + hypot(B, A);
	double tmp;
	if (C <= -1.25e-117) {
		tmp = 180.0 * (atan(((C - t_0) / B)) / ((double) M_PI));
	} else if (C <= 6.6e+151) {
		tmp = 180.0 * (atan((t_0 / -B)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = A + Math.hypot(B, A);
	double tmp;
	if (C <= -1.25e-117) {
		tmp = 180.0 * (Math.atan(((C - t_0) / B)) / Math.PI);
	} else if (C <= 6.6e+151) {
		tmp = 180.0 * (Math.atan((t_0 / -B)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = A + math.hypot(B, A)
	tmp = 0
	if C <= -1.25e-117:
		tmp = 180.0 * (math.atan(((C - t_0) / B)) / math.pi)
	elif C <= 6.6e+151:
		tmp = 180.0 * (math.atan((t_0 / -B)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(A + hypot(B, A))
	tmp = 0.0
	if (C <= -1.25e-117)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - t_0) / B)) / pi));
	elseif (C <= 6.6e+151)
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 / Float64(-B))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = A + hypot(B, A);
	tmp = 0.0;
	if (C <= -1.25e-117)
		tmp = 180.0 * (atan(((C - t_0) / B)) / pi);
	elseif (C <= 6.6e+151)
		tmp = 180.0 * (atan((t_0 / -B)) / pi);
	else
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.25e-117], N[(180.0 * N[(N[ArcTan[N[(N[(C - t$95$0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.6e+151], N[(180.0 * N[(N[ArcTan[N[(t$95$0 / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.25e-117

   1. Initial program 78.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in C around 0 74.4%

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

      1. +-commutative 74.4%

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

      2. unpow2 74.4%

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

      3. unpow2 74.4%

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

      4. hypot-define 87.9%

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

   7. Simplified 87.9%

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

   if -1.25e-117 < C < 6.60000000000000049e151

   1. Initial program 51.7%

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

   3. Taylor expanded in C around 0 49.0%

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

      1. mul-1-neg 49.0%

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

      2. distribute-neg-frac2 49.0%

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

      3. +-commutative 49.0%

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

      4. unpow2 49.0%

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

      5. unpow2 49.0%

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

      6. hypot-define 73.5%

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

   5. Simplified 73.5%

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

   if 6.60000000000000049e151 < C

   1. Initial program 9.2%

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

   4. Applied egg-rr 67.5%

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

   5. Taylor expanded in C around inf 83.9%

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

      1. metadata-eval 83.9%

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

      2. cancel-sign-sub-inv 83.9%

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

      3. distribute-rgt1-in 83.9%

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

      4. metadata-eval 83.9%

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

      5. mul0-lft 83.9%

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

      6. div0 83.9%

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

      7. metadata-eval 83.9%

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

      8. neg-sub0 83.9%

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

      9. distribute-lft-neg-in 83.9%

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

      10. metadata-eval 83.9%

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

   7. Simplified 83.9%

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

   8. Taylor expanded in B around 0 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-*r/ 85.9%

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

      3. associate-*l/ 86.1%

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

      4. associate-/l* 86.2%

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

      5. associate-*r/ 86.2%

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

      6. *-commutative 86.2%

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

      7. associate-*l/ 86.2%

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

      8. associate-*r/ 86.2%

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

   10. Simplified 86.2%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.25 \cdot 10^{-117}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.6 \cdot 10^{+151}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.5 \cdot 10^{+233}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 4 \cdot 10^{-151}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.5e+233)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (if (<= A 4e-151)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (/ (+ A (hypot B A)) (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.5e+233) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (A <= 4e-151) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} 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 <= -2.5e+233) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (A <= 4e-151) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} 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 <= -2.5e+233:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif A <= 4e-151:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	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 <= -2.5e+233)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (A <= 4e-151)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	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 <= -2.5e+233)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (A <= 4e-151)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.5e+233], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4e-151], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $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 < -2.50000000000000004e233

   1. Initial program 6.5%

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

   3. Taylor expanded in B around 0 6.5%

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

   5. Simplified 11.8%

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

   6. Taylor expanded in A around -inf 47.7%

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

   7. Taylor expanded in B around 0 92.5%

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

      1. associate-*r/ 92.6%

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

      2. *-rgt-identity 92.6%

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

      3. times-frac 92.8%

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

      4. /-rgt-identity 92.8%

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

   9. Simplified 92.8%

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

   if -2.50000000000000004e233 < A < 3.9999999999999998e-151

   1. Initial program 48.1%

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

   3. Taylor expanded in A around 0 44.9%

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

      1. unpow2 44.9%

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

      2. unpow2 44.9%

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

      3. hypot-define 74.7%

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

   5. Simplified 74.7%

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

   if 3.9999999999999998e-151 < A

   1. Initial program 71.4%

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

   3. Taylor expanded in C around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. distribute-neg-frac2 67.9%

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

      3. +-commutative 67.9%

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

      4. unpow2 67.9%

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

      5. unpow2 67.9%

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

      6. hypot-define 81.8%

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

   5. Simplified 81.8%

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

Alternative 4: 73.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.5 \cdot 10^{+233}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.5e+233)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (if (<= A 1.05e-39)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* (/ 180.0 PI) (atan (/ (- C (+ B A)) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.5e+233) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (A <= 1.05e-39) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (B + A)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.5e+233) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (A <= 1.05e-39) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (B + A)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.5e+233:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif A <= 1.05e-39:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (B + A)) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.5e+233)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (A <= 1.05e-39)
		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 + A)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.5e+233)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (A <= 1.05e-39)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = (180.0 / pi) * atan(((C - (B + A)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.5e+233], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.05e-39], 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 + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.50000000000000004e233

   1. Initial program 6.5%

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

   3. Taylor expanded in B around 0 6.5%

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

   5. Simplified 11.8%

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

   6. Taylor expanded in A around -inf 47.7%

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

   7. Taylor expanded in B around 0 92.5%

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

      1. associate-*r/ 92.6%

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

      2. *-rgt-identity 92.6%

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

      3. times-frac 92.8%

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

      4. /-rgt-identity 92.8%

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

   9. Simplified 92.8%

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

   if -2.50000000000000004e233 < A < 1.04999999999999997e-39

   1. Initial program 48.8%

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

   3. Taylor expanded in A around 0 44.5%

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

      1. unpow2 44.5%

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

      2. unpow2 44.5%

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

      3. hypot-define 74.1%

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

   5. Simplified 74.1%

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

   if 1.04999999999999997e-39 < A

   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. Step-by-step derivation

   3. Simplified 91.7%

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

   5. Taylor expanded in C around 0 77.5%

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

      1. +-commutative 77.5%

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

      2. unpow2 77.5%

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

      3. unpow2 77.5%

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

      4. hypot-define 88.3%

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

   7. Simplified 88.3%

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

      1. associate-*r/ 88.3%

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

   9. Applied egg-rr 88.3%

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

   10. Taylor expanded in A around 0 80.6%

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

   11. Taylor expanded in C around -inf 80.6%

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

       1. associate-*r/ 80.6%

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

       2. *-commutative 80.6%

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

       3. associate-/l* 80.6%

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

       4. mul-1-neg 80.6%

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

       5. distribute-neg-frac2 80.6%

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

       6. associate-+r+ 80.6%

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

       7. mul-1-neg 80.6%

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

       8. unsub-neg 80.6%

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

   13. Simplified 80.6%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.5 \cdot 10^{+233}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.5 \cdot 10^{+233}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.5e+233)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.5e+233) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.5e+233) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.5e+233:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.5e+233)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.5e+233)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.5e+233], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -2.50000000000000004e233

   1. Initial program 6.5%

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

   3. Taylor expanded in B around 0 6.5%

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

   5. Simplified 11.8%

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

   6. Taylor expanded in A around -inf 47.7%

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

   7. Taylor expanded in B around 0 92.5%

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

      1. associate-*r/ 92.6%

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

      2. *-rgt-identity 92.6%

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

      3. times-frac 92.8%

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

      4. /-rgt-identity 92.8%

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

   9. Simplified 92.8%

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

   if -2.50000000000000004e233 < A

   1. Initial program 58.6%

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

   3. Simplified 80.8%

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

Alternative 6: 47.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{if}\;C \leq -2.1 \cdot 10^{-115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.5 \cdot 10^{-212}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{-77}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;C \leq 17000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;C \leq 2.4 \cdot 10^{+29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 3.9 \cdot 10^{+99} \lor \neg \left(C \leq 2.1 \cdot 10^{+100}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan -1.0) PI)))
        (t_1 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))
   (if (<= C -2.1e-115)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= C 1.5e-212)
       t_0
       (if (<= C 3.5e-77)
         (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
         (if (<= C 17000000000.0)
           t_1
           (if (<= C 2.4e+29)
             (* 180.0 (/ (atan 1.0) PI))
             (if (or (<= C 3.9e+99) (not (<= C 2.1e+100))) t_1 t_0))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(-1.0) / ((double) M_PI));
	double t_1 = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	double tmp;
	if (C <= -2.1e-115) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= 1.5e-212) {
		tmp = t_0;
	} else if (C <= 3.5e-77) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (C <= 17000000000.0) {
		tmp = t_1;
	} else if (C <= 2.4e+29) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if ((C <= 3.9e+99) || !(C <= 2.1e+100)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(-1.0) / Math.PI);
	double t_1 = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	double tmp;
	if (C <= -2.1e-115) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= 1.5e-212) {
		tmp = t_0;
	} else if (C <= 3.5e-77) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (C <= 17000000000.0) {
		tmp = t_1;
	} else if (C <= 2.4e+29) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if ((C <= 3.9e+99) || !(C <= 2.1e+100)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(-1.0) / math.pi)
	t_1 = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	tmp = 0
	if C <= -2.1e-115:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= 1.5e-212:
		tmp = t_0
	elif C <= 3.5e-77:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif C <= 17000000000.0:
		tmp = t_1
	elif C <= 2.4e+29:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif (C <= 3.9e+99) or not (C <= 2.1e+100):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(-1.0) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi))
	tmp = 0.0
	if (C <= -2.1e-115)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= 1.5e-212)
		tmp = t_0;
	elseif (C <= 3.5e-77)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (C <= 17000000000.0)
		tmp = t_1;
	elseif (C <= 2.4e+29)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif ((C <= 3.9e+99) || !(C <= 2.1e+100))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(-1.0) / pi);
	t_1 = 180.0 * (atan((-0.5 * (B / C))) / pi);
	tmp = 0.0;
	if (C <= -2.1e-115)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= 1.5e-212)
		tmp = t_0;
	elseif (C <= 3.5e-77)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (C <= 17000000000.0)
		tmp = t_1;
	elseif (C <= 2.4e+29)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif ((C <= 3.9e+99) || ~((C <= 2.1e+100)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -2.1e-115], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.5e-212], t$95$0, If[LessEqual[C, 3.5e-77], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 17000000000.0], t$95$1, If[LessEqual[C, 2.4e+29], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[C, 3.9e+99], N[Not[LessEqual[C, 2.1e+100]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -2.10000000000000002e-115

   1. Initial program 78.7%

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

   3. Taylor expanded in C around -inf 64.4%

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

   if -2.10000000000000002e-115 < C < 1.5000000000000001e-212 or 3.89999999999999995e99 < C < 2.0999999999999999e100

   1. Initial program 54.6%

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

   3. Taylor expanded in B around inf 37.1%

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

   if 1.5000000000000001e-212 < C < 3.50000000000000013e-77

   1. Initial program 68.0%

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

   3. Taylor expanded in A around inf 42.9%

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

   if 3.50000000000000013e-77 < C < 1.7e10 or 2.4000000000000001e29 < C < 3.89999999999999995e99 or 2.0999999999999999e100 < C

   1. Initial program 23.0%

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

   3. Taylor expanded in C around inf 62.9%

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

   4. Taylor expanded in A around inf 62.9%

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

   if 1.7e10 < C < 2.4000000000000001e29

   1. Initial program 72.9%

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

   3. Taylor expanded in B around -inf 53.6%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.1 \cdot 10^{-115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.5 \cdot 10^{-212}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{-77}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;C \leq 17000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.4 \cdot 10^{+29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 3.9 \cdot 10^{+99} \lor \neg \left(C \leq 2.1 \cdot 10^{+100}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -4.7 \cdot 10^{-15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.2 \cdot 10^{-255}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.35 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{+35}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.1 \cdot 10^{+115} \lor \neg \left(C \leq 6.2 \cdot 10^{+115}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -4.7e-15)
   (* 180.0 (/ (atan (/ (- C B) B)) PI))
   (if (<= C 5.2e-255)
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
     (if (<= C 2.35e-216)
       (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
       (if (<= C 8.2e+35)
         (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
         (if (or (<= C 6.1e+115) (not (<= C 6.2e+115)))
           (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
           (/ (* -180.0 (atan (/ A B))) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.7e-15) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (C <= 5.2e-255) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else if (C <= 2.35e-216) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (C <= 8.2e+35) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if ((C <= 6.1e+115) || !(C <= 6.2e+115)) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = (-180.0 * atan((A / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.7e-15) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (C <= 5.2e-255) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else if (C <= 2.35e-216) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (C <= 8.2e+35) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if ((C <= 6.1e+115) || !(C <= 6.2e+115)) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = (-180.0 * Math.atan((A / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -4.7e-15:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif C <= 5.2e-255:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	elif C <= 2.35e-216:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif C <= 8.2e+35:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif (C <= 6.1e+115) or not (C <= 6.2e+115):
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = (-180.0 * math.atan((A / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -4.7e-15)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (C <= 5.2e-255)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	elseif (C <= 2.35e-216)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (C <= 8.2e+35)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif ((C <= 6.1e+115) || !(C <= 6.2e+115))
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(A / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -4.7e-15)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (C <= 5.2e-255)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	elseif (C <= 2.35e-216)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (C <= 8.2e+35)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif ((C <= 6.1e+115) || ~((C <= 6.2e+115)))
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = (-180.0 * atan((A / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -4.7e-15], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 5.2e-255], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.35e-216], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 8.2e+35], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[C, 6.1e+115], N[Not[LessEqual[C, 6.2e+115]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(-180.0 * N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if C < -4.6999999999999999e-15

   1. Initial program 82.9%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in C around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. unpow2 80.1%

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

      3. unpow2 80.1%

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

      4. hypot-define 93.7%

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

   7. Simplified 93.7%

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

   8. Taylor expanded in A around 0 86.1%

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

   if -4.6999999999999999e-15 < C < 5.20000000000000041e-255

   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. Taylor expanded in C around 0 53.4%

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

      1. mul-1-neg 53.4%

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

      2. distribute-neg-frac2 53.4%

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

      3. +-commutative 53.4%

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

      4. unpow2 53.4%

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

      5. unpow2 53.4%

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

      6. hypot-define 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in A around 0 56.5%

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

      1. sub-neg 56.5%

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

      2. metadata-eval 56.5%

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

      3. +-commutative 56.5%

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

      4. mul-1-neg 56.5%

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

      5. unsub-neg 56.5%

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

   8. Simplified 56.5%

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

   if 5.20000000000000041e-255 < C < 2.35e-216

   1. Initial program 37.9%

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

   3. Taylor expanded in A around -inf 67.0%

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

      1. associate-*r/ 67.0%

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

   5. Simplified 67.0%

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

   if 2.35e-216 < C < 8.1999999999999997e35

   1. Initial program 56.4%

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

   3. Taylor expanded in C around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. distribute-neg-frac2 56.4%

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

      3. +-commutative 56.4%

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

      4. unpow2 56.4%

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

      5. unpow2 56.4%

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

      6. hypot-define 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in B around -inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

   8. Simplified 64.4%

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

   if 8.1999999999999997e35 < C < 6.09999999999999966e115 or 6.2000000000000001e115 < C

   1. Initial program 19.9%

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

   3. Taylor expanded in C around inf 69.5%

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

   4. Taylor expanded in A around inf 69.5%

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

   if 6.09999999999999966e115 < C < 6.2000000000000001e115

   1. Initial program 100.0%

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

   3. Taylor expanded in B around inf 100.0%

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

   4. Taylor expanded in A around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

      1. associate-*r/ 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. atan-neg 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. distribute-rgt-neg-out 100.0%

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

      2. distribute-lft-neg-in 100.0%

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

      3. metadata-eval 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -4.7 \cdot 10^{-15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.2 \cdot 10^{-255}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.35 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{+35}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.1 \cdot 10^{+115} \lor \neg \left(C \leq 6.2 \cdot 10^{+115}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -5.6 \cdot 10^{-16}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{-255}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.3 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.22 \cdot 10^{+36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.1 \cdot 10^{+115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{+115}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -5.6e-16)
   (* (/ 180.0 PI) (atan (+ -1.0 (/ C B))))
   (if (<= C 4.6e-255)
     (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI)
     (if (<= C 2.3e-216)
       (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
       (if (<= C 1.22e+36)
         (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
         (if (<= C 6.1e+115)
           (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
           (if (<= C 6.2e+115)
             (/ (* -180.0 (atan (/ A B))) PI)
             (* (/ 180.0 PI) (atan (/ (* B -0.5) C))))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -5.6e-16) {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 + (C / B)));
	} else if (C <= 4.6e-255) {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	} else if (C <= 2.3e-216) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (C <= 1.22e+36) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (C <= 6.1e+115) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (C <= 6.2e+115) {
		tmp = (-180.0 * atan((A / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -5.6e-16) {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 + (C / B)));
	} else if (C <= 4.6e-255) {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	} else if (C <= 2.3e-216) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (C <= 1.22e+36) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (C <= 6.1e+115) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (C <= 6.2e+115) {
		tmp = (-180.0 * Math.atan((A / B))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -5.6e-16:
		tmp = (180.0 / math.pi) * math.atan((-1.0 + (C / B)))
	elif C <= 4.6e-255:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	elif C <= 2.3e-216:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif C <= 1.22e+36:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif C <= 6.1e+115:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif C <= 6.2e+115:
		tmp = (-180.0 * math.atan((A / B))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -5.6e-16)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 + Float64(C / B))));
	elseif (C <= 4.6e-255)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	elseif (C <= 2.3e-216)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (C <= 1.22e+36)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (C <= 6.1e+115)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (C <= 6.2e+115)
		tmp = Float64(Float64(-180.0 * atan(Float64(A / B))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -5.6e-16)
		tmp = (180.0 / pi) * atan((-1.0 + (C / B)));
	elseif (C <= 4.6e-255)
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	elseif (C <= 2.3e-216)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (C <= 1.22e+36)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (C <= 6.1e+115)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (C <= 6.2e+115)
		tmp = (-180.0 * atan((A / B))) / pi;
	else
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -5.6e-16], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.6e-255], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 2.3e-216], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.22e+36], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.1e+115], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.2e+115], N[(N[(-180.0 * N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if C < -5.6000000000000003e-16

   1. Initial program 82.9%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in C around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. unpow2 80.1%

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

      3. unpow2 80.1%

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

      4. hypot-define 93.7%

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

   7. Simplified 93.7%

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

   8. Taylor expanded in A around 0 86.1%

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

      1. associate-*r/ 86.1%

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

      2. div-sub 86.1%

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

      3. pow1 86.1%

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

      4. pow1 86.1%

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

      5. pow-div 86.1%

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

      6. metadata-eval 86.1%

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

      7. metadata-eval 86.1%

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

   10. Applied egg-rr 86.1%

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

       1. *-commutative 86.1%

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

       2. associate-/l* 86.2%

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

       3. sub-neg 86.2%

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

       4. metadata-eval 86.2%

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

       5. +-commutative 86.2%

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

   12. Simplified 86.2%

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

   if -5.6000000000000003e-16 < C < 4.5999999999999997e-255

   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. Step-by-step derivation

   3. Simplified 80.3%

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

   5. Taylor expanded in C around 0 59.2%

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

      1. +-commutative 59.2%

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

      2. unpow2 59.2%

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

      3. unpow2 59.2%

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

      4. hypot-define 78.7%

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

   7. Simplified 78.7%

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

      1. associate-*r/ 78.7%

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

   9. Applied egg-rr 78.7%

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

   10. Taylor expanded in A around 0 63.1%

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

   11. Taylor expanded in C around 0 56.5%

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

       1. associate-*r/ 56.5%

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

       2. distribute-lft-in 56.5%

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

       3. mul-1-neg 56.5%

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

       4. sub-neg 56.5%

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

       5. div-sub 56.5%

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

       6. associate-*r/ 56.5%

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

       7. *-inverses 56.5%

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

       8. sub-neg 56.5%

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

       9. mul-1-neg 56.5%

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

       10. distribute-neg-in 56.5%

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

       11. +-commutative 56.5%

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

       12. distribute-neg-in 56.5%

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

       13. metadata-eval 56.5%

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

       14. sub-neg 56.5%

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

   13. Simplified 56.5%

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

   if 4.5999999999999997e-255 < C < 2.29999999999999997e-216

   1. Initial program 37.9%

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

   3. Taylor expanded in A around -inf 67.0%

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

      1. associate-*r/ 67.0%

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

   5. Simplified 67.0%

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

   if 2.29999999999999997e-216 < C < 1.21999999999999995e36

   1. Initial program 56.4%

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

   3. Taylor expanded in C around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. distribute-neg-frac2 56.4%

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

      3. +-commutative 56.4%

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

      4. unpow2 56.4%

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

      5. unpow2 56.4%

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

      6. hypot-define 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in B around -inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

   8. Simplified 64.4%

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

   if 1.21999999999999995e36 < C < 6.09999999999999966e115

   1. Initial program 35.5%

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

   3. Taylor expanded in C around inf 56.6%

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

   4. Taylor expanded in A around inf 56.6%

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

   if 6.09999999999999966e115 < C < 6.2000000000000001e115

   1. Initial program 100.0%

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

   3. Taylor expanded in B around inf 100.0%

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

   4. Taylor expanded in A around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

      1. associate-*r/ 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. atan-neg 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. distribute-rgt-neg-out 100.0%

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

      2. distribute-lft-neg-in 100.0%

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

      3. metadata-eval 100.0%

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

   10. Simplified 100.0%

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

   if 6.2000000000000001e115 < C

   1. Initial program 13.5%

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

   4. Applied egg-rr 64.0%

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

   5. Taylor expanded in C around inf 73.1%

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

      1. metadata-eval 73.1%

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

      2. cancel-sign-sub-inv 73.1%

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

      3. distribute-rgt1-in 73.1%

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

      4. metadata-eval 73.1%

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

      5. mul0-lft 73.1%

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

      6. div0 73.1%

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

      7. metadata-eval 73.1%

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

      8. neg-sub0 73.1%

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

      9. distribute-lft-neg-in 73.1%

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

      10. metadata-eval 73.1%

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

   7. Simplified 73.1%

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

      1. inv-pow 73.1%

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

      2. add-sqr-sqrt 39.2%

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

      3. unpow-prod-down 39.1%

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

      4. associate-*r/ 39.1%

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

      5. associate-*r/ 39.1%

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

   9. Applied egg-rr 39.1%

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

       1. pow-sqr 39.3%

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

       2. associate-/r* 39.3%

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

       3. associate-*r/ 39.3%

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

       4. *-commutative 39.3%

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

       5. associate-*l/ 39.3%

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

       6. metadata-eval 39.3%

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

   11. Simplified 39.3%

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

   12. Taylor expanded in B around 0 74.9%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi \cdot {\left(\sqrt{0.005555555555555556}\right)}^{2}}} \]
   13. Step-by-step derivation

       1. *-commutative 74.9%

          \[\leadsto \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\color{blue}{{\left(\sqrt{0.005555555555555556}\right)}^{2} \cdot \pi}} \]

       2. unpow2 74.9%

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

       3. rem-square-sqrt 74.9%

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

       4. *-commutative 74.9%

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

       5. associate-*l/ 74.9%

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

       6. associate-*r/ 74.8%

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

       7. *-lft-identity 74.8%

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

       8. times-frac 74.7%

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

       9. metadata-eval 74.7%

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

       10. associate-/l* 74.8%

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

       11. associate-*l/ 74.9%

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

       12. associate-*r/ 74.9%

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

   14. Simplified 74.9%

       \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -5.6 \cdot 10^{-16}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{-255}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.3 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.22 \cdot 10^{+36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.1 \cdot 10^{+115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{+115}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -2.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 3.2 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.1 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{+35}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.1 \cdot 10^{+115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{+115}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -2.6e-12)
   (* (/ 180.0 PI) (atan (+ -1.0 (/ C B))))
   (if (<= C 3.2e-256)
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
     (if (<= C 2.1e-216)
       (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
       (if (<= C 8.2e+35)
         (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
         (if (<= C 6.1e+115)
           (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
           (if (<= C 6.2e+115)
             (/ (* -180.0 (atan (/ A B))) PI)
             (* (/ 180.0 PI) (atan (/ (* B -0.5) C))))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.6e-12) {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 + (C / B)));
	} else if (C <= 3.2e-256) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else if (C <= 2.1e-216) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (C <= 8.2e+35) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (C <= 6.1e+115) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (C <= 6.2e+115) {
		tmp = (-180.0 * atan((A / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.6e-12) {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 + (C / B)));
	} else if (C <= 3.2e-256) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else if (C <= 2.1e-216) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (C <= 8.2e+35) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (C <= 6.1e+115) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (C <= 6.2e+115) {
		tmp = (-180.0 * Math.atan((A / B))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -2.6e-12:
		tmp = (180.0 / math.pi) * math.atan((-1.0 + (C / B)))
	elif C <= 3.2e-256:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	elif C <= 2.1e-216:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif C <= 8.2e+35:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif C <= 6.1e+115:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif C <= 6.2e+115:
		tmp = (-180.0 * math.atan((A / B))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -2.6e-12)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 + Float64(C / B))));
	elseif (C <= 3.2e-256)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	elseif (C <= 2.1e-216)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (C <= 8.2e+35)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (C <= 6.1e+115)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (C <= 6.2e+115)
		tmp = Float64(Float64(-180.0 * atan(Float64(A / B))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -2.6e-12)
		tmp = (180.0 / pi) * atan((-1.0 + (C / B)));
	elseif (C <= 3.2e-256)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	elseif (C <= 2.1e-216)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (C <= 8.2e+35)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (C <= 6.1e+115)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (C <= 6.2e+115)
		tmp = (-180.0 * atan((A / B))) / pi;
	else
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -2.6e-12], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.2e-256], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.1e-216], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 8.2e+35], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.1e+115], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.2e+115], N[(N[(-180.0 * N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if C < -2.59999999999999983e-12

   1. Initial program 82.9%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in C around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. unpow2 80.1%

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

      3. unpow2 80.1%

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

      4. hypot-define 93.7%

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

   7. Simplified 93.7%

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

   8. Taylor expanded in A around 0 86.1%

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

      1. associate-*r/ 86.1%

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

      2. div-sub 86.1%

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

      3. pow1 86.1%

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

      4. pow1 86.1%

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

      5. pow-div 86.1%

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

      6. metadata-eval 86.1%

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

      7. metadata-eval 86.1%

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

   10. Applied egg-rr 86.1%

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

       1. *-commutative 86.1%

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

       2. associate-/l* 86.2%

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

       3. sub-neg 86.2%

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

       4. metadata-eval 86.2%

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

       5. +-commutative 86.2%

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

   12. Simplified 86.2%

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

   if -2.59999999999999983e-12 < C < 3.1999999999999999e-256

   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. Taylor expanded in C around 0 53.4%

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

      1. mul-1-neg 53.4%

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

      2. distribute-neg-frac2 53.4%

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

      3. +-commutative 53.4%

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

      4. unpow2 53.4%

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

      5. unpow2 53.4%

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

      6. hypot-define 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in A around 0 56.5%

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

      1. sub-neg 56.5%

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

      2. metadata-eval 56.5%

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

      3. +-commutative 56.5%

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

      4. mul-1-neg 56.5%

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

      5. unsub-neg 56.5%

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

   8. Simplified 56.5%

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

   if 3.1999999999999999e-256 < C < 2.1000000000000002e-216

   1. Initial program 37.9%

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

   3. Taylor expanded in A around -inf 67.0%

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

      1. associate-*r/ 67.0%

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

   5. Simplified 67.0%

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

   if 2.1000000000000002e-216 < C < 8.1999999999999997e35

   1. Initial program 56.4%

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

   3. Taylor expanded in C around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. distribute-neg-frac2 56.4%

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

      3. +-commutative 56.4%

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

      4. unpow2 56.4%

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

      5. unpow2 56.4%

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

      6. hypot-define 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in B around -inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

   8. Simplified 64.4%

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

   if 8.1999999999999997e35 < C < 6.09999999999999966e115

   1. Initial program 35.5%

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

   3. Taylor expanded in C around inf 56.6%

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

   4. Taylor expanded in A around inf 56.6%

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

   if 6.09999999999999966e115 < C < 6.2000000000000001e115

   1. Initial program 100.0%

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

   3. Taylor expanded in B around inf 100.0%

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

   4. Taylor expanded in A around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

      1. associate-*r/ 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. atan-neg 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. distribute-rgt-neg-out 100.0%

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

      2. distribute-lft-neg-in 100.0%

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

      3. metadata-eval 100.0%

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

   10. Simplified 100.0%

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

   if 6.2000000000000001e115 < C

   1. Initial program 13.5%

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

   4. Applied egg-rr 64.0%

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

   5. Taylor expanded in C around inf 73.1%

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

      1. metadata-eval 73.1%

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

      2. cancel-sign-sub-inv 73.1%

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

      3. distribute-rgt1-in 73.1%

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

      4. metadata-eval 73.1%

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

      5. mul0-lft 73.1%

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

      6. div0 73.1%

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

      7. metadata-eval 73.1%

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

      8. neg-sub0 73.1%

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

      9. distribute-lft-neg-in 73.1%

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

      10. metadata-eval 73.1%

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

   7. Simplified 73.1%

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

      1. inv-pow 73.1%

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

      2. add-sqr-sqrt 39.2%

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

      3. unpow-prod-down 39.1%

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

      4. associate-*r/ 39.1%

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

      5. associate-*r/ 39.1%

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

   9. Applied egg-rr 39.1%

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

       1. pow-sqr 39.3%

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

       2. associate-/r* 39.3%

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

       3. associate-*r/ 39.3%

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

       4. *-commutative 39.3%

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

       5. associate-*l/ 39.3%

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

       6. metadata-eval 39.3%

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

   11. Simplified 39.3%

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

   12. Taylor expanded in B around 0 74.9%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi \cdot {\left(\sqrt{0.005555555555555556}\right)}^{2}}} \]
   13. Step-by-step derivation

       1. *-commutative 74.9%

          \[\leadsto \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\color{blue}{{\left(\sqrt{0.005555555555555556}\right)}^{2} \cdot \pi}} \]

       2. unpow2 74.9%

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

       3. rem-square-sqrt 74.9%

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

       4. *-commutative 74.9%

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

       5. associate-*l/ 74.9%

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

       6. associate-*r/ 74.8%

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

       7. *-lft-identity 74.8%

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

       8. times-frac 74.7%

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

       9. metadata-eval 74.7%

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

       10. associate-/l* 74.8%

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

       11. associate-*l/ 74.9%

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

       12. associate-*r/ 74.9%

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

   14. Simplified 74.9%

       \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 3.2 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.1 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{+35}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.1 \cdot 10^{+115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{+115}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.38 \cdot 10^{-17}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 3.6 \cdot 10^{-255}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.9 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 7.6 \cdot 10^{+35}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.1 \cdot 10^{+115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{+115}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.38e-17)
   (* (/ 180.0 PI) (atan (+ -1.0 (/ C B))))
   (if (<= C 3.6e-255)
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
     (if (<= C 1.9e-216)
       (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
       (if (<= C 7.6e+35)
         (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
         (if (<= C 6.1e+115)
           (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
           (if (<= C 6.2e+115)
             (/ (* -180.0 (atan (/ A B))) PI)
             (* (/ 180.0 PI) (atan (* B (/ -0.5 C)))))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.38e-17) {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 + (C / B)));
	} else if (C <= 3.6e-255) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else if (C <= 1.9e-216) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (C <= 7.6e+35) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (C <= 6.1e+115) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (C <= 6.2e+115) {
		tmp = (-180.0 * atan((A / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.38e-17) {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 + (C / B)));
	} else if (C <= 3.6e-255) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else if (C <= 1.9e-216) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (C <= 7.6e+35) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (C <= 6.1e+115) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (C <= 6.2e+115) {
		tmp = (-180.0 * Math.atan((A / B))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.38e-17:
		tmp = (180.0 / math.pi) * math.atan((-1.0 + (C / B)))
	elif C <= 3.6e-255:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	elif C <= 1.9e-216:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif C <= 7.6e+35:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif C <= 6.1e+115:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif C <= 6.2e+115:
		tmp = (-180.0 * math.atan((A / B))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.38e-17)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 + Float64(C / B))));
	elseif (C <= 3.6e-255)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	elseif (C <= 1.9e-216)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (C <= 7.6e+35)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (C <= 6.1e+115)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (C <= 6.2e+115)
		tmp = Float64(Float64(-180.0 * atan(Float64(A / B))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.38e-17)
		tmp = (180.0 / pi) * atan((-1.0 + (C / B)));
	elseif (C <= 3.6e-255)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	elseif (C <= 1.9e-216)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (C <= 7.6e+35)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (C <= 6.1e+115)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (C <= 6.2e+115)
		tmp = (-180.0 * atan((A / B))) / pi;
	else
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.38e-17], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.6e-255], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.9e-216], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 7.6e+35], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.1e+115], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.2e+115], N[(N[(-180.0 * N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if C < -1.3800000000000001e-17

   1. Initial program 82.9%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in C around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. unpow2 80.1%

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

      3. unpow2 80.1%

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

      4. hypot-define 93.7%

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

   7. Simplified 93.7%

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

   8. Taylor expanded in A around 0 86.1%

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

      1. associate-*r/ 86.1%

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

      2. div-sub 86.1%

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

      3. pow1 86.1%

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

      4. pow1 86.1%

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

      5. pow-div 86.1%

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

      6. metadata-eval 86.1%

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

      7. metadata-eval 86.1%

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

   10. Applied egg-rr 86.1%

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

       1. *-commutative 86.1%

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

       2. associate-/l* 86.2%

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

       3. sub-neg 86.2%

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

       4. metadata-eval 86.2%

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

       5. +-commutative 86.2%

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

   12. Simplified 86.2%

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

   if -1.3800000000000001e-17 < C < 3.6000000000000002e-255

   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. Taylor expanded in C around 0 53.4%

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

      1. mul-1-neg 53.4%

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

      2. distribute-neg-frac2 53.4%

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

      3. +-commutative 53.4%

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

      4. unpow2 53.4%

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

      5. unpow2 53.4%

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

      6. hypot-define 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in A around 0 56.5%

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

      1. sub-neg 56.5%

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

      2. metadata-eval 56.5%

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

      3. +-commutative 56.5%

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

      4. mul-1-neg 56.5%

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

      5. unsub-neg 56.5%

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

   8. Simplified 56.5%

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

   if 3.6000000000000002e-255 < C < 1.9e-216

   1. Initial program 37.9%

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

   3. Taylor expanded in A around -inf 67.0%

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

      1. associate-*r/ 67.0%

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

   5. Simplified 67.0%

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

   if 1.9e-216 < C < 7.5999999999999999e35

   1. Initial program 56.4%

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

   3. Taylor expanded in C around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. distribute-neg-frac2 56.4%

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

      3. +-commutative 56.4%

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

      4. unpow2 56.4%

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

      5. unpow2 56.4%

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

      6. hypot-define 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in B around -inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

   8. Simplified 64.4%

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

   if 7.5999999999999999e35 < C < 6.09999999999999966e115

   1. Initial program 35.5%

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

   3. Taylor expanded in C around inf 56.6%

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

   4. Taylor expanded in A around inf 56.6%

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

   if 6.09999999999999966e115 < C < 6.2000000000000001e115

   1. Initial program 100.0%

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

   3. Taylor expanded in B around inf 100.0%

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

   4. Taylor expanded in A around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

      1. associate-*r/ 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. atan-neg 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. distribute-rgt-neg-out 100.0%

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

      2. distribute-lft-neg-in 100.0%

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

      3. metadata-eval 100.0%

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

   10. Simplified 100.0%

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

   if 6.2000000000000001e115 < C

   1. Initial program 13.5%

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

   4. Applied egg-rr 64.0%

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

   5. Taylor expanded in C around inf 73.1%

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

      1. metadata-eval 73.1%

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

      2. cancel-sign-sub-inv 73.1%

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

      3. distribute-rgt1-in 73.1%

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

      4. metadata-eval 73.1%

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

      5. mul0-lft 73.1%

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

      6. div0 73.1%

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

      7. metadata-eval 73.1%

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

      8. neg-sub0 73.1%

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

      9. distribute-lft-neg-in 73.1%

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

      10. metadata-eval 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in B around 0 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-*r/ 74.8%

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

      3. associate-*l/ 74.9%

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

      4. associate-/l* 74.9%

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

      5. associate-*r/ 74.9%

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

      6. *-commutative 74.9%

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

      7. associate-*l/ 74.9%

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

      8. associate-*r/ 74.9%

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

   10. Simplified 74.9%

       \[\leadsto \color{blue}{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.38 \cdot 10^{-17}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 + \frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 3.6 \cdot 10^{-255}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.9 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 7.6 \cdot 10^{+35}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.1 \cdot 10^{+115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{+115}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -2.7 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.4 \cdot 10^{-260}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.2 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 7.6 \cdot 10^{+35}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.46 \cdot 10^{+115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{+115}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -2.7e-16)
   (* 180.0 (/ (atan (/ (- C B) B)) PI))
   (if (<= C 6.4e-260)
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
     (if (<= C 4.2e-216)
       (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
       (if (<= C 7.6e+35)
         (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
         (if (<= C 1.46e+115)
           (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
           (if (<= C 6.2e+115)
             (/ (* -180.0 (atan (/ A B))) PI)
             (* (/ 180.0 PI) (atan (* B (/ -0.5 C)))))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.7e-16) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (C <= 6.4e-260) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else if (C <= 4.2e-216) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (C <= 7.6e+35) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (C <= 1.46e+115) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (C <= 6.2e+115) {
		tmp = (-180.0 * atan((A / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.7e-16) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (C <= 6.4e-260) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else if (C <= 4.2e-216) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (C <= 7.6e+35) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (C <= 1.46e+115) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (C <= 6.2e+115) {
		tmp = (-180.0 * Math.atan((A / B))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -2.7e-16:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif C <= 6.4e-260:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	elif C <= 4.2e-216:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif C <= 7.6e+35:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif C <= 1.46e+115:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif C <= 6.2e+115:
		tmp = (-180.0 * math.atan((A / B))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -2.7e-16)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (C <= 6.4e-260)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	elseif (C <= 4.2e-216)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (C <= 7.6e+35)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (C <= 1.46e+115)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (C <= 6.2e+115)
		tmp = Float64(Float64(-180.0 * atan(Float64(A / B))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -2.7e-16)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (C <= 6.4e-260)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	elseif (C <= 4.2e-216)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (C <= 7.6e+35)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (C <= 1.46e+115)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (C <= 6.2e+115)
		tmp = (-180.0 * atan((A / B))) / pi;
	else
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -2.7e-16], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.4e-260], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.2e-216], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 7.6e+35], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.46e+115], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.2e+115], N[(N[(-180.0 * N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if C < -2.69999999999999999e-16

   1. Initial program 82.9%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in C around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. unpow2 80.1%

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

      3. unpow2 80.1%

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

      4. hypot-define 93.7%

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

   7. Simplified 93.7%

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

   8. Taylor expanded in A around 0 86.1%

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

   if -2.69999999999999999e-16 < C < 6.3999999999999999e-260

   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. Taylor expanded in C around 0 53.4%

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

      1. mul-1-neg 53.4%

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

      2. distribute-neg-frac2 53.4%

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

      3. +-commutative 53.4%

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

      4. unpow2 53.4%

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

      5. unpow2 53.4%

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

      6. hypot-define 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in A around 0 56.5%

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

      1. sub-neg 56.5%

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

      2. metadata-eval 56.5%

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

      3. +-commutative 56.5%

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

      4. mul-1-neg 56.5%

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

      5. unsub-neg 56.5%

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

   8. Simplified 56.5%

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

   if 6.3999999999999999e-260 < C < 4.2000000000000003e-216

   1. Initial program 37.9%

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

   3. Taylor expanded in A around -inf 67.0%

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

      1. associate-*r/ 67.0%

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

   5. Simplified 67.0%

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

   if 4.2000000000000003e-216 < C < 7.5999999999999999e35

   1. Initial program 56.4%

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

   3. Taylor expanded in C around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. distribute-neg-frac2 56.4%

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

      3. +-commutative 56.4%

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

      4. unpow2 56.4%

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

      5. unpow2 56.4%

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

      6. hypot-define 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in B around -inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

   8. Simplified 64.4%

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

   if 7.5999999999999999e35 < C < 1.46e115

   1. Initial program 35.5%

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

   3. Taylor expanded in C around inf 56.6%

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

   4. Taylor expanded in A around inf 56.6%

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

   if 1.46e115 < C < 6.2000000000000001e115

   1. Initial program 100.0%

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

   3. Taylor expanded in B around inf 100.0%

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

   4. Taylor expanded in A around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

      1. associate-*r/ 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. atan-neg 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. distribute-rgt-neg-out 100.0%

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

      2. distribute-lft-neg-in 100.0%

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

      3. metadata-eval 100.0%

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

   10. Simplified 100.0%

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

   if 6.2000000000000001e115 < C

   1. Initial program 13.5%

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

   4. Applied egg-rr 64.0%

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

   5. Taylor expanded in C around inf 73.1%

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

      1. metadata-eval 73.1%

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

      2. cancel-sign-sub-inv 73.1%

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

      3. distribute-rgt1-in 73.1%

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

      4. metadata-eval 73.1%

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

      5. mul0-lft 73.1%

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

      6. div0 73.1%

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

      7. metadata-eval 73.1%

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

      8. neg-sub0 73.1%

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

      9. distribute-lft-neg-in 73.1%

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

      10. metadata-eval 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in B around 0 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-*r/ 74.8%

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

      3. associate-*l/ 74.9%

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

      4. associate-/l* 74.9%

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

      5. associate-*r/ 74.9%

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

      6. *-commutative 74.9%

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

      7. associate-*l/ 74.9%

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

      8. associate-*r/ 74.9%

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

   10. Simplified 74.9%

       \[\leadsto \color{blue}{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right) \cdot \frac{180}{\pi}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.7 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.4 \cdot 10^{-260}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.2 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 7.6 \cdot 10^{+35}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.46 \cdot 10^{+115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{+115}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -2.05 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 4 \cdot 10^{-219}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.6 \cdot 10^{+140} \lor \neg \left(C \leq 6.6 \cdot 10^{+151}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -2.05e-32)
   (* 180.0 (/ (atan (+ (/ C B) 1.0)) PI))
   (if (<= C 4e-219)
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
     (if (<= C 1e-54)
       (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
       (if (or (<= C 1.6e+140) (not (<= C 6.6e+151)))
         (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
         (* 180.0 (/ (atan -1.0) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.05e-32) {
		tmp = 180.0 * (atan(((C / B) + 1.0)) / ((double) M_PI));
	} else if (C <= 4e-219) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else if (C <= 1e-54) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if ((C <= 1.6e+140) || !(C <= 6.6e+151)) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((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 (C <= -2.05e-32) {
		tmp = 180.0 * (Math.atan(((C / B) + 1.0)) / Math.PI);
	} else if (C <= 4e-219) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else if (C <= 1e-54) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if ((C <= 1.6e+140) || !(C <= 6.6e+151)) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -2.05e-32:
		tmp = 180.0 * (math.atan(((C / B) + 1.0)) / math.pi)
	elif C <= 4e-219:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	elif C <= 1e-54:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif (C <= 1.6e+140) or not (C <= 6.6e+151):
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -2.05e-32)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + 1.0)) / pi));
	elseif (C <= 4e-219)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	elseif (C <= 1e-54)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif ((C <= 1.6e+140) || !(C <= 6.6e+151))
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / 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 (C <= -2.05e-32)
		tmp = 180.0 * (atan(((C / B) + 1.0)) / pi);
	elseif (C <= 4e-219)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	elseif (C <= 1e-54)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif ((C <= 1.6e+140) || ~((C <= 6.6e+151)))
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -2.05e-32], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4e-219], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1e-54], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[C, 1.6e+140], N[Not[LessEqual[C, 6.6e+151]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -2.04999999999999988e-32

   1. Initial program 81.7%

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

   3. Taylor expanded in A around 0 77.5%

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

      1. unpow2 77.5%

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

      2. unpow2 77.5%

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

      3. hypot-define 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in B around -inf 74.8%

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

   if -2.04999999999999988e-32 < C < 4.0000000000000001e-219

   1. Initial program 59.4%

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

   3. Taylor expanded in C around 0 52.0%

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

      1. mul-1-neg 52.0%

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

      2. distribute-neg-frac2 52.0%

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

      3. +-commutative 52.0%

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

      4. unpow2 52.0%

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

      5. unpow2 52.0%

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

      6. hypot-define 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in A around 0 56.1%

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

      1. sub-neg 56.1%

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

      2. metadata-eval 56.1%

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

      3. +-commutative 56.1%

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

      4. mul-1-neg 56.1%

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

      5. unsub-neg 56.1%

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

   8. Simplified 56.1%

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

   if 4.0000000000000001e-219 < C < 1e-54

   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. Taylor expanded in C around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. distribute-neg-frac2 62.1%

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

      3. +-commutative 62.1%

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

      4. unpow2 62.1%

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

      5. unpow2 62.1%

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

      6. hypot-define 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in B around -inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. unsub-neg 65.8%

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

   8. Simplified 65.8%

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

   if 1e-54 < C < 1.60000000000000005e140 or 6.60000000000000049e151 < C

   1. Initial program 24.8%

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

   3. Taylor expanded in C around inf 63.8%

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

   4. Taylor expanded in A around inf 63.8%

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

   if 1.60000000000000005e140 < C < 6.60000000000000049e151

   1. Initial program 35.6%

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

   3. Taylor expanded in B around inf 50.8%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.05 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 4 \cdot 10^{-219}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.6 \cdot 10^{+140} \lor \neg \left(C \leq 6.6 \cdot 10^{+151}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.8% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1 \cdot 10^{+89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.2 \cdot 10^{-255}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 7.1 \cdot 10^{-214}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 10^{-194}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 1.36 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))
   (if (<= C -1e+89)
     (* 180.0 (/ (atan (+ (/ C B) 1.0)) PI))
     (if (<= C 5.2e-255)
       t_0
       (if (<= C 7.1e-214)
         (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
         (if (<= C 1e-194)
           t_0
           (if (<= C 1.36e-39)
             (* 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 t_0 = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	double tmp;
	if (C <= -1e+89) {
		tmp = 180.0 * (atan(((C / B) + 1.0)) / ((double) M_PI));
	} else if (C <= 5.2e-255) {
		tmp = t_0;
	} else if (C <= 7.1e-214) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (C <= 1e-194) {
		tmp = t_0;
	} else if (C <= 1.36e-39) {
		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 t_0 = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	double tmp;
	if (C <= -1e+89) {
		tmp = 180.0 * (Math.atan(((C / B) + 1.0)) / Math.PI);
	} else if (C <= 5.2e-255) {
		tmp = t_0;
	} else if (C <= 7.1e-214) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (C <= 1e-194) {
		tmp = t_0;
	} else if (C <= 1.36e-39) {
		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):
	t_0 = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	tmp = 0
	if C <= -1e+89:
		tmp = 180.0 * (math.atan(((C / B) + 1.0)) / math.pi)
	elif C <= 5.2e-255:
		tmp = t_0
	elif C <= 7.1e-214:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif C <= 1e-194:
		tmp = t_0
	elif C <= 1.36e-39:
		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)
	t_0 = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi))
	tmp = 0.0
	if (C <= -1e+89)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + 1.0)) / pi));
	elseif (C <= 5.2e-255)
		tmp = t_0;
	elseif (C <= 7.1e-214)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (C <= 1e-194)
		tmp = t_0;
	elseif (C <= 1.36e-39)
		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)
	t_0 = 180.0 * (atan((-1.0 - (A / B))) / pi);
	tmp = 0.0;
	if (C <= -1e+89)
		tmp = 180.0 * (atan(((C / B) + 1.0)) / pi);
	elseif (C <= 5.2e-255)
		tmp = t_0;
	elseif (C <= 7.1e-214)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (C <= 1e-194)
		tmp = t_0;
	elseif (C <= 1.36e-39)
		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_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1e+89], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 5.2e-255], t$95$0, If[LessEqual[C, 7.1e-214], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1e-194], t$95$0, If[LessEqual[C, 1.36e-39], 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 5 regimes

2. if C < -9.99999999999999995e88

   1. Initial program 82.5%

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

   3. Taylor expanded in A around 0 82.5%

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

      1. unpow2 82.5%

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

      2. unpow2 82.5%

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

      3. hypot-define 96.3%

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

   5. Simplified 96.3%

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

   6. Taylor expanded in B around -inf 82.7%

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

   if -9.99999999999999995e88 < C < 5.20000000000000041e-255 or 7.1000000000000001e-214 < C < 1.00000000000000002e-194

   1. Initial program 66.1%

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

   3. Taylor expanded in C around 0 55.3%

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

      1. mul-1-neg 55.3%

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

      2. distribute-neg-frac2 55.3%

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

      3. +-commutative 55.3%

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

      4. unpow2 55.3%

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

      5. unpow2 55.3%

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

      6. hypot-define 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in A around 0 58.5%

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

      1. sub-neg 58.5%

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

      2. metadata-eval 58.5%

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

      3. +-commutative 58.5%

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

      4. mul-1-neg 58.5%

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

      5. unsub-neg 58.5%

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

   8. Simplified 58.5%

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

   if 5.20000000000000041e-255 < C < 7.1000000000000001e-214

   1. Initial program 36.0%

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

   3. Taylor expanded in A around -inf 62.2%

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

      1. associate-*r/ 62.2%

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

   5. Simplified 62.2%

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

   if 1.00000000000000002e-194 < C < 1.35999999999999994e-39

   1. Initial program 65.0%

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

   3. Taylor expanded in C around 0 65.1%

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

      1. mul-1-neg 65.1%

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

      2. distribute-neg-frac2 65.1%

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

      3. +-commutative 65.1%

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

      4. unpow2 65.1%

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

      5. unpow2 65.1%

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

      6. hypot-define 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in B around -inf 69.9%

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

      1. mul-1-neg 69.9%

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

      2. unsub-neg 69.9%

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

   8. Simplified 69.9%

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

   if 1.35999999999999994e-39 < C

   1. Initial program 25.7%

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

   3. Taylor expanded in C around inf 62.5%

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

   4. Taylor expanded in A around inf 62.5%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1 \cdot 10^{+89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.2 \cdot 10^{-255}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 7.1 \cdot 10^{-214}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 10^{-194}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.36 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -4.2 \cdot 10^{-116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -5 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{-62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{+14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 4 \cdot 10^{+78}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -4.2e-116)
   (* 180.0 (/ (atan (/ C B)) PI))
   (if (<= C -5e-252)
     (* 180.0 (/ (atan -1.0) PI))
     (if (<= C 4.6e-62)
       (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
       (if (<= C 3.5e+14)
         (* 180.0 (/ (atan 1.0) PI))
         (if (<= C 4e+78)
           (/ (* -180.0 (atan (/ A B))) PI)
           (* 180.0 (/ (atan (/ 0.0 B)) PI))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.2e-116) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (C <= -5e-252) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (C <= 4.6e-62) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (C <= 3.5e+14) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (C <= 4e+78) {
		tmp = (-180.0 * atan((A / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.2e-116) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (C <= -5e-252) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (C <= 4.6e-62) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (C <= 3.5e+14) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (C <= 4e+78) {
		tmp = (-180.0 * Math.atan((A / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -4.2e-116:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif C <= -5e-252:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif C <= 4.6e-62:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif C <= 3.5e+14:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif C <= 4e+78:
		tmp = (-180.0 * math.atan((A / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -4.2e-116)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (C <= -5e-252)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (C <= 4.6e-62)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (C <= 3.5e+14)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (C <= 4e+78)
		tmp = Float64(Float64(-180.0 * atan(Float64(A / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -4.2e-116)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (C <= -5e-252)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (C <= 4.6e-62)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (C <= 3.5e+14)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (C <= 4e+78)
		tmp = (-180.0 * atan((A / B))) / pi;
	else
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -4.2e-116], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -5e-252], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.6e-62], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.5e+14], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4e+78], N[(N[(-180.0 * N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if C < -4.1999999999999998e-116

   1. Initial program 78.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in C around 0 74.4%

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

      1. +-commutative 74.4%

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

      2. unpow2 74.4%

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

      3. unpow2 74.4%

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

      4. hypot-define 87.9%

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

   7. Simplified 87.9%

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

   8. Taylor expanded in C around inf 63.2%

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

   if -4.1999999999999998e-116 < C < -5.00000000000000008e-252

   1. Initial program 55.9%

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

   3. Taylor expanded in B around inf 40.4%

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

   if -5.00000000000000008e-252 < C < 4.60000000000000001e-62

   1. Initial program 60.7%

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

   3. Taylor expanded in A around inf 34.6%

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

   if 4.60000000000000001e-62 < C < 3.5e14

   1. Initial program 26.3%

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

   3. Taylor expanded in B around -inf 41.7%

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

   if 3.5e14 < C < 4.00000000000000003e78

   1. Initial program 51.3%

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

   3. Taylor expanded in B around inf 41.2%

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

   4. Taylor expanded in A around inf 35.6%

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

      1. associate-*r/ 35.6%

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

      2. mul-1-neg 35.6%

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

   6. Simplified 35.6%

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

      1. associate-*r/ 35.6%

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

      2. distribute-frac-neg 35.6%

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

      3. atan-neg 35.6%

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

   8. Applied egg-rr 35.6%

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

      1. distribute-rgt-neg-out 35.6%

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

      2. distribute-lft-neg-in 35.6%

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

      3. metadata-eval 35.6%

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

   10. Simplified 35.6%

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

   if 4.00000000000000003e78 < C

   1. Initial program 18.5%

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

   3. Taylor expanded in C around inf 37.1%

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

      1. associate-*r/ 37.1%

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

      2. distribute-rgt1-in 37.1%

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

      3. metadata-eval 37.1%

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

      4. mul0-lft 37.1%

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

      5. metadata-eval 37.1%

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

   5. Simplified 37.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -4.2 \cdot 10^{-116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -5 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{-62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{+14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 4 \cdot 10^{+78}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 37.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.36 \cdot 10^{-118}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.8 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 1.7 \cdot 10^{-75}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 195000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{+73}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* -180.0 (atan (/ A B))) PI)))
   (if (<= C -1.36e-118)
     (* 180.0 (/ (atan (/ C B)) PI))
     (if (<= C 4.8e-203)
       (* 180.0 (/ (atan -1.0) PI))
       (if (<= C 1.7e-75)
         t_0
         (if (<= C 195000000000.0)
           (* 180.0 (/ (atan 1.0) PI))
           (if (<= C 8.2e+73) t_0 (* 180.0 (/ (atan (/ 0.0 B)) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (-180.0 * atan((A / B))) / ((double) M_PI);
	double tmp;
	if (C <= -1.36e-118) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (C <= 4.8e-203) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (C <= 1.7e-75) {
		tmp = t_0;
	} else if (C <= 195000000000.0) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (C <= 8.2e+73) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (-180.0 * Math.atan((A / B))) / Math.PI;
	double tmp;
	if (C <= -1.36e-118) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (C <= 4.8e-203) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (C <= 1.7e-75) {
		tmp = t_0;
	} else if (C <= 195000000000.0) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (C <= 8.2e+73) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (-180.0 * math.atan((A / B))) / math.pi
	tmp = 0
	if C <= -1.36e-118:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif C <= 4.8e-203:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif C <= 1.7e-75:
		tmp = t_0
	elif C <= 195000000000.0:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif C <= 8.2e+73:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(-180.0 * atan(Float64(A / B))) / pi)
	tmp = 0.0
	if (C <= -1.36e-118)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (C <= 4.8e-203)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (C <= 1.7e-75)
		tmp = t_0;
	elseif (C <= 195000000000.0)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (C <= 8.2e+73)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (-180.0 * atan((A / B))) / pi;
	tmp = 0.0;
	if (C <= -1.36e-118)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (C <= 4.8e-203)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (C <= 1.7e-75)
		tmp = t_0;
	elseif (C <= 195000000000.0)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (C <= 8.2e+73)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(-180.0 * N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[C, -1.36e-118], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.8e-203], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.7e-75], t$95$0, If[LessEqual[C, 195000000000.0], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 8.2e+73], t$95$0, N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -1.36000000000000009e-118

   1. Initial program 78.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in C around 0 74.4%

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

      1. +-commutative 74.4%

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

      2. unpow2 74.4%

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

      3. unpow2 74.4%

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

      4. hypot-define 87.9%

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

   7. Simplified 87.9%

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

   8. Taylor expanded in C around inf 63.2%

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

   if -1.36000000000000009e-118 < C < 4.7999999999999997e-203

   1. Initial program 54.3%

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

   3. Taylor expanded in B around inf 35.4%

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

   if 4.7999999999999997e-203 < C < 1.70000000000000008e-75 or 1.95e11 < C < 8.1999999999999996e73

   1. Initial program 62.5%

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

   3. Taylor expanded in B around inf 48.6%

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

   4. Taylor expanded in A around inf 39.8%

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

      1. associate-*r/ 39.8%

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

      2. mul-1-neg 39.8%

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

   6. Simplified 39.8%

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

      1. associate-*r/ 39.8%

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

      2. distribute-frac-neg 39.8%

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

      3. atan-neg 39.8%

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

   8. Applied egg-rr 39.8%

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

      1. distribute-rgt-neg-out 39.8%

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

      2. distribute-lft-neg-in 39.8%

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

      3. metadata-eval 39.8%

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

   10. Simplified 39.8%

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

   if 1.70000000000000008e-75 < C < 1.95e11

   1. Initial program 34.1%

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

   3. Taylor expanded in B around -inf 35.7%

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

   if 8.1999999999999996e73 < C

   1. Initial program 18.5%

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

   3. Taylor expanded in C around inf 37.1%

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

      1. associate-*r/ 37.1%

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

      2. distribute-rgt1-in 37.1%

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

      3. metadata-eval 37.1%

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

      4. mul0-lft 37.1%

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

      5. metadata-eval 37.1%

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

   5. Simplified 37.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 16: 58.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -3.55 \cdot 10^{-34}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 8 \cdot 10^{+28} \lor \neg \left(C \leq 3.9 \cdot 10^{+99}\right) \land C \leq 1.2 \cdot 10^{+102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -3.55e-34)
   (* 180.0 (/ (atan (+ (/ C B) 1.0)) PI))
   (if (or (<= C 8e+28) (and (not (<= C 3.9e+99)) (<= C 1.2e+102)))
     (* 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 <= -3.55e-34) {
		tmp = 180.0 * (atan(((C / B) + 1.0)) / ((double) M_PI));
	} else if ((C <= 8e+28) || (!(C <= 3.9e+99) && (C <= 1.2e+102))) {
		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 <= -3.55e-34) {
		tmp = 180.0 * (Math.atan(((C / B) + 1.0)) / Math.PI);
	} else if ((C <= 8e+28) || (!(C <= 3.9e+99) && (C <= 1.2e+102))) {
		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 <= -3.55e-34:
		tmp = 180.0 * (math.atan(((C / B) + 1.0)) / math.pi)
	elif (C <= 8e+28) or (not (C <= 3.9e+99) and (C <= 1.2e+102)):
		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 <= -3.55e-34)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + 1.0)) / pi));
	elseif ((C <= 8e+28) || (!(C <= 3.9e+99) && (C <= 1.2e+102)))
		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 <= -3.55e-34)
		tmp = 180.0 * (atan(((C / B) + 1.0)) / pi);
	elseif ((C <= 8e+28) || (~((C <= 3.9e+99)) && (C <= 1.2e+102)))
		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, -3.55e-34], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[C, 8e+28], And[N[Not[LessEqual[C, 3.9e+99]], $MachinePrecision], LessEqual[C, 1.2e+102]]], 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 < -3.55000000000000018e-34

   1. Initial program 81.7%

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

   3. Taylor expanded in A around 0 77.5%

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

      1. unpow2 77.5%

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

      2. unpow2 77.5%

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

      3. hypot-define 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in B around -inf 74.8%

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

   if -3.55000000000000018e-34 < C < 7.99999999999999967e28 or 3.89999999999999995e99 < C < 1.19999999999999997e102

   1. Initial program 57.7%

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

   3. Taylor expanded in C around 0 53.4%

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

      1. mul-1-neg 53.4%

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

      2. distribute-neg-frac2 53.4%

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

      3. +-commutative 53.4%

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

      4. unpow2 53.4%

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

      5. unpow2 53.4%

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

      6. hypot-define 77.9%

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

   5. Simplified 77.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 52.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A}{B} - 1\right)}}{\pi} \]
   7. Step-by-step derivation

      1. sub-neg 52.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A}{B} + \left(-1\right)\right)}}{\pi} \]

      2. metadata-eval 52.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{A}{B} + \color{blue}{-1}\right)}{\pi} \]

      3. +-commutative 52.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 + -1 \cdot \frac{A}{B}\right)}}{\pi} \]

      4. mul-1-neg 52.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 + \color{blue}{\left(-\frac{A}{B}\right)}\right)}{\pi} \]

      5. unsub-neg 52.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 - \frac{A}{B}\right)}}{\pi} \]

   8. Simplified 52.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 - \frac{A}{B}\right)}}{\pi} \]

   if 7.99999999999999967e28 < C < 3.89999999999999995e99 or 1.19999999999999997e102 < C

   1. Initial program 21.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in C around inf 70.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   4. Taylor expanded in A around inf 70.0%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -3.55 \cdot 10^{-34}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 8 \cdot 10^{+28} \lor \neg \left(C \leq 3.9 \cdot 10^{+99}\right) \land C \leq 1.2 \cdot 10^{+102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.65 \cdot 10^{-114}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.1 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 4.5 \cdot 10^{-214} \lor \neg \left(C \leq 1.95 \cdot 10^{-153}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.65e-114)
   (* 180.0 (/ (atan (/ C B)) PI))
   (if (<= C 2.1e-292)
     (* 180.0 (/ (atan -1.0) PI))
     (if (or (<= C 4.5e-214) (not (<= C 1.95e-153)))
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
       (/ (* -180.0 (atan (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.65e-114) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (C <= 2.1e-292) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if ((C <= 4.5e-214) || !(C <= 1.95e-153)) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = (-180.0 * atan((A / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.65e-114) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (C <= 2.1e-292) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if ((C <= 4.5e-214) || !(C <= 1.95e-153)) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = (-180.0 * Math.atan((A / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.65e-114:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif C <= 2.1e-292:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif (C <= 4.5e-214) or not (C <= 1.95e-153):
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = (-180.0 * math.atan((A / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.65e-114)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (C <= 2.1e-292)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif ((C <= 4.5e-214) || !(C <= 1.95e-153))
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(A / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.65e-114)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (C <= 2.1e-292)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif ((C <= 4.5e-214) || ~((C <= 1.95e-153)))
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = (-180.0 * atan((A / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.65e-114], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.1e-292], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[C, 4.5e-214], N[Not[LessEqual[C, 1.95e-153]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(-180.0 * N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.65000000000000017e-114

   1. Initial program 78.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

   3. Simplified 89.7%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in C around 0 74.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + \sqrt{{A}^{2} + {B}^{2}}\right)}}{B}\right)}{\pi} \]
   6. Step-by-step derivation

      1. +-commutative 74.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {A}^{2}}}\right)}{B}\right)}{\pi} \]

      2. unpow2 74.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {A}^{2}}\right)}{B}\right)}{\pi} \]

      3. unpow2 74.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{A \cdot A}}\right)}{B}\right)}{\pi} \]

      4. hypot-define 87.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A\right)}\right)}{B}\right)}{\pi} \]

   7. Simplified 87.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + \mathsf{hypot}\left(B, A\right)\right)}}{B}\right)}{\pi} \]

   8. Taylor expanded in C around inf 63.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B}\right)}}{\pi} \]

   if -1.65000000000000017e-114 < C < 2.09999999999999989e-292

   1. Initial program 54.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around inf 40.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

   if 2.09999999999999989e-292 < C < 4.5000000000000001e-214 or 1.9500000000000001e-153 < C

   1. Initial program 37.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in C around inf 50.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   4. Taylor expanded in A around inf 50.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]

   if 4.5000000000000001e-214 < C < 1.9500000000000001e-153

   1. Initial program 58.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around inf 52.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{B}\right)\right)}{\pi} \]

   4. Taylor expanded in A around inf 40.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A}{B}\right)}}{\pi} \]
   5. Step-by-step derivation

      1. associate-*r/ 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-1 \cdot A}{B}\right)}}{\pi} \]

      2. mul-1-neg 40.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{-A}}{B}\right)}{\pi} \]

   6. Simplified 40.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-A}{B}\right)}}{\pi} \]
   7. Step-by-step derivation

      1. associate-*r/ 40.0%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}} \]

      2. distribute-frac-neg 40.0%

         \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-\frac{A}{B}\right)}}{\pi} \]

      3. atan-neg 40.0%

         \[\leadsto \frac{180 \cdot \color{blue}{\left(-\tan^{-1} \left(\frac{A}{B}\right)\right)}}{\pi} \]

   8. Applied egg-rr 40.0%

      \[\leadsto \color{blue}{\frac{180 \cdot \left(-\tan^{-1} \left(\frac{A}{B}\right)\right)}{\pi}} \]
   9. Step-by-step derivation

      1. distribute-rgt-neg-out 40.0%

         \[\leadsto \frac{\color{blue}{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}}{\pi} \]

      2. distribute-lft-neg-in 40.0%

         \[\leadsto \frac{\color{blue}{\left(-180\right) \cdot \tan^{-1} \left(\frac{A}{B}\right)}}{\pi} \]

      3. metadata-eval 40.0%

         \[\leadsto \frac{\color{blue}{-180} \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi} \]

   10. Simplified 40.0%

       \[\leadsto \color{blue}{\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.65 \cdot 10^{-114}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.1 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 4.5 \cdot 10^{-214} \lor \neg \left(C \leq 1.95 \cdot 10^{-153}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 62.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{if}\;B \leq -6.8 \cdot 10^{-208}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-254}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-43}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 8 \cdot 10^{+125}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ (/ (- C A) B) 1.0)) PI))))
   (if (<= B -6.8e-208)
     t_0
     (if (<= B -4.3e-254)
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
       (if (<= B 1.15e-43)
         t_0
         (if (<= B 8e+125)
           (* 180.0 (/ (atan (/ (- C B) B)) PI))
           (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((((C - A) / B) + 1.0)) / ((double) M_PI));
	double tmp;
	if (B <= -6.8e-208) {
		tmp = t_0;
	} else if (B <= -4.3e-254) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= 1.15e-43) {
		tmp = t_0;
	} else if (B <= 8e+125) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((((C - A) / B) + 1.0)) / Math.PI);
	double tmp;
	if (B <= -6.8e-208) {
		tmp = t_0;
	} else if (B <= -4.3e-254) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= 1.15e-43) {
		tmp = t_0;
	} else if (B <= 8e+125) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((((C - A) / B) + 1.0)) / math.pi)
	tmp = 0
	if B <= -6.8e-208:
		tmp = t_0
	elif B <= -4.3e-254:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= 1.15e-43:
		tmp = t_0
	elif B <= 8e+125:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + 1.0)) / pi))
	tmp = 0.0
	if (B <= -6.8e-208)
		tmp = t_0;
	elseif (B <= -4.3e-254)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= 1.15e-43)
		tmp = t_0;
	elseif (B <= 8e+125)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((((C - A) / B) + 1.0)) / pi);
	tmp = 0.0;
	if (B <= -6.8e-208)
		tmp = t_0;
	elseif (B <= -4.3e-254)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= 1.15e-43)
		tmp = t_0;
	elseif (B <= 8e+125)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -6.8e-208], t$95$0, If[LessEqual[B, -4.3e-254], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.15e-43], t$95$0, If[LessEqual[B, 8e+125], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -6.8e-208 or -4.2999999999999997e-254 < B < 1.1499999999999999e-43

   1. Initial program 58.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf 61.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate--l+ 61.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)}}{\pi} \]

      2. div-sub 64.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\pi} \]

   5. Simplified 64.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   if -6.8e-208 < B < -4.2999999999999997e-254

   1. Initial program 28.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in C around inf 65.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   4. Taylor expanded in A around inf 65.0%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]

   if 1.1499999999999999e-43 < B < 7.9999999999999994e125

   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. Step-by-step derivation

   3. Simplified 79.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in C around 0 77.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + \sqrt{{A}^{2} + {B}^{2}}\right)}}{B}\right)}{\pi} \]
   6. Step-by-step derivation

      1. +-commutative 77.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {A}^{2}}}\right)}{B}\right)}{\pi} \]

      2. unpow2 77.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {A}^{2}}\right)}{B}\right)}{\pi} \]

      3. unpow2 77.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{A \cdot A}}\right)}{B}\right)}{\pi} \]

      4. hypot-define 77.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A\right)}\right)}{B}\right)}{\pi} \]

   7. Simplified 77.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + \mathsf{hypot}\left(B, A\right)\right)}}{B}\right)}{\pi} \]

   8. Taylor expanded in A around 0 71.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C - B}{B}\right)}}{\pi} \]

   if 7.9999999999999994e125 < B

   1. Initial program 35.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in C around 0 35.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + \sqrt{{A}^{2} + {B}^{2}}}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. mul-1-neg 35.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-\frac{A + \sqrt{{A}^{2} + {B}^{2}}}{B}\right)}}{\pi} \]

      2. distribute-neg-frac2 35.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{A + \sqrt{{A}^{2} + {B}^{2}}}{-B}\right)}}{\pi} \]

      3. +-commutative 35.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A + \sqrt{\color{blue}{{B}^{2} + {A}^{2}}}}{-B}\right)}{\pi} \]

      4. unpow2 35.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A + \sqrt{\color{blue}{B \cdot B} + {A}^{2}}}{-B}\right)}{\pi} \]

      5. unpow2 35.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A + \sqrt{B \cdot B + \color{blue}{A \cdot A}}}{-B}\right)}{\pi} \]

      6. hypot-define 85.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A + \color{blue}{\mathsf{hypot}\left(B, A\right)}}{-B}\right)}{\pi} \]

   5. Simplified 85.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}}{\pi} \]

   6. Taylor expanded in A around 0 85.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A}{B} - 1\right)}}{\pi} \]
   7. Step-by-step derivation

      1. sub-neg 85.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A}{B} + \left(-1\right)\right)}}{\pi} \]

      2. metadata-eval 85.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{A}{B} + \color{blue}{-1}\right)}{\pi} \]

      3. +-commutative 85.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 + -1 \cdot \frac{A}{B}\right)}}{\pi} \]

      4. mul-1-neg 85.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 + \color{blue}{\left(-\frac{A}{B}\right)}\right)}{\pi} \]

      5. unsub-neg 85.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 - \frac{A}{B}\right)}}{\pi} \]

   8. Simplified 85.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 - \frac{A}{B}\right)}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{-208}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-254}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-43}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{+125}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 44.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8.6 \cdot 10^{-120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.4 \cdot 10^{-223} \lor \neg \left(B \leq 2.3 \cdot 10^{-158}\right) \land B \leq 9.5 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8.6e-120)
   (* 180.0 (/ (atan 1.0) PI))
   (if (or (<= B 6.4e-223) (and (not (<= B 2.3e-158)) (<= B 9.5e-54)))
     (* 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 <= -8.6e-120) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if ((B <= 6.4e-223) || (!(B <= 2.3e-158) && (B <= 9.5e-54))) {
		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 <= -8.6e-120) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if ((B <= 6.4e-223) || (!(B <= 2.3e-158) && (B <= 9.5e-54))) {
		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 <= -8.6e-120:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif (B <= 6.4e-223) or (not (B <= 2.3e-158) and (B <= 9.5e-54)):
		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 <= -8.6e-120)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif ((B <= 6.4e-223) || (!(B <= 2.3e-158) && (B <= 9.5e-54)))
		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 <= -8.6e-120)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif ((B <= 6.4e-223) || (~((B <= 2.3e-158)) && (B <= 9.5e-54)))
		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, -8.6e-120], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 6.4e-223], And[N[Not[LessEqual[B, 2.3e-158]], $MachinePrecision], LessEqual[B, 9.5e-54]]], 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 < -8.59999999999999964e-120

   1. Initial program 44.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf 48.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -8.59999999999999964e-120 < B < 6.4000000000000001e-223 or 2.2999999999999999e-158 < B < 9.4999999999999994e-54

   1. Initial program 67.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in C around inf 26.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 26.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}\right)}}{\pi} \]

      2. distribute-rgt1-in 26.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      3. metadata-eval 26.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      4. mul0-lft 26.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      5. metadata-eval 26.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   5. Simplified 26.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]

   if 6.4000000000000001e-223 < B < 2.2999999999999999e-158 or 9.4999999999999994e-54 < B

   1. Initial program 55.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around inf 53.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.6 \cdot 10^{-120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6.4 \cdot 10^{-223} \lor \neg \left(B \leq 2.3 \cdot 10^{-158}\right) \land B \leq 9.5 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.4% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{if}\;C \leq -7.6 \cdot 10^{-115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8 \cdot 10^{-293}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 3 \cdot 10^{+38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 6.6 \cdot 10^{+151}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan -1.0) PI))))
   (if (<= C -7.6e-115)
     (* 180.0 (/ (atan (/ C B)) PI))
     (if (<= C 8e-293)
       t_0
       (if (<= C 3e+38)
         (* 180.0 (/ (atan 1.0) PI))
         (if (<= C 6.6e+151) t_0 (* 180.0 (/ (atan (/ 0.0 B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(-1.0) / ((double) M_PI));
	double tmp;
	if (C <= -7.6e-115) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (C <= 8e-293) {
		tmp = t_0;
	} else if (C <= 3e+38) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (C <= 6.6e+151) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(-1.0) / Math.PI);
	double tmp;
	if (C <= -7.6e-115) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (C <= 8e-293) {
		tmp = t_0;
	} else if (C <= 3e+38) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (C <= 6.6e+151) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(-1.0) / math.pi)
	tmp = 0
	if C <= -7.6e-115:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif C <= 8e-293:
		tmp = t_0
	elif C <= 3e+38:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif C <= 6.6e+151:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(-1.0) / pi))
	tmp = 0.0
	if (C <= -7.6e-115)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (C <= 8e-293)
		tmp = t_0;
	elseif (C <= 3e+38)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (C <= 6.6e+151)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(-1.0) / pi);
	tmp = 0.0;
	if (C <= -7.6e-115)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (C <= 8e-293)
		tmp = t_0;
	elseif (C <= 3e+38)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (C <= 6.6e+151)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -7.6e-115], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 8e-293], t$95$0, If[LessEqual[C, 3e+38], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.6e+151], t$95$0, N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -7.59999999999999984e-115

   1. Initial program 78.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

   3. Simplified 89.7%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in C around 0 74.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + \sqrt{{A}^{2} + {B}^{2}}\right)}}{B}\right)}{\pi} \]
   6. Step-by-step derivation

      1. +-commutative 74.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {A}^{2}}}\right)}{B}\right)}{\pi} \]

      2. unpow2 74.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {A}^{2}}\right)}{B}\right)}{\pi} \]

      3. unpow2 74.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{A \cdot A}}\right)}{B}\right)}{\pi} \]

      4. hypot-define 87.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A\right)}\right)}{B}\right)}{\pi} \]

   7. Simplified 87.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + \mathsf{hypot}\left(B, A\right)\right)}}{B}\right)}{\pi} \]

   8. Taylor expanded in C around inf 63.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B}\right)}}{\pi} \]

   if -7.59999999999999984e-115 < C < 8.0000000000000004e-293 or 3.0000000000000001e38 < C < 6.60000000000000049e151

   1. Initial program 46.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around inf 31.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

   if 8.0000000000000004e-293 < C < 3.0000000000000001e38

   1. Initial program 57.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf 30.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if 6.60000000000000049e151 < C

   1. Initial program 9.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in C around inf 52.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate-*r/ 52.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}\right)}}{\pi} \]

      2. distribute-rgt1-in 52.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)}{\pi} \]

      3. metadata-eval 52.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B}\right)}{\pi} \]

      4. mul0-lft 52.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B}\right)}{\pi} \]

      5. metadata-eval 52.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]

   5. Simplified 52.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 21: 65.8% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7 \cdot 10^{-209}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-254}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(B + \left(A - C\right)\right) \cdot \frac{-1}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7e-209)
   (* 180.0 (/ (atan (+ (/ (- C A) B) 1.0)) PI))
   (if (<= B -4.3e-254)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (* 180.0 (/ (atan (* (+ B (- A C)) (/ -1.0 B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7e-209) {
		tmp = 180.0 * (atan((((C - A) / B) + 1.0)) / ((double) M_PI));
	} else if (B <= -4.3e-254) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B + (A - C)) * (-1.0 / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -7e-209) {
		tmp = 180.0 * (Math.atan((((C - A) / B) + 1.0)) / Math.PI);
	} else if (B <= -4.3e-254) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B + (A - C)) * (-1.0 / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7e-209:
		tmp = 180.0 * (math.atan((((C - A) / B) + 1.0)) / math.pi)
	elif B <= -4.3e-254:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B + (A - C)) * (-1.0 / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -7e-209)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + 1.0)) / pi));
	elseif (B <= -4.3e-254)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + Float64(A - C)) * Float64(-1.0 / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -7e-209)
		tmp = 180.0 * (atan((((C - A) / B) + 1.0)) / pi);
	elseif (B <= -4.3e-254)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = 180.0 * (atan(((B + (A - C)) * (-1.0 / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7e-209], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4.3e-254], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B + N[(A - C), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -7.00000000000000004e-209

   1. Initial program 48.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf 64.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate--l+ 64.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)}}{\pi} \]

      2. div-sub 66.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\pi} \]

   5. Simplified 66.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   if -7.00000000000000004e-209 < B < -4.2999999999999997e-254

   1. Initial program 28.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in C around inf 65.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   4. Taylor expanded in A around inf 65.0%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]

   if -4.2999999999999997e-254 < B

   1. Initial program 62.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around inf 73.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{B}\right)\right)}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7 \cdot 10^{-209}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-254}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(B + \left(A - C\right)\right) \cdot \frac{-1}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 65.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7 \cdot 10^{-209}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-257}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7e-209)
   (* 180.0 (/ (atan (+ (/ (- C A) B) 1.0)) PI))
   (if (<= B -4.8e-257)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (* (/ 180.0 PI) (atan (/ (- C (+ B A)) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7e-209) {
		tmp = 180.0 * (atan((((C - A) / B) + 1.0)) / ((double) M_PI));
	} else if (B <= -4.8e-257) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (B + A)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -7e-209) {
		tmp = 180.0 * (Math.atan((((C - A) / B) + 1.0)) / Math.PI);
	} else if (B <= -4.8e-257) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (B + A)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7e-209:
		tmp = 180.0 * (math.atan((((C - A) / B) + 1.0)) / math.pi)
	elif B <= -4.8e-257:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (B + A)) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -7e-209)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + 1.0)) / pi));
	elseif (B <= -4.8e-257)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(B + A)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -7e-209)
		tmp = 180.0 * (atan((((C - A) / B) + 1.0)) / pi);
	elseif (B <= -4.8e-257)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = (180.0 / pi) * atan(((C - (B + A)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7e-209], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4.8e-257], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -7.00000000000000004e-209

   1. Initial program 48.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf 64.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate--l+ 64.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)}}{\pi} \]

      2. div-sub 66.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\pi} \]

   5. Simplified 66.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   if -7.00000000000000004e-209 < B < -4.80000000000000033e-257

   1. Initial program 28.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in C around inf 65.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   4. Taylor expanded in A around inf 65.0%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]

   if -4.80000000000000033e-257 < B

   1. Initial program 62.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

   3. Simplified 82.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in C around 0 58.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + \sqrt{{A}^{2} + {B}^{2}}\right)}}{B}\right)}{\pi} \]
   6. Step-by-step derivation

      1. +-commutative 58.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {A}^{2}}}\right)}{B}\right)}{\pi} \]

      2. unpow2 58.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {A}^{2}}\right)}{B}\right)}{\pi} \]

      3. unpow2 58.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{A \cdot A}}\right)}{B}\right)}{\pi} \]

      4. hypot-define 74.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A\right)}\right)}{B}\right)}{\pi} \]

   7. Simplified 74.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + \mathsf{hypot}\left(B, A\right)\right)}}{B}\right)}{\pi} \]
   8. Step-by-step derivation

      1. associate-*r/ 74.4%

         \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}{\pi}} \]

   9. Applied egg-rr 74.4%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}{\pi}} \]

   10. Taylor expanded in A around 0 73.8%

       \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{C - \color{blue}{\left(A + B\right)}}{B}\right)}{\pi} \]

   11. Taylor expanded in C around -inf 73.8%

       \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{A + \left(B + -1 \cdot C\right)}{B}\right)}{\pi}} \]
   12. Step-by-step derivation

       1. associate-*r/ 73.8%

          \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(-1 \cdot \frac{A + \left(B + -1 \cdot C\right)}{B}\right)}{\pi}} \]

       2. *-commutative 73.8%

          \[\leadsto \frac{\color{blue}{\tan^{-1} \left(-1 \cdot \frac{A + \left(B + -1 \cdot C\right)}{B}\right) \cdot 180}}{\pi} \]

       3. associate-/l* 73.8%

          \[\leadsto \color{blue}{\tan^{-1} \left(-1 \cdot \frac{A + \left(B + -1 \cdot C\right)}{B}\right) \cdot \frac{180}{\pi}} \]

       4. mul-1-neg 73.8%

          \[\leadsto \tan^{-1} \color{blue}{\left(-\frac{A + \left(B + -1 \cdot C\right)}{B}\right)} \cdot \frac{180}{\pi} \]

       5. distribute-neg-frac2 73.8%

          \[\leadsto \tan^{-1} \color{blue}{\left(\frac{A + \left(B + -1 \cdot C\right)}{-B}\right)} \cdot \frac{180}{\pi} \]

       6. associate-+r+ 73.8%

          \[\leadsto \tan^{-1} \left(\frac{\color{blue}{\left(A + B\right) + -1 \cdot C}}{-B}\right) \cdot \frac{180}{\pi} \]

       7. mul-1-neg 73.8%

          \[\leadsto \tan^{-1} \left(\frac{\left(A + B\right) + \color{blue}{\left(-C\right)}}{-B}\right) \cdot \frac{180}{\pi} \]

       8. unsub-neg 73.8%

          \[\leadsto \tan^{-1} \left(\frac{\color{blue}{\left(A + B\right) - C}}{-B}\right) \cdot \frac{180}{\pi} \]

   13. Simplified 73.8%

       \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(A + B\right) - C}{-B}\right) \cdot \frac{180}{\pi}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7 \cdot 10^{-209}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-257}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 65.8% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7 \cdot 10^{-209}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-254}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7e-209)
   (* 180.0 (/ (atan (+ (/ (- C A) B) 1.0)) PI))
   (if (<= B -4.3e-254)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7e-209) {
		tmp = 180.0 * (atan((((C - A) / B) + 1.0)) / ((double) M_PI));
	} else if (B <= -4.3e-254) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -7e-209) {
		tmp = 180.0 * (Math.atan((((C - A) / B) + 1.0)) / Math.PI);
	} else if (B <= -4.3e-254) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7e-209:
		tmp = 180.0 * (math.atan((((C - A) / B) + 1.0)) / math.pi)
	elif B <= -4.3e-254:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -7e-209)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + 1.0)) / pi));
	elseif (B <= -4.3e-254)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -7e-209)
		tmp = 180.0 * (atan((((C - A) / B) + 1.0)) / pi);
	elseif (B <= -4.3e-254)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7e-209], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4.3e-254], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -7.00000000000000004e-209

   1. Initial program 48.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf 64.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. associate--l+ 64.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)}}{\pi} \]

      2. div-sub 66.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\pi} \]

   5. Simplified 66.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   if -7.00000000000000004e-209 < B < -4.2999999999999997e-254

   1. Initial program 28.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in C around inf 65.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   4. Taylor expanded in A around inf 65.0%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]

   if -4.2999999999999997e-254 < B

   1. Initial program 62.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

   3. Simplified 82.6%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in C around 0 58.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + \sqrt{{A}^{2} + {B}^{2}}\right)}}{B}\right)}{\pi} \]
   6. Step-by-step derivation

      1. +-commutative 58.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{{B}^{2} + {A}^{2}}}\right)}{B}\right)}{\pi} \]

      2. unpow2 58.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + {A}^{2}}\right)}{B}\right)}{\pi} \]

      3. unpow2 58.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{A \cdot A}}\right)}{B}\right)}{\pi} \]

      4. hypot-define 74.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \color{blue}{\mathsf{hypot}\left(B, A\right)}\right)}{B}\right)}{\pi} \]

   7. Simplified 74.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + \mathsf{hypot}\left(B, A\right)\right)}}{B}\right)}{\pi} \]

   8. Taylor expanded in A around 0 73.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + B\right)}}{B}\right)}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7 \cdot 10^{-209}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq -4.3 \cdot 10^{-254}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 52.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -3.9 \cdot 10^{-120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.8 \cdot 10^{-265}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -3.9e-120)
   (* 180.0 (/ (atan (+ (/ C B) 1.0)) PI))
   (if (<= C 3.8e-265)
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.9e-120) {
		tmp = 180.0 * (atan(((C / B) + 1.0)) / ((double) M_PI));
	} else if (C <= 3.8e-265) {
		tmp = 180.0 * (atan(-1.0) / ((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 <= -3.9e-120) {
		tmp = 180.0 * (Math.atan(((C / B) + 1.0)) / Math.PI);
	} else if (C <= 3.8e-265) {
		tmp = 180.0 * (Math.atan(-1.0) / 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 <= -3.9e-120:
		tmp = 180.0 * (math.atan(((C / B) + 1.0)) / math.pi)
	elif C <= 3.8e-265:
		tmp = 180.0 * (math.atan(-1.0) / 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 <= -3.9e-120)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + 1.0)) / pi));
	elseif (C <= 3.8e-265)
		tmp = Float64(180.0 * Float64(atan(-1.0) / 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 <= -3.9e-120)
		tmp = 180.0 * (atan(((C / B) + 1.0)) / pi);
	elseif (C <= 3.8e-265)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -3.9e-120], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.8e-265], N[(180.0 * N[(N[ArcTan[-1.0], $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 < -3.9000000000000002e-120

   1. Initial program 78.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in A around 0 74.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   4. Step-by-step derivation

      1. unpow2 74.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{\color{blue}{B \cdot B} + {C}^{2}}}{B}\right)}{\pi} \]

      2. unpow2 74.5%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{B \cdot B + \color{blue}{C \cdot C}}}{B}\right)}{\pi} \]

      3. hypot-define 84.6%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\mathsf{hypot}\left(B, C\right)}}{B}\right)}{\pi} \]

   5. Simplified 84.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}{\pi} \]

   6. Taylor expanded in B around -inf 68.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C}{B}\right)}}{\pi} \]

   if -3.9000000000000002e-120 < C < 3.7999999999999998e-265

   1. Initial program 58.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around inf 40.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

   if 3.7999999999999998e-265 < C

   1. Initial program 37.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in C around inf 48.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + -0.5 \cdot \frac{B}{C}\right)}}{\pi} \]

   4. Taylor expanded in A around inf 48.8%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -3.9 \cdot 10^{-120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.8 \cdot 10^{-265}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 38.8% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.4 \cdot 10^{-120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.4e-120)
   (* 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 <= -4.4e-120) {
		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 <= -4.4e-120) {
		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 <= -4.4e-120:
		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 <= -4.4e-120)
		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 <= -4.4e-120)
		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, -4.4e-120], 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 < -4.40000000000000025e-120

   1. Initial program 44.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf 48.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -4.40000000000000025e-120 < B

   1. Initial program 61.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around inf 31.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 26: 21.0% 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 56.2%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
2. Add Preprocessing

3. Taylor expanded in B around inf 22.4%

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024107 
(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)))