ABCF->ab-angle angle

Percentage Accurate: 54.3% → 80.3%

Time: 21.8s

Alternatives: 16

Speedup: 3.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.3% 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: 80.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -5.1 \cdot 10^{+229}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -2.25 \cdot 10^{+207}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -13500000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))))
   (if (<= A -5.1e+229)
     t_0
     (if (<= A -2.25e+207)
       (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))
       (if (<= A -13500000.0)
         t_0
         (/ (* 180.0 (atan (/ (- (- C A) (hypot (- A C) B)) B))) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	double tmp;
	if (A <= -5.1e+229) {
		tmp = t_0;
	} else if (A <= -2.25e+207) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	} else if (A <= -13500000.0) {
		tmp = t_0;
	} else {
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	double tmp;
	if (A <= -5.1e+229) {
		tmp = t_0;
	} else if (A <= -2.25e+207) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	} else if (A <= -13500000.0) {
		tmp = t_0;
	} else {
		tmp = (180.0 * Math.atan((((C - A) - Math.hypot((A - C), B)) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	tmp = 0
	if A <= -5.1e+229:
		tmp = t_0
	elif A <= -2.25e+207:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	elif A <= -13500000.0:
		tmp = t_0
	else:
		tmp = (180.0 * math.atan((((C - A) - math.hypot((A - C), B)) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi))
	tmp = 0.0
	if (A <= -5.1e+229)
		tmp = t_0;
	elseif (A <= -2.25e+207)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	elseif (A <= -13500000.0)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((B * 0.5) / A)) / pi);
	tmp = 0.0;
	if (A <= -5.1e+229)
		tmp = t_0;
	elseif (A <= -2.25e+207)
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	elseif (A <= -13500000.0)
		tmp = t_0;
	else
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -5.1e+229], t$95$0, If[LessEqual[A, -2.25e+207], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -13500000.0], t$95$0, N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.0999999999999996e229 or -2.25000000000000002e207 < A < -1.35e7

   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 A around -inf 80.3%

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

      1. associate-*r/ 80.3%

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

   5. Simplified 80.3%

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

   if -5.0999999999999996e229 < A < -2.25000000000000002e207

   1. Initial program 21.4%

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

      1. associate-*l/ 21.4%

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

      2. *-lft-identity 21.4%

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

      3. +-commutative 21.4%

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

      4. unpow2 21.4%

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

      5. unpow2 21.4%

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

      6. hypot-define 100.0%

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

   3. Simplified 100.0%

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

   if -1.35e7 < A

   1. Initial program 58.7%

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

      1. associate-*r/ 58.7%

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

      2. associate-*l/ 58.7%

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

      3. *-un-lft-identity 58.7%

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

      4. unpow2 58.7%

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

      5. unpow2 58.7%

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

      6. hypot-define 87.1%

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

   4. Applied egg-rr 87.1%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.1 \cdot 10^{+229}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.25 \cdot 10^{+207}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -13500000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_1 := 180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-86}:\\ \;\;\;\;\frac{t\_1}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{\mathsf{fma}\left(B, \frac{C}{A}, B\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\pi}{t\_1}}\\ \end{array} \end{array} \]

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))))))
        (t_1 (* 180.0 (atan (/ (- (- C A) (hypot (- A C) B)) B)))))
   (if (<= t_0 -1e-86)
     (/ t_1 PI)
     (if (<= t_0 0.0)
       (/ (* -180.0 (atan (* -0.5 (/ (fma B (/ C A) B) A)))) PI)
       (/ 1.0 (/ PI t_1))))))

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 t_1 = 180.0 * atan((((C - A) - hypot((A - C), B)) / B));
	double tmp;
	if (t_0 <= -1e-86) {
		tmp = t_1 / ((double) M_PI);
	} else if (t_0 <= 0.0) {
		tmp = (-180.0 * atan((-0.5 * (fma(B, (C / A), B) / A)))) / ((double) M_PI);
	} else {
		tmp = 1.0 / (((double) M_PI) / t_1);
	}
	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)))))
	t_1 = Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B)))
	tmp = 0.0
	if (t_0 <= -1e-86)
		tmp = Float64(t_1 / pi);
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(-180.0 * atan(Float64(-0.5 * Float64(fma(B, Float64(C / A), B) / A)))) / pi);
	else
		tmp = Float64(1.0 / Float64(pi / t_1));
	end
	return 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]}, Block[{t$95$1 = N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-86], N[(t$95$1 / Pi), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[(-180.0 * N[ArcTan[N[(-0.5 * N[(N[(B * N[(C / A), $MachinePrecision] + B), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(1.0 / N[(Pi / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 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)))))) < -1.00000000000000008e-86

   1. Initial program 52.2%

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

      1. associate-*r/ 52.2%

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

      2. associate-*l/ 52.2%

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

      3. *-un-lft-identity 52.2%

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

      4. unpow2 52.2%

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

      5. unpow2 52.2%

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

      6. hypot-define 84.5%

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

   4. Applied egg-rr 84.5%

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

   if -1.00000000000000008e-86 < (*.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 18.4%

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

   3. Taylor expanded in A around -inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. distribute-neg-frac2 65.2%

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

      3. distribute-lft-out 65.2%

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

      4. associate-/l* 66.0%

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

   5. Simplified 66.0%

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

      1. associate-*r/ 66.1%

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

      2. distribute-frac-neg2 66.1%

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

      3. atan-neg 66.1%

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

      4. +-commutative 66.1%

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

      5. fma-define 66.1%

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

   7. Applied egg-rr 66.1%

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

      1. distribute-rgt-neg-out 66.1%

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

      2. distribute-lft-neg-in 66.1%

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

      3. metadata-eval 66.1%

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

      4. associate-/l* 66.1%

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

   9. Simplified 66.1%

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

   if -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 54.0%

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

   4. Applied egg-rr 90.3%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -1 \cdot 10^{-86}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{\mathsf{fma}\left(B, \frac{C}{A}, B\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\pi}{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.8 \cdot 10^{+229} \lor \neg \left(A \leq -2.5 \cdot 10^{+203}\right) \land A \leq -7000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (or (<= A -5.8e+229) (and (not (<= A -2.5e+203)) (<= A -7000000.0)))
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if ((A <= -5.8e+229) || (!(A <= -2.5e+203) && (A <= -7000000.0))) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if ((A <= -5.8e+229) || (!(A <= -2.5e+203) && (A <= -7000000.0))) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if (A <= -5.8e+229) or (not (A <= -2.5e+203) and (A <= -7000000.0)):
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if ((A <= -5.8e+229) || (!(A <= -2.5e+203) && (A <= -7000000.0)))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if ((A <= -5.8e+229) || (~((A <= -2.5e+203)) && (A <= -7000000.0)))
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	else
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[Or[LessEqual[A, -5.8e+229], And[N[Not[LessEqual[A, -2.5e+203]], $MachinePrecision], LessEqual[A, -7000000.0]]], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -5.79999999999999963e229 or -2.49999999999999997e203 < A < -7e6

   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 A around -inf 80.3%

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

      1. associate-*r/ 80.3%

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

   5. Simplified 80.3%

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

   if -5.79999999999999963e229 < A < -2.49999999999999997e203 or -7e6 < A

   1. Initial program 57.3%

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

      1. associate-*l/ 57.3%

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

      2. *-lft-identity 57.3%

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

      3. +-commutative 57.3%

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

      4. unpow2 57.3%

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

      5. unpow2 57.3%

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

      6. hypot-define 87.5%

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

   3. Simplified 87.5%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.8 \cdot 10^{+229} \lor \neg \left(A \leq -2.5 \cdot 10^{+203}\right) \land A \leq -7000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -13500000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{-33}:\\ \;\;\;\;\frac{1}{\frac{\pi}{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -13500000.0)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 1.05e-33)
     (/ 1.0 (/ PI (* 180.0 (atan (/ (- C (hypot B C)) B)))))
     (/ (* -180.0 (atan (/ (+ A (hypot A B)) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -13500000.0) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 1.05e-33) {
		tmp = 1.0 / (((double) M_PI) / (180.0 * atan(((C - hypot(B, C)) / B))));
	} else {
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -13500000.0) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 1.05e-33) {
		tmp = 1.0 / (Math.PI / (180.0 * Math.atan(((C - Math.hypot(B, C)) / B))));
	} else {
		tmp = (-180.0 * Math.atan(((A + Math.hypot(A, B)) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -13500000.0:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 1.05e-33:
		tmp = 1.0 / (math.pi / (180.0 * math.atan(((C - math.hypot(B, C)) / B))))
	else:
		tmp = (-180.0 * math.atan(((A + math.hypot(A, B)) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -13500000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 1.05e-33)
		tmp = Float64(1.0 / Float64(pi / Float64(180.0 * atan(Float64(Float64(C - hypot(B, C)) / B)))));
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(A + hypot(A, B)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -13500000.0)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 1.05e-33)
		tmp = 1.0 / (pi / (180.0 * atan(((C - hypot(B, C)) / B))));
	else
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -13500000.0], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.05e-33], N[(1.0 / N[(Pi / N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-180.0 * N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.35e7

   1. Initial program 20.7%

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

   3. Taylor expanded in A around -inf 75.8%

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

      1. associate-*r/ 75.8%

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

   5. Simplified 75.8%

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

   if -1.35e7 < A < 1.05e-33

   1. Initial program 49.2%

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

   4. Applied egg-rr 80.7%

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

   5. Taylor expanded in A around 0 47.6%

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

      1. unpow2 47.6%

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

      2. unpow2 47.6%

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

      3. hypot-define 78.8%

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

   7. Simplified 78.8%

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

   if 1.05e-33 < A

   1. Initial program 72.3%

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

   3. Taylor expanded in C around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-neg-frac2 70.7%

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

      3. +-commutative 70.7%

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

      4. unpow2 70.7%

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

      5. unpow2 70.7%

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

      6. hypot-define 88.9%

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

   5. Simplified 88.9%

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

      1. associate-*r/ 88.9%

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

      2. distribute-frac-neg2 88.9%

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

      3. atan-neg 88.9%

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

   7. Applied egg-rr 88.9%

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

      1. distribute-rgt-neg-out 88.9%

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

      2. distribute-lft-neg-in 88.9%

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

      3. metadata-eval 88.9%

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

      4. hypot-undefine 70.8%

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

      5. unpow2 70.8%

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

      6. unpow2 70.8%

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

      7. +-commutative 70.8%

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

      8. unpow2 70.8%

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

      9. unpow2 70.8%

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

      10. hypot-define 88.9%

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

   9. Simplified 88.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -13500000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{-33}:\\ \;\;\;\;\frac{1}{\frac{\pi}{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -13500000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -13500000.0)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 1.25e-17)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (+ (/ (- C A) B) -1.0)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -13500000.0) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 1.25e-17) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -13500000.0) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 1.25e-17) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C - A) / B) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -13500000.0:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 1.25e-17:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C - A) / B) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -13500000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 1.25e-17)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -13500000.0)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 1.25e-17)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -13500000.0], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.25e-17], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.35e7

   1. Initial program 20.7%

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

   3. Taylor expanded in A around -inf 75.8%

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

      1. associate-*r/ 75.8%

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

   5. Simplified 75.8%

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

   if -1.35e7 < A < 1.25e-17

   1. Initial program 49.3%

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

   3. Taylor expanded in A around 0 47.1%

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

      1. unpow2 47.1%

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

      2. unpow2 47.1%

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

      3. hypot-define 79.0%

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

   5. Simplified 79.0%

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

   if 1.25e-17 < A

   1. Initial program 73.8%

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

      1. +-commutative 73.8%

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

      2. unpow2 73.8%

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

      3. unpow2 73.8%

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

      4. hypot-undefine 96.0%

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

      5. sub-neg 96.0%

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

      6. distribute-lft-in 90.5%

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

      7. hypot-undefine 73.6%

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

      8. unpow2 73.6%

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

      9. unpow2 73.6%

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

      10. +-commutative 73.6%

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

      11. unpow2 73.6%

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

      12. unpow2 73.6%

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

      13. hypot-define 90.5%

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

   4. Applied egg-rr 90.5%

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

   5. Taylor expanded in B around inf 80.6%

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

      1. +-commutative 80.6%

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

      2. associate--r+ 80.6%

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

      3. div-sub 80.6%

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

   7. Simplified 80.6%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -13500000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -13500000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.25 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -13500000.0)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 2.25e-36)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (/ (* -180.0 (atan (/ (+ A (hypot A B)) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -13500000.0) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 2.25e-36) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -13500000.0) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 2.25e-36) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = (-180.0 * Math.atan(((A + Math.hypot(A, B)) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -13500000.0:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 2.25e-36:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = (-180.0 * math.atan(((A + math.hypot(A, B)) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -13500000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 2.25e-36)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(A + hypot(A, B)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -13500000.0)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 2.25e-36)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -13500000.0], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.25e-36], 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 * N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.35e7

   1. Initial program 20.7%

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

   3. Taylor expanded in A around -inf 75.8%

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

      1. associate-*r/ 75.8%

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

   5. Simplified 75.8%

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

   if -1.35e7 < A < 2.25000000000000012e-36

   1. Initial program 49.2%

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

   3. Taylor expanded in A around 0 47.6%

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

      1. unpow2 47.6%

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

      2. unpow2 47.6%

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

      3. hypot-define 78.8%

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

   5. Simplified 78.8%

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

   if 2.25000000000000012e-36 < A

   1. Initial program 72.3%

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

   3. Taylor expanded in C around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-neg-frac2 70.7%

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

      3. +-commutative 70.7%

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

      4. unpow2 70.7%

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

      5. unpow2 70.7%

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

      6. hypot-define 88.9%

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

   5. Simplified 88.9%

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

      1. associate-*r/ 88.9%

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

      2. distribute-frac-neg2 88.9%

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

      3. atan-neg 88.9%

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

   7. Applied egg-rr 88.9%

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

      1. distribute-rgt-neg-out 88.9%

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

      2. distribute-lft-neg-in 88.9%

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

      3. metadata-eval 88.9%

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

      4. hypot-undefine 70.8%

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

      5. unpow2 70.8%

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

      6. unpow2 70.8%

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

      7. +-commutative 70.8%

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

      8. unpow2 70.8%

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

      9. unpow2 70.8%

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

      10. hypot-define 88.9%

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

   9. Simplified 88.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -13500000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.25 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8500000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8500000.0)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8500000.0) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8500000.0) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8500000.0:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8500000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8500000.0)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8500000.0], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -8.5e6

   1. Initial program 20.7%

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

   3. Taylor expanded in A around -inf 75.8%

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

      1. associate-*r/ 75.8%

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

   5. Simplified 75.8%

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

   if -8.5e6 < A

   1. Initial program 58.7%

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

   3. Simplified 87.0%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8500000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 44.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8.2 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-226}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-179}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{+71}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8.2e-63)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 9.5e-226)
     (* 180.0 (/ (atan 0.0) PI))
     (if (<= B 2.7e-179)
       (* 180.0 (/ (atan (/ A (- B))) PI))
       (if (<= B 1.05e+71)
         (* 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 (B <= -8.2e-63) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 9.5e-226) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (B <= 2.7e-179) {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	} else if (B <= 1.05e+71) {
		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 (B <= -8.2e-63) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 9.5e-226) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (B <= 2.7e-179) {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	} else if (B <= 1.05e+71) {
		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 B <= -8.2e-63:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 9.5e-226:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif B <= 2.7e-179:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	elif B <= 1.05e+71:
		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 (B <= -8.2e-63)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 9.5e-226)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (B <= 2.7e-179)
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	elseif (B <= 1.05e+71)
		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 (B <= -8.2e-63)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 9.5e-226)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (B <= 2.7e-179)
		tmp = 180.0 * (atan((A / -B)) / pi);
	elseif (B <= 1.05e+71)
		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[B, -8.2e-63], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.5e-226], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.7e-179], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.05e+71], 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 B < -8.1999999999999995e-63

   1. Initial program 50.0%

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

   3. Taylor expanded in B around -inf 60.9%

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

   if -8.1999999999999995e-63 < B < 9.5000000000000007e-226

   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. Step-by-step derivation

      1. +-commutative 51.3%

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

      2. unpow2 51.3%

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

      3. unpow2 51.3%

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

      4. hypot-undefine 85.2%

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

      5. sub-neg 85.2%

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

      6. distribute-lft-in 46.2%

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

      7. hypot-undefine 44.0%

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

      8. unpow2 44.0%

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

      9. unpow2 44.0%

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

      10. +-commutative 44.0%

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

      11. unpow2 44.0%

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

      12. unpow2 44.0%

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

      13. hypot-define 46.2%

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

   4. Applied egg-rr 46.2%

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

   5. Taylor expanded in A around -inf 14.4%

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

      1. distribute-lft1-in 14.4%

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

      2. metadata-eval 14.4%

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

      3. mul0-lft 41.3%

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

   7. Simplified 41.3%

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

   if 9.5000000000000007e-226 < B < 2.69999999999999988e-179

   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 C around 0 59.3%

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

      1. mul-1-neg 59.3%

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

      2. distribute-neg-frac2 59.3%

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

      3. +-commutative 59.3%

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

      4. unpow2 59.3%

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

      5. unpow2 59.3%

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

      6. hypot-define 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in A around 0 55.6%

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

   7. Taylor expanded in A around inf 47.9%

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

      1. neg-mul-1 47.9%

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

      2. distribute-neg-frac2 47.9%

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

   9. Simplified 47.9%

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

   if 2.69999999999999988e-179 < B < 1.04999999999999995e71

   1. Initial program 48.6%

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

      1. +-commutative 48.6%

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

      2. unpow2 48.6%

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

      3. unpow2 48.6%

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

      4. hypot-undefine 63.7%

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

      5. sub-neg 63.7%

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

      6. distribute-rgt-in 48.8%

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

      7. div-inv 48.6%

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

      8. hypot-undefine 48.0%

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

      9. unpow2 48.0%

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

      10. unpow2 48.0%

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

      11. +-commutative 48.0%

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

      12. unpow2 48.0%

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

      13. unpow2 48.0%

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

      14. hypot-define 48.6%

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

   4. Applied egg-rr 48.6%

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

   5. Taylor expanded in C around inf 40.3%

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

   if 1.04999999999999995e71 < B

   1. Initial program 36.3%

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

   3. Taylor expanded in B around inf 66.8%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.2 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-226}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-179}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{+71}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 44.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.1 \cdot 10^{-59}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-264}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 2.35 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{+69}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.1e-59)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.5e-264)
     (* 180.0 (/ (atan 0.0) PI))
     (if (<= B 2.35e-184)
       (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
       (if (<= B 5.6e+69)
         (* 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 (B <= -3.1e-59) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.5e-264) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (B <= 2.35e-184) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (B <= 5.6e+69) {
		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 (B <= -3.1e-59) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.5e-264) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (B <= 2.35e-184) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (B <= 5.6e+69) {
		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 B <= -3.1e-59:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.5e-264:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif B <= 2.35e-184:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif B <= 5.6e+69:
		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 (B <= -3.1e-59)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.5e-264)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (B <= 2.35e-184)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (B <= 5.6e+69)
		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 (B <= -3.1e-59)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.5e-264)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (B <= 2.35e-184)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (B <= 5.6e+69)
		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[B, -3.1e-59], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.5e-264], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.35e-184], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.6e+69], 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 B < -3.09999999999999999e-59

   1. Initial program 50.0%

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

   3. Taylor expanded in B around -inf 60.9%

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

   if -3.09999999999999999e-59 < B < 2.5e-264

   1. Initial program 51.9%

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

      1. +-commutative 51.9%

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

      2. unpow2 51.9%

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

      3. unpow2 51.9%

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

      4. hypot-undefine 86.6%

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

      5. sub-neg 86.6%

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

      6. distribute-lft-in 44.6%

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

      7. hypot-undefine 43.9%

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

      8. unpow2 43.9%

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

      9. unpow2 43.9%

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

      10. +-commutative 43.9%

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

      11. unpow2 43.9%

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

      12. unpow2 43.9%

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

      13. hypot-define 44.6%

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

   4. Applied egg-rr 44.6%

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

   5. Taylor expanded in A around -inf 15.8%

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

      1. distribute-lft1-in 15.8%

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

      2. metadata-eval 15.8%

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

      3. mul0-lft 44.2%

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

   7. Simplified 44.2%

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

   if 2.5e-264 < B < 2.3500000000000001e-184

   1. Initial program 65.4%

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

   3. Taylor expanded in C around -inf 51.3%

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

   if 2.3500000000000001e-184 < B < 5.59999999999999964e69

   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. Step-by-step derivation

      1. +-commutative 48.8%

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

      2. unpow2 48.8%

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

      3. unpow2 48.8%

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

      4. hypot-undefine 65.1%

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

      5. sub-neg 65.1%

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

      6. distribute-rgt-in 50.7%

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

      7. div-inv 50.5%

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

      8. hypot-undefine 48.2%

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

      9. unpow2 48.2%

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

      10. unpow2 48.2%

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

      11. +-commutative 48.2%

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

      12. unpow2 48.2%

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

      13. unpow2 48.2%

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

      14. hypot-define 50.5%

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

   4. Applied egg-rr 50.5%

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

   5. Taylor expanded in C around inf 38.9%

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

   if 5.59999999999999964e69 < B

   1. Initial program 36.3%

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

   3. Taylor expanded in B around inf 66.8%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.1 \cdot 10^{-59}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-264}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 2.35 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{+69}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.85 \cdot 10^{-96}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.2 \cdot 10^{-134}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{-305}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 3.7 \cdot 10^{-30}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.85e-96)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A -3.2e-134)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= A 1.1e-305)
       (* 180.0 (/ (atan -1.0) PI))
       (if (<= A 3.7e-30)
         (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
         (* 180.0 (/ (atan (* (/ A B) -2.0)) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.85e-96) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= -3.2e-134) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 1.1e-305) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 3.7e-30) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.85e-96) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= -3.2e-134) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 1.1e-305) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 3.7e-30) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.85e-96:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= -3.2e-134:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 1.1e-305:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 3.7e-30:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.85e-96)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= -3.2e-134)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 1.1e-305)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 3.7e-30)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.85e-96)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= -3.2e-134)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 1.1e-305)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 3.7e-30)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.85e-96], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -3.2e-134], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.1e-305], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.7e-30], 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[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -1.84999999999999993e-96

   1. Initial program 24.3%

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

   3. Taylor expanded in A around -inf 67.2%

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

      1. associate-*r/ 67.2%

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

   5. Simplified 67.2%

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

   if -1.84999999999999993e-96 < A < -3.2000000000000001e-134

   1. Initial program 42.0%

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

   3. Taylor expanded in B around -inf 57.2%

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

   if -3.2000000000000001e-134 < A < 1.09999999999999998e-305

   1. Initial program 63.5%

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

   3. Taylor expanded in B around inf 41.9%

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

   if 1.09999999999999998e-305 < A < 3.7000000000000003e-30

   1. Initial program 45.9%

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

      1. +-commutative 45.9%

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

      2. unpow2 45.9%

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

      3. unpow2 45.9%

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

      4. hypot-undefine 81.5%

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

      5. sub-neg 81.5%

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

      6. distribute-rgt-in 67.1%

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

      7. div-inv 66.7%

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

      8. hypot-undefine 43.3%

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

      9. unpow2 43.3%

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

      10. unpow2 43.3%

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

      11. +-commutative 43.3%

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

      12. unpow2 43.3%

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

      13. unpow2 43.3%

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

      14. hypot-define 66.7%

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

   4. Applied egg-rr 66.7%

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

   5. Taylor expanded in C around inf 39.8%

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

   if 3.7000000000000003e-30 < A

   1. Initial program 73.4%

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

   3. Taylor expanded in A around inf 63.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-2 \cdot \frac{A}{B}\right)}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.85 \cdot 10^{-96}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.2 \cdot 10^{-134}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{-305}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 3.7 \cdot 10^{-30}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.85 \cdot 10^{-96}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.7 \cdot 10^{-135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-306}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{-88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(1 + \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.85e-96)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A -3.7e-135)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= A 3.8e-306)
       (* 180.0 (/ (atan -1.0) PI))
       (if (<= A 1.55e-88)
         (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
         (/ (* -180.0 (atan (+ 1.0 (/ A B)))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.85e-96) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= -3.7e-135) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 3.8e-306) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 1.55e-88) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = (-180.0 * atan((1.0 + (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.85e-96) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= -3.7e-135) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 3.8e-306) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 1.55e-88) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = (-180.0 * Math.atan((1.0 + (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.85e-96:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= -3.7e-135:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 3.8e-306:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 1.55e-88:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = (-180.0 * math.atan((1.0 + (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.85e-96)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= -3.7e-135)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 3.8e-306)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 1.55e-88)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(1.0 + Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.85e-96)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= -3.7e-135)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 3.8e-306)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 1.55e-88)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = (-180.0 * atan((1.0 + (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.85e-96], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -3.7e-135], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.8e-306], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.55e-88], 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[(1.0 + N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -1.84999999999999993e-96

   1. Initial program 24.3%

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

   3. Taylor expanded in A around -inf 67.2%

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

      1. associate-*r/ 67.2%

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

   5. Simplified 67.2%

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

   if -1.84999999999999993e-96 < A < -3.6999999999999997e-135

   1. Initial program 42.0%

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

   3. Taylor expanded in B around -inf 57.2%

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

   if -3.6999999999999997e-135 < A < 3.8e-306

   1. Initial program 63.5%

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

   3. Taylor expanded in B around inf 41.9%

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

   if 3.8e-306 < A < 1.5499999999999999e-88

   1. Initial program 46.1%

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

      1. +-commutative 46.1%

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

      2. unpow2 46.1%

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

      3. unpow2 46.1%

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

      4. hypot-undefine 81.1%

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

      5. sub-neg 81.1%

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

      6. distribute-rgt-in 66.2%

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

      7. div-inv 65.8%

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

      8. hypot-undefine 42.8%

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

      9. unpow2 42.8%

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

      10. unpow2 42.8%

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

      11. +-commutative 42.8%

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

      12. unpow2 42.8%

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

      13. unpow2 42.8%

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

      14. hypot-define 65.8%

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

   4. Applied egg-rr 65.8%

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

   5. Taylor expanded in C around inf 39.2%

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

   if 1.5499999999999999e-88 < A

   1. Initial program 69.2%

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

   3. Taylor expanded in C around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. distribute-neg-frac2 67.8%

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

      3. +-commutative 67.8%

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

      4. unpow2 67.8%

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

      5. unpow2 67.8%

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

      6. hypot-define 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in A around 0 74.7%

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

      1. associate-*r/ 74.7%

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

      2. distribute-frac-neg2 74.7%

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

      3. atan-neg 74.7%

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

   8. Applied egg-rr 74.7%

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

      1. distribute-rgt-neg-out 74.7%

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

      2. distribute-lft-neg-in 74.7%

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

      3. metadata-eval 74.7%

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

      4. +-commutative 74.7%

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

      5. remove-double-neg 74.7%

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

      6. mul-1-neg 74.7%

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

      7. sub-neg 74.7%

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

      8. div-sub 74.7%

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

      9. *-inverses 74.7%

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

      10. associate-*r/ 74.7%

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

      11. cancel-sign-sub-inv 74.7%

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

      12. metadata-eval 74.7%

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

      13. *-lft-identity 74.7%

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

   10. Simplified 74.7%

       \[\leadsto \color{blue}{\frac{-180 \cdot \tan^{-1} \left(1 + \frac{A}{B}\right)}{\pi}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.85 \cdot 10^{-96}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.7 \cdot 10^{-135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-306}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{-88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(1 + \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{if}\;B \leq -3.3 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 10^{-225}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-180}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.25 \cdot 10^{-44}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan 0.0) PI))))
   (if (<= B -3.3e-61)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 1e-225)
       t_0
       (if (<= B 1.85e-180)
         (* 180.0 (/ (atan (/ A (- B))) PI))
         (if (<= B 3.25e-44) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(0.0) / ((double) M_PI));
	double tmp;
	if (B <= -3.3e-61) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1e-225) {
		tmp = t_0;
	} else if (B <= 1.85e-180) {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	} else if (B <= 3.25e-44) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(0.0) / Math.PI);
	double tmp;
	if (B <= -3.3e-61) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1e-225) {
		tmp = t_0;
	} else if (B <= 1.85e-180) {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	} else if (B <= 3.25e-44) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(0.0) / math.pi)
	tmp = 0
	if B <= -3.3e-61:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1e-225:
		tmp = t_0
	elif B <= 1.85e-180:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	elif B <= 3.25e-44:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(0.0) / pi))
	tmp = 0.0
	if (B <= -3.3e-61)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1e-225)
		tmp = t_0;
	elseif (B <= 1.85e-180)
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	elseif (B <= 3.25e-44)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(0.0) / pi);
	tmp = 0.0;
	if (B <= -3.3e-61)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1e-225)
		tmp = t_0;
	elseif (B <= 1.85e-180)
		tmp = 180.0 * (atan((A / -B)) / pi);
	elseif (B <= 3.25e-44)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3.3e-61], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1e-225], t$95$0, If[LessEqual[B, 1.85e-180], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.25e-44], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -3.29999999999999996e-61

   1. Initial program 50.0%

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

   3. Taylor expanded in B around -inf 60.9%

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

   if -3.29999999999999996e-61 < B < 9.9999999999999996e-226 or 1.85000000000000008e-180 < B < 3.25e-44

   1. Initial program 47.1%

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

      1. +-commutative 47.1%

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

      2. unpow2 47.1%

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

      3. unpow2 47.1%

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

      4. hypot-undefine 79.9%

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

      5. sub-neg 79.9%

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

      6. distribute-lft-in 44.5%

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

      7. hypot-undefine 41.7%

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

      8. unpow2 41.7%

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

      9. unpow2 41.7%

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

      10. +-commutative 41.7%

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

      11. unpow2 41.7%

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

      12. unpow2 41.7%

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

      13. hypot-define 44.5%

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

   4. Applied egg-rr 44.5%

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

   5. Taylor expanded in A around -inf 13.1%

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

      1. distribute-lft1-in 13.1%

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

      2. metadata-eval 13.1%

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

      3. mul0-lft 38.0%

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

   7. Simplified 38.0%

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

   if 9.9999999999999996e-226 < B < 1.85000000000000008e-180

   1. Initial program 77.7%

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

   3. Taylor expanded in C around 0 63.3%

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

      1. mul-1-neg 63.3%

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

      2. distribute-neg-frac2 63.3%

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

      3. +-commutative 63.3%

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

      4. unpow2 63.3%

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

      5. unpow2 63.3%

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

      6. hypot-define 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in A around 0 52.4%

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

   7. Taylor expanded in A around inf 51.2%

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

      1. neg-mul-1 51.2%

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

      2. distribute-neg-frac2 51.2%

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

   9. Simplified 51.2%

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

   if 3.25e-44 < B

   1. Initial program 43.8%

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

   3. Taylor expanded in B around inf 54.4%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.3 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 10^{-225}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-180}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.25 \cdot 10^{-44}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.7% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -0.0125:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -0.0125)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (* 180.0 (/ (atan (+ (/ (- C A) B) -1.0)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -0.0125) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -0.0125) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C - A) / B) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -0.0125:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C - A) / B) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -0.0125)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -0.0125)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	else
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -0.0125], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -0.012500000000000001

   1. Initial program 21.9%

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

   3. Taylor expanded in A around -inf 75.0%

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

      1. associate-*r/ 75.0%

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

   5. Simplified 75.0%

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

   if -0.012500000000000001 < A

   1. Initial program 58.5%

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

      1. +-commutative 58.5%

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

      2. unpow2 58.5%

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

      3. unpow2 58.5%

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

      4. hypot-undefine 87.0%

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

      5. sub-neg 87.0%

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

      6. distribute-lft-in 79.7%

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

      7. hypot-undefine 57.7%

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

      8. unpow2 57.7%

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

      9. unpow2 57.7%

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

      10. +-commutative 57.7%

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

      11. unpow2 57.7%

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

      12. unpow2 57.7%

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

      13. hypot-define 79.7%

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

   4. Applied egg-rr 79.7%

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

   5. Taylor expanded in B around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. associate--r+ 60.6%

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

      3. div-sub 60.6%

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

   7. Simplified 60.6%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -0.0125:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.0% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.6 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.6e-63)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.2e-42)
     (* 180.0 (/ (atan 0.0) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.6e-63) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.2e-42) {
		tmp = 180.0 * (atan(0.0) / ((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 <= -4.6e-63) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.2e-42) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4.6e-63:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.2e-42:
		tmp = 180.0 * (math.atan(0.0) / 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 <= -4.6e-63)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.2e-42)
		tmp = Float64(180.0 * Float64(atan(0.0) / 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 <= -4.6e-63)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.2e-42)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.6e-63], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.2e-42], N[(180.0 * N[(N[ArcTan[0.0], $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 < -4.6e-63

   1. Initial program 50.0%

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

   3. Taylor expanded in B around -inf 60.9%

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

   if -4.6e-63 < B < 2.20000000000000005e-42

   1. Initial program 51.1%

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

      1. +-commutative 51.1%

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

      2. unpow2 51.1%

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

      3. unpow2 51.1%

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

      4. hypot-undefine 80.5%

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

      5. sub-neg 80.5%

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

      6. distribute-lft-in 48.2%

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

      7. hypot-undefine 45.8%

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

      8. unpow2 45.8%

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

      9. unpow2 45.8%

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

      10. +-commutative 45.8%

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

      11. unpow2 45.8%

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

      12. unpow2 45.8%

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

      13. hypot-define 48.2%

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

   4. Applied egg-rr 48.2%

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

   5. Taylor expanded in A around -inf 12.4%

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

      1. distribute-lft1-in 12.4%

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

      2. metadata-eval 12.4%

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

      3. mul0-lft 35.0%

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

   7. Simplified 35.0%

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

   if 2.20000000000000005e-42 < B

   1. Initial program 43.8%

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

   3. Taylor expanded in B around inf 54.4%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.6 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-42}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 28.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 3.25 \cdot 10^{-44}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 3.25e-44) (* 180.0 (/ (atan 0.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 3.25e-44) {
		tmp = 180.0 * (atan(0.0) / ((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 <= 3.25e-44) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 3.25e-44:
		tmp = 180.0 * (math.atan(0.0) / 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 <= 3.25e-44)
		tmp = Float64(180.0 * Float64(atan(0.0) / 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 <= 3.25e-44)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 3.25e-44], N[(180.0 * N[(N[ArcTan[0.0], $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 < 3.25e-44

   1. Initial program 50.6%

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

      1. +-commutative 50.6%

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

      2. unpow2 50.6%

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

      3. unpow2 50.6%

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

      4. hypot-undefine 80.0%

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

      5. sub-neg 80.0%

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

      6. distribute-lft-in 61.0%

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

      7. hypot-undefine 47.5%

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

      8. unpow2 47.5%

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

      9. unpow2 47.5%

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

      10. +-commutative 47.5%

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

      11. unpow2 47.5%

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

      12. unpow2 47.5%

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

      13. hypot-define 61.0%

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

   4. Applied egg-rr 61.0%

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

   5. Taylor expanded in A around -inf 8.7%

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

      1. distribute-lft1-in 8.7%

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

      2. metadata-eval 8.7%

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

      3. mul0-lft 22.0%

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

   7. Simplified 22.0%

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

   if 3.25e-44 < B

   1. Initial program 43.8%

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

   3. Taylor expanded in B around inf 54.4%

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

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 3.25 \cdot 10^{-44}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 21.2% 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 48.6%

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

3. Taylor expanded in B around inf 20.2%

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

4. Final simplification 20.2%

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

Reproduce

herbie shell --seed 2024075 
(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)))