ABCF->ab-angle angle

Percentage Accurate: 53.3% → 79.2%

Time: 17.1s

Alternatives: 20

Speedup: 3.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.3% 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: 79.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.6 \cdot 10^{-60}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot B + -0.5 \cdot \frac{B \cdot C}{A}}{-A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.6e-60)
   (/ (* 180.0 (atan (/ (+ (* -0.5 B) (* -0.5 (/ (* B C) A))) (- 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 <= -8.6e-60) {
		tmp = (180.0 * atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -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 <= -8.6e-60) {
		tmp = (180.0 * Math.atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -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 <= -8.6e-60:
		tmp = (180.0 * math.atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -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 <= -8.6e-60)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(-0.5 * B) + Float64(-0.5 * Float64(Float64(B * C) / A))) / Float64(-A)))) / pi);
	else
		tmp = Float64(Float64(180.0 * 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 <= -8.6e-60)
		tmp = (180.0 * atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -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, -8.6e-60], N[(N[(180.0 * N[ArcTan[N[(N[(N[(-0.5 * B), $MachinePrecision] + N[(-0.5 * N[(N[(B * C), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-A)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -8.6000000000000001e-60

   1. Initial program 29.5%

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

      1. associate-*r/ 29.5%

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

   4. Applied egg-rr 51.6%

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

   5. Taylor expanded in A around -inf 75.7%

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

   if -8.6000000000000001e-60 < A

   1. Initial program 67.5%

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

      1. associate-*r/ 67.5%

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

   4. Applied egg-rr 87.1%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.6 \cdot 10^{-60}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot B + -0.5 \cdot \frac{B \cdot C}{A}}{-A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.6 \cdot 10^{-60}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot B + -0.5 \cdot \frac{B \cdot C}{A}}{-A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-52}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.6e-60)
   (/ (* 180.0 (atan (/ (+ (* -0.5 B) (* -0.5 (/ (* B C) A))) (- A)))) PI)
   (if (<= A 1.8e-52)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (/ (* -180.0 (atan (/ (+ A (hypot B A)) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.6e-60) {
		tmp = (180.0 * atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -A))) / ((double) M_PI);
	} else if (A <= 1.8e-52) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = (-180.0 * atan(((A + hypot(B, A)) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.6e-60) {
		tmp = (180.0 * Math.atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -A))) / Math.PI;
	} else if (A <= 1.8e-52) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = (-180.0 * Math.atan(((A + Math.hypot(B, A)) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.6e-60:
		tmp = (180.0 * math.atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -A))) / math.pi
	elif A <= 1.8e-52:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = (-180.0 * math.atan(((A + math.hypot(B, A)) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.6e-60)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(-0.5 * B) + Float64(-0.5 * Float64(Float64(B * C) / A))) / Float64(-A)))) / pi);
	elseif (A <= 1.8e-52)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(A + hypot(B, A)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.6e-60)
		tmp = (180.0 * atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -A))) / pi;
	elseif (A <= 1.8e-52)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = (-180.0 * atan(((A + hypot(B, A)) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.6e-60], N[(N[(180.0 * N[ArcTan[N[(N[(N[(-0.5 * B), $MachinePrecision] + N[(-0.5 * N[(N[(B * C), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-A)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.8e-52], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(-180.0 * N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.6000000000000001e-60

   1. Initial program 29.5%

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

      1. associate-*r/ 29.5%

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

   4. Applied egg-rr 51.6%

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

   5. Taylor expanded in A around -inf 75.7%

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

   if -8.6000000000000001e-60 < A < 1.79999999999999994e-52

   1. Initial program 60.2%

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

   3. Taylor expanded in A around 0 56.9%

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

      1. +-commutative 56.9%

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

      2. unpow2 56.9%

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

      3. unpow2 56.9%

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

      4. hypot-define 81.7%

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

   5. Simplified 81.7%

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

   if 1.79999999999999994e-52 < A

   1. Initial program 76.5%

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

   3. Taylor expanded in C around 0 73.1%

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

      1. associate-*r/ 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unpow2 73.1%

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

      4. unpow2 73.1%

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

      5. hypot-define 85.8%

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

   5. Simplified 85.8%

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

      1. associate-*r/ 85.9%

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

      2. distribute-frac-neg 85.9%

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

      3. atan-neg 85.9%

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

   7. Applied egg-rr 85.9%

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

      1. distribute-rgt-neg-out 85.9%

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

      2. distribute-lft-neg-in 85.9%

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

      3. metadata-eval 85.9%

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

      4. hypot-undefine 73.2%

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

      5. unpow2 73.2%

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

      6. unpow2 73.2%

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

      7. +-commutative 73.2%

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

      8. unpow2 73.2%

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

      9. unpow2 73.2%

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

      10. hypot-define 85.9%

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

   9. Simplified 85.9%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.6 \cdot 10^{-60}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot B + -0.5 \cdot \frac{B \cdot C}{A}}{-A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-52}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.2 \cdot 10^{-60}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot B + -0.5 \cdot \frac{B \cdot C}{A}}{-A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.9 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 + \frac{C - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.2e-60)
   (/ (* 180.0 (atan (/ (+ (* -0.5 B) (* -0.5 (/ (* B C) A))) (- A)))) PI)
   (if (<= A 5.9e-36)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (/ 180.0 (/ PI (atan (+ -1.0 (/ (- C A) B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.2e-60) {
		tmp = (180.0 * atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -A))) / ((double) M_PI);
	} else if (A <= 5.9e-36) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((-1.0 + ((C - A) / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.2e-60) {
		tmp = (180.0 * Math.atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -A))) / Math.PI;
	} else if (A <= 5.9e-36) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((-1.0 + ((C - A) / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.2e-60:
		tmp = (180.0 * math.atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -A))) / math.pi
	elif A <= 5.9e-36:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((-1.0 + ((C - A) / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.2e-60)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(-0.5 * B) + Float64(-0.5 * Float64(Float64(B * C) / A))) / Float64(-A)))) / pi);
	elseif (A <= 5.9e-36)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-1.0 + Float64(Float64(C - A) / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.2e-60)
		tmp = (180.0 * atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -A))) / pi;
	elseif (A <= 5.9e-36)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = 180.0 / (pi / atan((-1.0 + ((C - A) / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.2e-60], N[(N[(180.0 * N[ArcTan[N[(N[(N[(-0.5 * B), $MachinePrecision] + N[(-0.5 * N[(N[(B * C), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-A)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 5.9e-36], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(-1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.20000000000000025e-60

   1. Initial program 29.5%

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

      1. associate-*r/ 29.5%

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

   4. Applied egg-rr 51.6%

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

   5. Taylor expanded in A around -inf 75.7%

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

   if -8.20000000000000025e-60 < A < 5.89999999999999995e-36

   1. Initial program 59.1%

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

   3. Taylor expanded in A around 0 56.0%

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

      1. +-commutative 56.0%

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

      2. unpow2 56.0%

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

      3. unpow2 56.0%

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

      4. hypot-define 80.6%

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

   5. Simplified 80.6%

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

   if 5.89999999999999995e-36 < A

   1. Initial program 78.8%

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

      1. *-commutative 78.8%

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

      2. associate--l- 78.8%

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

      3. +-commutative 78.8%

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

      4. unpow2 78.8%

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

      5. unpow2 78.8%

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

      6. hypot-undefine 92.0%

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

      7. div-inv 92.0%

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

      8. clear-num 92.0%

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

      9. un-div-inv 92.0%

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

   4. Applied egg-rr 92.0%

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

   5. Taylor expanded in B around inf 79.5%

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

      1. +-commutative 79.5%

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

      2. associate--r+ 79.5%

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

      3. div-sub 79.5%

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

   7. Simplified 79.5%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.2 \cdot 10^{-60}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot B + -0.5 \cdot \frac{B \cdot C}{A}}{-A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.9 \cdot 10^{-36}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 + \frac{C - A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.6 \cdot 10^{-60}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot B + -0.5 \cdot \frac{B \cdot C}{A}}{-A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.6e-60)
   (/ (* 180.0 (atan (/ (+ (* -0.5 B) (* -0.5 (/ (* B C) A))) (- 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 <= -8.6e-60) {
		tmp = (180.0 * atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -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 <= -8.6e-60) {
		tmp = (180.0 * Math.atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -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 <= -8.6e-60:
		tmp = (180.0 * math.atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -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 <= -8.6e-60)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(-0.5 * B) + Float64(-0.5 * Float64(Float64(B * C) / A))) / Float64(-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 <= -8.6e-60)
		tmp = (180.0 * atan((((-0.5 * B) + (-0.5 * ((B * C) / A))) / -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, -8.6e-60], N[(N[(180.0 * N[ArcTan[N[(N[(N[(-0.5 * B), $MachinePrecision] + N[(-0.5 * N[(N[(B * C), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-A)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $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 < -8.6000000000000001e-60

   1. Initial program 29.5%

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

      1. associate-*r/ 29.5%

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

   4. Applied egg-rr 51.6%

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

   5. Taylor expanded in A around -inf 75.7%

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

   if -8.6000000000000001e-60 < A

   1. Initial program 67.5%

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

   3. Simplified 87.1%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.6 \cdot 10^{-60}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot B + -0.5 \cdot \frac{B \cdot C}{A}}{-A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -1.1 \cdot 10^{-306}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t\_0 + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{180 \cdot \left(-\tan^{-1} \left(-0.5 \cdot \frac{B + B \cdot \frac{C}{A}}{A}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + t\_0\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -1.1e-306)
     (/ (* 180.0 (atan (+ t_0 1.0))) PI)
     (if (<= B 8.5e+24)
       (/ (* 180.0 (- (atan (* -0.5 (/ (+ B (* B (/ C A))) A))))) PI)
       (/ (* 180.0 (atan (+ -1.0 t_0))) PI)))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.1e-306) {
		tmp = (180.0 * atan((t_0 + 1.0))) / ((double) M_PI);
	} else if (B <= 8.5e+24) {
		tmp = (180.0 * -atan((-0.5 * ((B + (B * (C / A))) / A)))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((-1.0 + t_0))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.1e-306) {
		tmp = (180.0 * Math.atan((t_0 + 1.0))) / Math.PI;
	} else if (B <= 8.5e+24) {
		tmp = (180.0 * -Math.atan((-0.5 * ((B + (B * (C / A))) / A)))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan((-1.0 + t_0))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -1.1e-306:
		tmp = (180.0 * math.atan((t_0 + 1.0))) / math.pi
	elif B <= 8.5e+24:
		tmp = (180.0 * -math.atan((-0.5 * ((B + (B * (C / A))) / A)))) / math.pi
	else:
		tmp = (180.0 * math.atan((-1.0 + t_0))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -1.1e-306)
		tmp = Float64(Float64(180.0 * atan(Float64(t_0 + 1.0))) / pi);
	elseif (B <= 8.5e+24)
		tmp = Float64(Float64(180.0 * Float64(-atan(Float64(-0.5 * Float64(Float64(B + Float64(B * Float64(C / A))) / A))))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 + t_0))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -1.1e-306)
		tmp = (180.0 * atan((t_0 + 1.0))) / pi;
	elseif (B <= 8.5e+24)
		tmp = (180.0 * -atan((-0.5 * ((B + (B * (C / A))) / A)))) / pi;
	else
		tmp = (180.0 * atan((-1.0 + t_0))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -1.1e-306], N[(N[(180.0 * N[ArcTan[N[(t$95$0 + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 8.5e+24], N[(N[(180.0 * (-N[ArcTan[N[(-0.5 * N[(N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.10000000000000008e-306

   1. Initial program 66.0%

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

      1. associate-*r/ 66.0%

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

   4. Applied egg-rr 80.7%

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

   5. Taylor expanded in B around -inf 73.9%

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

      1. associate--l+ 73.9%

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

      2. div-sub 73.9%

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

   7. Simplified 73.9%

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

   if -1.10000000000000008e-306 < B < 8.49999999999999959e24

   1. Initial program 47.0%

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

      1. associate-*r/ 47.0%

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

   4. Applied egg-rr 64.6%

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

   5. Taylor expanded in A around -inf 56.2%

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

      1. pow1 56.2%

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

      2. mul-1-neg 56.2%

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

      3. atan-neg 56.2%

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

      4. distribute-lft-out 56.2%

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

      5. associate-/l* 57.9%

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

   7. Applied egg-rr 57.9%

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

      1. unpow1 57.9%

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

      2. associate-/l* 57.9%

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

   9. Simplified 57.9%

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

   if 8.49999999999999959e24 < B

   1. Initial program 45.2%

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

      1. associate-*r/ 45.2%

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

   4. Applied egg-rr 82.1%

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

   5. Taylor expanded in B around inf 76.5%

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

      1. +-commutative 76.5%

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

      2. associate--r+ 76.5%

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

      3. div-sub 76.5%

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

   7. Simplified 76.5%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.1 \cdot 10^{-306}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{180 \cdot \left(-\tan^{-1} \left(-0.5 \cdot \frac{B + B \cdot \frac{C}{A}}{A}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.0% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.8 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-302}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{+19}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + B}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.8e-202)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (if (<= B 1.95e-302)
     (/ 180.0 (/ PI (atan (/ (* C 2.0) B))))
     (if (<= B 1.25e+19)
       (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
       (* 180.0 (/ (atan (/ (+ A B) (- B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.8e-202) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= 1.95e-302) {
		tmp = 180.0 / (((double) M_PI) / atan(((C * 2.0) / B)));
	} else if (B <= 1.25e+19) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 * (atan(((A + B) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.8e-202) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= 1.95e-302) {
		tmp = 180.0 / (Math.PI / Math.atan(((C * 2.0) / B)));
	} else if (B <= 1.25e+19) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 * (Math.atan(((A + B) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.8e-202:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= 1.95e-302:
		tmp = 180.0 / (math.pi / math.atan(((C * 2.0) / B)))
	elif B <= 1.25e+19:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = 180.0 * (math.atan(((A + B) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.8e-202)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= 1.95e-302)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C * 2.0) / B))));
	elseif (B <= 1.25e+19)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + B) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.8e-202)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= 1.95e-302)
		tmp = 180.0 / (pi / atan(((C * 2.0) / B)));
	elseif (B <= 1.25e+19)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 * (atan(((A + B) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.8e-202], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.95e-302], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.25e+19], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A + B), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.8000000000000001e-202

   1. Initial program 65.0%

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

   3. Taylor expanded in C around 0 51.0%

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

      1. associate-*r/ 51.0%

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

      2. mul-1-neg 51.0%

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

      3. unpow2 51.0%

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

      4. unpow2 51.0%

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

      5. hypot-define 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in B around -inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unsub-neg 58.8%

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

   8. Simplified 58.8%

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

   if -2.8000000000000001e-202 < B < 1.95e-302

   1. Initial program 69.8%

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

      1. *-commutative 69.8%

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

      2. associate--l- 69.4%

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

      3. +-commutative 69.4%

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

      4. unpow2 69.4%

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

      5. unpow2 69.4%

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

      6. hypot-undefine 75.3%

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

      7. div-inv 75.3%

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

      8. clear-num 75.3%

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

      9. un-div-inv 75.3%

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

   4. Applied egg-rr 79.6%

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

   5. Taylor expanded in C around -inf 65.0%

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

      1. *-commutative 65.0%

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

   7. Simplified 65.0%

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

   if 1.95e-302 < B < 1.25e19

   1. Initial program 48.4%

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

      1. associate-*l/ 48.4%

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

      2. *-lft-identity 48.4%

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

      3. +-commutative 48.4%

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

      4. unpow2 48.4%

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

      5. unpow2 48.4%

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

      6. hypot-define 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in A around -inf 49.1%

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

      1. associate-*r/ 49.1%

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

      2. associate-/l* 49.4%

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

   7. Applied egg-rr 49.4%

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

      1. *-commutative 49.4%

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

      2. associate-/l* 49.4%

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

      3. *-commutative 49.4%

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

      4. associate-/r* 45.0%

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

      5. associate-*l/ 45.0%

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

   9. Simplified 45.0%

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

   10. Taylor expanded in B around 0 48.9%

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

   if 1.25e19 < 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 C around 0 38.4%

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

      1. associate-*r/ 38.4%

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

      2. mul-1-neg 38.4%

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

      3. unpow2 38.4%

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

      4. unpow2 38.4%

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

      5. hypot-define 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in A around 0 68.0%

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

      1. +-commutative 68.0%

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

   8. Simplified 68.0%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.8 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{-302}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{+19}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + B}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.4% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -5.4 \cdot 10^{-307}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t\_0 + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B + \frac{B \cdot C}{A}}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + t\_0\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -5.4e-307)
     (/ (* 180.0 (atan (+ t_0 1.0))) PI)
     (if (<= B 8.5e+24)
       (* 180.0 (/ (atan (* 0.5 (/ (+ B (/ (* B C) A)) A))) PI))
       (/ (* 180.0 (atan (+ -1.0 t_0))) PI)))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -5.4e-307) {
		tmp = (180.0 * atan((t_0 + 1.0))) / ((double) M_PI);
	} else if (B <= 8.5e+24) {
		tmp = 180.0 * (atan((0.5 * ((B + ((B * C) / A)) / A))) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((-1.0 + t_0))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -5.4e-307) {
		tmp = (180.0 * Math.atan((t_0 + 1.0))) / Math.PI;
	} else if (B <= 8.5e+24) {
		tmp = 180.0 * (Math.atan((0.5 * ((B + ((B * C) / A)) / A))) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((-1.0 + t_0))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -5.4e-307:
		tmp = (180.0 * math.atan((t_0 + 1.0))) / math.pi
	elif B <= 8.5e+24:
		tmp = 180.0 * (math.atan((0.5 * ((B + ((B * C) / A)) / A))) / math.pi)
	else:
		tmp = (180.0 * math.atan((-1.0 + t_0))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -5.4e-307)
		tmp = Float64(Float64(180.0 * atan(Float64(t_0 + 1.0))) / pi);
	elseif (B <= 8.5e+24)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(Float64(B + Float64(Float64(B * C) / A)) / A))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 + t_0))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -5.4e-307)
		tmp = (180.0 * atan((t_0 + 1.0))) / pi;
	elseif (B <= 8.5e+24)
		tmp = 180.0 * (atan((0.5 * ((B + ((B * C) / A)) / A))) / pi);
	else
		tmp = (180.0 * atan((-1.0 + t_0))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -5.4e-307], N[(N[(180.0 * N[ArcTan[N[(t$95$0 + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 8.5e+24], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(N[(B + N[(N[(B * C), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -5.39999999999999971e-307

   1. Initial program 66.0%

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

      1. associate-*r/ 66.0%

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

   4. Applied egg-rr 80.7%

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

   5. Taylor expanded in B around -inf 73.9%

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

      1. associate--l+ 73.9%

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

      2. div-sub 73.9%

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

   7. Simplified 73.9%

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

   if -5.39999999999999971e-307 < B < 8.49999999999999959e24

   1. Initial program 47.0%

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

   3. Taylor expanded in A around -inf 56.2%

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

      1. associate-*r/ 56.2%

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

      2. mul-1-neg 56.2%

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

      3. distribute-lft-out 56.2%

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

      4. *-commutative 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in B around 0 56.2%

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

   if 8.49999999999999959e24 < B

   1. Initial program 45.2%

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

      1. associate-*r/ 45.2%

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

   4. Applied egg-rr 82.1%

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

   5. Taylor expanded in B around inf 76.5%

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

      1. +-commutative 76.5%

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

      2. associate--r+ 76.5%

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

      3. div-sub 76.5%

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

   7. Simplified 76.5%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.4 \cdot 10^{-307}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B + \frac{B \cdot C}{A}}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.4 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-301}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}}\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{+53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.4e-203)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (if (<= B 1.8e-301)
     (/ 180.0 (/ PI (atan (/ (* C 2.0) B))))
     (if (<= B 3.3e+53)
       (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.4e-203) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= 1.8e-301) {
		tmp = 180.0 / (((double) M_PI) / atan(((C * 2.0) / B)));
	} else if (B <= 3.3e+53) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.4e-203) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= 1.8e-301) {
		tmp = 180.0 / (Math.PI / Math.atan(((C * 2.0) / B)));
	} else if (B <= 3.3e+53) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -6.4e-203:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= 1.8e-301:
		tmp = 180.0 / (math.pi / math.atan(((C * 2.0) / B)))
	elif B <= 3.3e+53:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -6.4e-203)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= 1.8e-301)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C * 2.0) / B))));
	elseif (B <= 3.3e+53)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -6.4e-203)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= 1.8e-301)
		tmp = 180.0 / (pi / atan(((C * 2.0) / B)));
	elseif (B <= 3.3e+53)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -6.4e-203], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.8e-301], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.3e+53], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -6.40000000000000001e-203

   1. Initial program 65.0%

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

   3. Taylor expanded in C around 0 51.0%

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

      1. associate-*r/ 51.0%

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

      2. mul-1-neg 51.0%

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

      3. unpow2 51.0%

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

      4. unpow2 51.0%

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

      5. hypot-define 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in B around -inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unsub-neg 58.8%

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

   8. Simplified 58.8%

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

   if -6.40000000000000001e-203 < B < 1.80000000000000004e-301

   1. Initial program 69.8%

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

      1. *-commutative 69.8%

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

      2. associate--l- 69.4%

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

      3. +-commutative 69.4%

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

      4. unpow2 69.4%

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

      5. unpow2 69.4%

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

      6. hypot-undefine 75.3%

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

      7. div-inv 75.3%

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

      8. clear-num 75.3%

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

      9. un-div-inv 75.3%

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

   4. Applied egg-rr 79.6%

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

   5. Taylor expanded in C around -inf 65.0%

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

      1. *-commutative 65.0%

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

   7. Simplified 65.0%

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

   if 1.80000000000000004e-301 < B < 3.3000000000000002e53

   1. Initial program 49.7%

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

      1. associate-*l/ 49.7%

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

      2. *-lft-identity 49.7%

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

      3. +-commutative 49.7%

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

      4. unpow2 49.7%

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

      5. unpow2 49.7%

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

      6. hypot-define 65.9%

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

   3. Simplified 65.9%

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

   5. Taylor expanded in A around -inf 47.0%

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

      1. associate-*r/ 47.0%

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

      2. associate-/l* 47.3%

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

   7. Applied egg-rr 47.3%

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

      1. *-commutative 47.3%

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

      2. associate-/l* 47.3%

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

      3. *-commutative 47.3%

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

      4. associate-/r* 43.5%

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

      5. associate-*l/ 43.5%

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

   9. Simplified 43.5%

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

   10. Taylor expanded in B around 0 46.9%

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

   if 3.3000000000000002e53 < B

   1. Initial program 41.4%

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

   3. Taylor expanded in B around inf 68.5%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.4 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-301}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}}\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{+53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-301}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.8e-203)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (if (<= B 1.55e-301)
     (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
     (if (<= B 3.5e+57)
       (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.8e-203) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= 1.55e-301) {
		tmp = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	} else if (B <= 3.5e+57) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.8e-203) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= 1.55e-301) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else if (B <= 3.5e+57) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -6.8e-203:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= 1.55e-301:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	elif B <= 3.5e+57:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -6.8e-203)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= 1.55e-301)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	elseif (B <= 3.5e+57)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -6.8e-203)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= 1.55e-301)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	elseif (B <= 3.5e+57)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -6.8e-203], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.55e-301], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.5e+57], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -6.7999999999999998e-203

   1. Initial program 65.0%

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

   3. Taylor expanded in C around 0 51.0%

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

      1. associate-*r/ 51.0%

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

      2. mul-1-neg 51.0%

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

      3. unpow2 51.0%

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

      4. unpow2 51.0%

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

      5. hypot-define 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in B around -inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unsub-neg 58.8%

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

   8. Simplified 58.8%

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

   if -6.7999999999999998e-203 < B < 1.55000000000000007e-301

   1. Initial program 69.8%

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

   3. Taylor expanded in C around -inf 65.0%

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

      1. associate-*r/ 65.0%

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

      2. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   if 1.55000000000000007e-301 < B < 3.4999999999999997e57

   1. Initial program 49.7%

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

      1. associate-*l/ 49.7%

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

      2. *-lft-identity 49.7%

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

      3. +-commutative 49.7%

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

      4. unpow2 49.7%

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

      5. unpow2 49.7%

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

      6. hypot-define 65.9%

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

   3. Simplified 65.9%

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

   5. Taylor expanded in A around -inf 47.0%

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

      1. associate-*r/ 47.0%

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

      2. associate-/l* 47.3%

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

   7. Applied egg-rr 47.3%

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

      1. *-commutative 47.3%

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

      2. associate-/l* 47.3%

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

      3. *-commutative 47.3%

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

      4. associate-/r* 43.5%

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

      5. associate-*l/ 43.5%

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

   9. Simplified 43.5%

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

   10. Taylor expanded in B around 0 46.9%

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

   if 3.4999999999999997e57 < B

   1. Initial program 41.4%

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

   3. Taylor expanded in B around inf 68.5%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-301}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.8 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{+57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.6e-202)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (if (<= B 8.8e-302)
     (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
     (if (<= B 1.22e+57)
       (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.6e-202) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= 8.8e-302) {
		tmp = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	} else if (B <= 1.22e+57) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((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 <= -2.6e-202) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= 8.8e-302) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else if (B <= 1.22e+57) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.6e-202:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= 8.8e-302:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	elif B <= 1.22e+57:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / 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 <= -2.6e-202)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= 8.8e-302)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	elseif (B <= 1.22e+57)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / 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 <= -2.6e-202)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= 8.8e-302)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	elseif (B <= 1.22e+57)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.6e-202], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.8e-302], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.22e+57], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.60000000000000009e-202

   1. Initial program 65.0%

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

   3. Taylor expanded in C around 0 51.0%

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

      1. associate-*r/ 51.0%

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

      2. mul-1-neg 51.0%

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

      3. unpow2 51.0%

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

      4. unpow2 51.0%

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

      5. hypot-define 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in B around -inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unsub-neg 58.8%

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

   8. Simplified 58.8%

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

   if -2.60000000000000009e-202 < B < 8.8000000000000003e-302

   1. Initial program 69.8%

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

   3. Taylor expanded in C around -inf 65.0%

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

      1. associate-*r/ 65.0%

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

      2. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   if 8.8000000000000003e-302 < B < 1.22e57

   1. Initial program 49.7%

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

   3. Taylor expanded in A around -inf 46.8%

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

      1. associate-*r/ 46.8%

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

   5. Simplified 46.8%

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

   if 1.22e57 < B

   1. Initial program 41.4%

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

   3. Taylor expanded in B around inf 68.5%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-202}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.8 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.22 \cdot 10^{+57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq 9 \cdot 10^{-72}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t\_0 + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;\tan^{-1} \left(\frac{1}{\frac{\frac{A}{B}}{0.5}}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + t\_0\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B 9e-72)
     (/ (* 180.0 (atan (+ t_0 1.0))) PI)
     (if (<= B 8.5e+24)
       (* (atan (/ 1.0 (/ (/ A B) 0.5))) (/ 180.0 PI))
       (/ (* 180.0 (atan (+ -1.0 t_0))) PI)))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 9e-72) {
		tmp = (180.0 * atan((t_0 + 1.0))) / ((double) M_PI);
	} else if (B <= 8.5e+24) {
		tmp = atan((1.0 / ((A / B) / 0.5))) * (180.0 / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((-1.0 + t_0))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 9e-72) {
		tmp = (180.0 * Math.atan((t_0 + 1.0))) / Math.PI;
	} else if (B <= 8.5e+24) {
		tmp = Math.atan((1.0 / ((A / B) / 0.5))) * (180.0 / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((-1.0 + t_0))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= 9e-72:
		tmp = (180.0 * math.atan((t_0 + 1.0))) / math.pi
	elif B <= 8.5e+24:
		tmp = math.atan((1.0 / ((A / B) / 0.5))) * (180.0 / math.pi)
	else:
		tmp = (180.0 * math.atan((-1.0 + t_0))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= 9e-72)
		tmp = Float64(Float64(180.0 * atan(Float64(t_0 + 1.0))) / pi);
	elseif (B <= 8.5e+24)
		tmp = Float64(atan(Float64(1.0 / Float64(Float64(A / B) / 0.5))) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 + t_0))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= 9e-72)
		tmp = (180.0 * atan((t_0 + 1.0))) / pi;
	elseif (B <= 8.5e+24)
		tmp = atan((1.0 / ((A / B) / 0.5))) * (180.0 / pi);
	else
		tmp = (180.0 * atan((-1.0 + t_0))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, 9e-72], N[(N[(180.0 * N[ArcTan[N[(t$95$0 + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 8.5e+24], N[(N[ArcTan[N[(1.0 / N[(N[(A / B), $MachinePrecision] / 0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < 9e-72

   1. Initial program 64.9%

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

      1. associate-*r/ 64.9%

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

   4. Applied egg-rr 82.3%

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

   5. Taylor expanded in B around -inf 69.5%

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

      1. associate--l+ 69.5%

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

      2. div-sub 69.5%

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

   7. Simplified 69.5%

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

   if 9e-72 < B < 8.49999999999999959e24

   1. Initial program 27.9%

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

      1. associate-*l/ 27.9%

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

      2. *-lft-identity 27.9%

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

      3. +-commutative 27.9%

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

      4. unpow2 27.9%

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

      5. unpow2 27.9%

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

      6. hypot-define 30.1%

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

   3. Simplified 30.1%

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

   5. Taylor expanded in A around -inf 50.1%

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

      1. associate-*r/ 50.2%

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

      2. associate-/l* 50.8%

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

   7. Applied egg-rr 50.8%

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

      1. *-commutative 50.8%

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

      2. associate-/l* 50.8%

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

      3. *-commutative 50.8%

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

      4. associate-/r* 53.8%

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

      5. associate-*l/ 53.8%

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

   9. Simplified 53.8%

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

       1. *-un-lft-identity 53.8%

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

       2. associate-/l* 53.7%

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

   11. Applied egg-rr 53.7%

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

       1. *-lft-identity 53.7%

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

       2. metadata-eval 53.7%

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

       3. associate-*r/ 53.7%

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

       4. associate-*l* 53.7%

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

       5. *-commutative 53.7%

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

       6. associate-/r/ 53.9%

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

       7. associate-/r* 53.9%

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

       8. *-commutative 53.9%

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

       9. unpow2 53.9%

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

       10. times-frac 57.8%

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

       11. *-inverses 57.8%

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

   13. Simplified 57.8%

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

   if 8.49999999999999959e24 < B

   1. Initial program 45.2%

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

      1. associate-*r/ 45.2%

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

   4. Applied egg-rr 82.1%

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

   5. Taylor expanded in B around inf 76.5%

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

      1. +-commutative 76.5%

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

      2. associate--r+ 76.5%

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

      3. div-sub 76.5%

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

   7. Simplified 76.5%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 9 \cdot 10^{-72}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;\tan^{-1} \left(\frac{1}{\frac{\frac{A}{B}}{0.5}}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq 9 \cdot 10^{-71}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t\_0 + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{+26}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + t\_0\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B 9e-71)
     (/ (* 180.0 (atan (+ t_0 1.0))) PI)
     (if (<= B 5e+26)
       (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
       (/ (* 180.0 (atan (+ -1.0 t_0))) PI)))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 9e-71) {
		tmp = (180.0 * atan((t_0 + 1.0))) / ((double) M_PI);
	} else if (B <= 5e+26) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else {
		tmp = (180.0 * atan((-1.0 + t_0))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 9e-71) {
		tmp = (180.0 * Math.atan((t_0 + 1.0))) / Math.PI;
	} else if (B <= 5e+26) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = (180.0 * Math.atan((-1.0 + t_0))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= 9e-71:
		tmp = (180.0 * math.atan((t_0 + 1.0))) / math.pi
	elif B <= 5e+26:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = (180.0 * math.atan((-1.0 + t_0))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= 9e-71)
		tmp = Float64(Float64(180.0 * atan(Float64(t_0 + 1.0))) / pi);
	elseif (B <= 5e+26)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 + t_0))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= 9e-71)
		tmp = (180.0 * atan((t_0 + 1.0))) / pi;
	elseif (B <= 5e+26)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = (180.0 * atan((-1.0 + t_0))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, 9e-71], N[(N[(180.0 * N[ArcTan[N[(t$95$0 + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 5e+26], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < 9.0000000000000004e-71

   1. Initial program 64.9%

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

      1. associate-*r/ 64.9%

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

   4. Applied egg-rr 82.3%

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

   5. Taylor expanded in B around -inf 69.5%

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

      1. associate--l+ 69.5%

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

      2. div-sub 69.5%

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

   7. Simplified 69.5%

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

   if 9.0000000000000004e-71 < B < 5.0000000000000001e26

   1. Initial program 27.9%

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

      1. associate-*l/ 27.9%

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

      2. *-lft-identity 27.9%

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

      3. +-commutative 27.9%

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

      4. unpow2 27.9%

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

      5. unpow2 27.9%

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

      6. hypot-define 30.1%

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

   3. Simplified 30.1%

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

   5. Taylor expanded in A around -inf 50.1%

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

      1. associate-*r/ 50.2%

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

      2. associate-/l* 50.8%

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

   7. Applied egg-rr 50.8%

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

      1. *-commutative 50.8%

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

      2. associate-/l* 50.8%

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

      3. *-commutative 50.8%

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

      4. associate-/r* 53.8%

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

      5. associate-*l/ 53.8%

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

   9. Simplified 53.8%

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

   10. Taylor expanded in B around 0 57.8%

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

   if 5.0000000000000001e26 < B

   1. Initial program 45.2%

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

      1. associate-*r/ 45.2%

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

   4. Applied egg-rr 82.1%

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

   5. Taylor expanded in B around inf 76.5%

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

      1. +-commutative 76.5%

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

      2. associate--r+ 76.5%

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

      3. div-sub 76.5%

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

   7. Simplified 76.5%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 9 \cdot 10^{-71}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{+26}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq 5.5 \cdot 10^{-71}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t\_0 + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 + t\_0\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B 5.5e-71)
     (/ (* 180.0 (atan (+ t_0 1.0))) PI)
     (if (<= B 8.5e+24)
       (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
       (/ 180.0 (/ PI (atan (+ -1.0 t_0))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 5.5e-71) {
		tmp = (180.0 * atan((t_0 + 1.0))) / ((double) M_PI);
	} else if (B <= 8.5e+24) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((-1.0 + t_0)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 5.5e-71) {
		tmp = (180.0 * Math.atan((t_0 + 1.0))) / Math.PI;
	} else if (B <= 8.5e+24) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((-1.0 + t_0)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= 5.5e-71:
		tmp = (180.0 * math.atan((t_0 + 1.0))) / math.pi
	elif B <= 8.5e+24:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = 180.0 / (math.pi / math.atan((-1.0 + t_0)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= 5.5e-71)
		tmp = Float64(Float64(180.0 * atan(Float64(t_0 + 1.0))) / pi);
	elseif (B <= 8.5e+24)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-1.0 + t_0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= 5.5e-71)
		tmp = (180.0 * atan((t_0 + 1.0))) / pi;
	elseif (B <= 8.5e+24)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 / (pi / atan((-1.0 + t_0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, 5.5e-71], N[(N[(180.0 * N[ArcTan[N[(t$95$0 + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 8.5e+24], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(-1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < 5.4999999999999997e-71

   1. Initial program 64.9%

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

      1. associate-*r/ 64.9%

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

   4. Applied egg-rr 82.3%

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

   5. Taylor expanded in B around -inf 69.5%

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

      1. associate--l+ 69.5%

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

      2. div-sub 69.5%

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

   7. Simplified 69.5%

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

   if 5.4999999999999997e-71 < B < 8.49999999999999959e24

   1. Initial program 27.9%

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

      1. associate-*l/ 27.9%

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

      2. *-lft-identity 27.9%

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

      3. +-commutative 27.9%

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

      4. unpow2 27.9%

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

      5. unpow2 27.9%

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

      6. hypot-define 30.1%

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

   3. Simplified 30.1%

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

   5. Taylor expanded in A around -inf 50.1%

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

      1. associate-*r/ 50.2%

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

      2. associate-/l* 50.8%

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

   7. Applied egg-rr 50.8%

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

      1. *-commutative 50.8%

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

      2. associate-/l* 50.8%

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

      3. *-commutative 50.8%

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

      4. associate-/r* 53.8%

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

      5. associate-*l/ 53.8%

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

   9. Simplified 53.8%

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

   10. Taylor expanded in B around 0 57.8%

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

   if 8.49999999999999959e24 < B

   1. Initial program 45.2%

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

      1. *-commutative 45.2%

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

      2. associate--l- 45.2%

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

      3. +-commutative 45.2%

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

      4. unpow2 45.2%

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

      5. unpow2 45.2%

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

      6. hypot-undefine 82.1%

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

      7. div-inv 82.1%

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

      8. clear-num 82.0%

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

      9. un-div-inv 82.0%

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

   4. Applied egg-rr 82.0%

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

   5. Taylor expanded in B around inf 76.5%

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

      1. +-commutative 76.5%

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

      2. associate--r+ 76.5%

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

      3. div-sub 76.5%

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

   7. Simplified 76.5%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 5.5 \cdot 10^{-71}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 + \frac{C - A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq 5.5 \cdot 10^{-71}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_0 + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 + t\_0\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B 5.5e-71)
     (* 180.0 (/ (atan (+ t_0 1.0)) PI))
     (if (<= B 8.5e+24)
       (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
       (/ 180.0 (/ PI (atan (+ -1.0 t_0))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 5.5e-71) {
		tmp = 180.0 * (atan((t_0 + 1.0)) / ((double) M_PI));
	} else if (B <= 8.5e+24) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((-1.0 + t_0)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= 5.5e-71) {
		tmp = 180.0 * (Math.atan((t_0 + 1.0)) / Math.PI);
	} else if (B <= 8.5e+24) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((-1.0 + t_0)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= 5.5e-71:
		tmp = 180.0 * (math.atan((t_0 + 1.0)) / math.pi)
	elif B <= 8.5e+24:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = 180.0 / (math.pi / math.atan((-1.0 + t_0)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= 5.5e-71)
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 + 1.0)) / pi));
	elseif (B <= 8.5e+24)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-1.0 + t_0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= 5.5e-71)
		tmp = 180.0 * (atan((t_0 + 1.0)) / pi);
	elseif (B <= 8.5e+24)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 / (pi / atan((-1.0 + t_0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, 5.5e-71], N[(180.0 * N[(N[ArcTan[N[(t$95$0 + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.5e+24], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(-1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < 5.4999999999999997e-71

   1. Initial program 64.9%

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

   3. Taylor expanded in B around -inf 69.5%

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

      1. associate--l+ 69.5%

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

      2. div-sub 69.5%

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

   5. Simplified 69.5%

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

   if 5.4999999999999997e-71 < B < 8.49999999999999959e24

   1. Initial program 27.9%

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

      1. associate-*l/ 27.9%

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

      2. *-lft-identity 27.9%

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

      3. +-commutative 27.9%

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

      4. unpow2 27.9%

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

      5. unpow2 27.9%

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

      6. hypot-define 30.1%

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

   3. Simplified 30.1%

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

   5. Taylor expanded in A around -inf 50.1%

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

      1. associate-*r/ 50.2%

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

      2. associate-/l* 50.8%

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

   7. Applied egg-rr 50.8%

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

      1. *-commutative 50.8%

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

      2. associate-/l* 50.8%

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

      3. *-commutative 50.8%

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

      4. associate-/r* 53.8%

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

      5. associate-*l/ 53.8%

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

   9. Simplified 53.8%

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

   10. Taylor expanded in B around 0 57.8%

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

   if 8.49999999999999959e24 < B

   1. Initial program 45.2%

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

      1. *-commutative 45.2%

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

      2. associate--l- 45.2%

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

      3. +-commutative 45.2%

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

      4. unpow2 45.2%

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

      5. unpow2 45.2%

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

      6. hypot-undefine 82.1%

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

      7. div-inv 82.1%

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

      8. clear-num 82.0%

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

      9. un-div-inv 82.0%

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

   4. Applied egg-rr 82.0%

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

   5. Taylor expanded in B around inf 76.5%

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

      1. +-commutative 76.5%

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

      2. associate--r+ 76.5%

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

      3. div-sub 76.5%

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

   7. Simplified 76.5%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 5.5 \cdot 10^{-71}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 + \frac{C - A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 9 \cdot 10^{-71}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{+19}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + B}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 9e-71)
   (* 180.0 (/ (atan (+ (/ (- C A) B) 1.0)) PI))
   (if (<= B 1.25e+19)
     (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
     (* 180.0 (/ (atan (/ (+ A B) (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 9e-71) {
		tmp = 180.0 * (atan((((C - A) / B) + 1.0)) / ((double) M_PI));
	} else if (B <= 1.25e+19) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 * (atan(((A + B) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 9e-71) {
		tmp = 180.0 * (Math.atan((((C - A) / B) + 1.0)) / Math.PI);
	} else if (B <= 1.25e+19) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 * (Math.atan(((A + B) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 9e-71:
		tmp = 180.0 * (math.atan((((C - A) / B) + 1.0)) / math.pi)
	elif B <= 1.25e+19:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = 180.0 * (math.atan(((A + B) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 9e-71)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + 1.0)) / pi));
	elseif (B <= 1.25e+19)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + B) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 9e-71)
		tmp = 180.0 * (atan((((C - A) / B) + 1.0)) / pi);
	elseif (B <= 1.25e+19)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 * (atan(((A + B) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 9e-71], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.25e+19], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A + B), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 9.0000000000000004e-71

   1. Initial program 64.9%

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

   3. Taylor expanded in B around -inf 69.5%

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

      1. associate--l+ 69.5%

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

      2. div-sub 69.5%

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

   5. Simplified 69.5%

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

   if 9.0000000000000004e-71 < B < 1.25e19

   1. Initial program 30.1%

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

      1. associate-*l/ 30.1%

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

      2. *-lft-identity 30.1%

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

      3. +-commutative 30.1%

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

      4. unpow2 30.1%

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

      5. unpow2 30.1%

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

      6. hypot-define 32.4%

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

   3. Simplified 32.4%

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

   5. Taylor expanded in A around -inf 54.3%

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

      1. associate-*r/ 54.4%

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

      2. associate-/l* 55.2%

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

   7. Applied egg-rr 55.2%

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

      1. *-commutative 55.2%

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

      2. associate-/l* 55.1%

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

      3. *-commutative 55.1%

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

      4. associate-/r* 58.4%

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

      5. associate-*l/ 58.4%

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

   9. Simplified 58.4%

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

   10. Taylor expanded in B around 0 62.8%

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

   if 1.25e19 < 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 C around 0 38.4%

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

      1. associate-*r/ 38.4%

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

      2. mul-1-neg 38.4%

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

      3. unpow2 38.4%

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

      4. unpow2 38.4%

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

      5. hypot-define 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in A around 0 68.0%

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

      1. +-commutative 68.0%

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

   8. Simplified 68.0%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 9 \cdot 10^{-71}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{+19}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + B}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.2 \cdot 10^{-144}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.68 \cdot 10^{-102}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.2e-144)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.68e-102)
     (/ (* 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 <= -1.2e-144) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.68e-102) {
		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 <= -1.2e-144) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.68e-102) {
		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 <= -1.2e-144:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.68e-102:
		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 <= -1.2e-144)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.68e-102)
		tmp = Float64(Float64(180.0 * 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 <= -1.2e-144)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.68e-102)
		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, -1.2e-144], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.68e-102], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.19999999999999997e-144

   1. Initial program 66.0%

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

   3. Taylor expanded in B around -inf 46.5%

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

   if -1.19999999999999997e-144 < B < 1.68000000000000004e-102

   1. Initial program 60.5%

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

      1. associate-*r/ 60.5%

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

   4. Applied egg-rr 81.5%

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

      1. div-sub 54.4%

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

   6. Applied egg-rr 54.4%

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

   7. Taylor expanded in C around inf 14.4%

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

      1. distribute-lft1-in 14.4%

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

      2. metadata-eval 14.4%

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

      3. mul0-lft 30.1%

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

      4. metadata-eval 30.1%

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

   9. Simplified 30.1%

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

   if 1.68000000000000004e-102 < B

   1. Initial program 43.6%

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

   3. Taylor expanded in B around inf 44.5%

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

Alternative 17: 53.1% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.6 \cdot 10^{-104}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.6e-104)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.6e-104) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((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 <= -6.6e-104) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / 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 <= -6.6e-104:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / 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 <= -6.6e-104)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.6e-104)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.6e-104], 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[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -6.60000000000000004e-104

   1. Initial program 31.6%

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

   3. Taylor expanded in A around -inf 63.2%

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

      1. associate-*r/ 63.2%

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

   5. Simplified 63.2%

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

   if -6.60000000000000004e-104 < A

   1. Initial program 68.4%

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

   3. Taylor expanded in C around 0 52.3%

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

      1. associate-*r/ 52.3%

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

      2. mul-1-neg 52.3%

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

      3. unpow2 52.3%

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

      4. unpow2 52.3%

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

      5. hypot-define 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in B around -inf 50.6%

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

      1. mul-1-neg 50.6%

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

      2. unsub-neg 50.6%

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

   8. Simplified 50.6%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.6 \cdot 10^{-104}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.0% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 6.4 \cdot 10^{+66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 6.4e+66)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 6.4e+66) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 6.4e+66) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 6.4e+66:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 6.4e+66)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 6.4e+66)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 6.4e+66], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $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 < 6.3999999999999999e66

   1. Initial program 61.3%

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

   3. Taylor expanded in C around 0 45.2%

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

      1. associate-*r/ 45.2%

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

      2. mul-1-neg 45.2%

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

      3. unpow2 45.2%

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

      4. unpow2 45.2%

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

      5. hypot-define 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in B around -inf 47.1%

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

      1. mul-1-neg 47.1%

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

      2. unsub-neg 47.1%

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

   8. Simplified 47.1%

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

   if 6.3999999999999999e66 < B

   1. Initial program 38.9%

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

   3. Taylor expanded in B around inf 70.5%

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

Alternative 19: 40.1% accurate, 3.8× speedup

Math

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

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -4.999999999999985e-310

   1. Initial program 65.6%

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

   3. Taylor expanded in B around -inf 37.7%

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

   if -4.999999999999985e-310 < B

   1. Initial program 46.5%

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

   3. Taylor expanded in B around inf 36.0%

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

Alternative 20: 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 57.1%

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

3. Taylor expanded in B around inf 17.0%

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

Reproduce

herbie shell --seed 2024145 
(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)))