ABCF->ab-angle angle

Percentage Accurate: 53.5% → 81.6%

Time: 34.9s

Alternatives: 26

Speedup: 3.4×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.6 \cdot 10^{+141}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-1}{B} \cdot \left(\left(A - C\right) + \mathsf{hypot}\left(A - C, B\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.6e+141)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (* (/ 180.0 PI) (atan (* (/ -1.0 B) (+ (- A C) (hypot (- A C) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.6e+141) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((-1.0 / B) * ((A - C) + hypot((A - C), B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.6e+141) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((-1.0 / B) * ((A - C) + Math.hypot((A - C), B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.6e+141:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((-1.0 / B) * ((A - C) + math.hypot((A - C), B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.6e+141)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(-1.0 / B) * Float64(Float64(A - C) + hypot(Float64(A - C), B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.6e+141)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	else
		tmp = (180.0 / pi) * atan(((-1.0 / B) * ((A - C) + hypot((A - C), B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.6e+141], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(-1.0 / B), $MachinePrecision] * N[(N[(A - C), $MachinePrecision] + N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -5.59999999999999982e141

   1. Initial program 9.1%

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

   3. Taylor expanded in A around -inf 84.2%

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

      1. associate-*r/ 84.2%

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

   5. Simplified 84.2%

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

   if -5.59999999999999982e141 < A

   1. Initial program 66.5%

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

   3. Taylor expanded in B around 0 65.6%

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

   5. Simplified 83.4%

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

      1. div-inv 83.5%

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

      2. hypot-undefine 65.6%

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

      3. unpow2 65.6%

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

      4. unpow2 65.6%

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

      5. +-commutative 65.6%

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

      6. associate--l- 66.6%

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

      7. *-commutative 66.6%

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

      8. unpow2 66.6%

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

      9. unpow2 66.6%

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

      10. hypot-define 84.4%

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

   7. Applied egg-rr 84.4%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.6 \cdot 10^{+141}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-1}{B} \cdot \left(\left(A - C\right) + \mathsf{hypot}\left(A - C, B\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.05 \cdot 10^{+138}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.7 \cdot 10^{-54}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.05e+138)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 3.7e-54)
     (* (/ 180.0 PI) (atan (* (/ 1.0 B) (- C (hypot B C)))))
     (* 180.0 (/ (atan (/ (+ A (hypot B A)) (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.05e+138) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 3.7e-54) {
		tmp = (180.0 / ((double) M_PI)) * atan(((1.0 / B) * (C - hypot(B, C))));
	} 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 <= -1.05e+138) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 3.7e-54) {
		tmp = (180.0 / Math.PI) * Math.atan(((1.0 / B) * (C - Math.hypot(B, C))));
	} 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 <= -1.05e+138:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 3.7e-54:
		tmp = (180.0 / math.pi) * math.atan(((1.0 / B) * (C - math.hypot(B, C))))
	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 <= -1.05e+138)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 3.7e-54)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(1.0 / B) * Float64(C - hypot(B, C)))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.05e+138)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 3.7e-54)
		tmp = (180.0 / pi) * atan(((1.0 / B) * (C - hypot(B, C))));
	else
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.05e+138], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.7e-54], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.05000000000000003e138

   1. Initial program 9.1%

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

   3. Taylor expanded in A around -inf 84.2%

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

      1. associate-*r/ 84.2%

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

   5. Simplified 84.2%

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

   if -1.05000000000000003e138 < A < 3.7000000000000003e-54

   1. Initial program 60.0%

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

   3. Taylor expanded in B around 0 58.5%

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

   5. Simplified 78.0%

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

      1. div-inv 78.0%

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

      2. hypot-undefine 58.5%

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

      3. unpow2 58.5%

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

      4. unpow2 58.5%

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

      5. +-commutative 58.5%

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

      6. associate--l- 60.0%

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

      7. *-commutative 60.0%

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

      8. unpow2 60.0%

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

      9. unpow2 60.0%

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

      10. hypot-define 79.5%

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

   7. Applied egg-rr 79.5%

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

   8. Taylor expanded in A around 0 56.4%

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

      1. unpow2 56.4%

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

      2. unpow2 56.4%

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

      3. hypot-define 75.7%

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

   10. Simplified 75.7%

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

   if 3.7000000000000003e-54 < A

   1. Initial program 78.3%

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

   3. Taylor expanded in C around 0 76.3%

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

      1. mul-1-neg 76.3%

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

      2. distribute-neg-frac2 76.3%

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

      3. +-commutative 76.3%

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

      4. unpow2 76.3%

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

      5. unpow2 76.3%

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

      6. hypot-define 88.8%

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

   5. Simplified 88.8%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.05 \cdot 10^{+138}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.7 \cdot 10^{-54}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.25 \cdot 10^{+134}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.25e+134)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 4.2e-122)
     (* (/ 180.0 PI) (atan (* (/ 1.0 B) (- C (hypot B C)))))
     (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B A))) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.25e+134) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 4.2e-122) {
		tmp = (180.0 / ((double) M_PI)) * atan(((1.0 / B) * (C - hypot(B, C))));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(B, A))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.25e+134) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 4.2e-122) {
		tmp = (180.0 / Math.PI) * Math.atan(((1.0 / B) * (C - Math.hypot(B, C))));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, A))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.25e+134:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 4.2e-122:
		tmp = (180.0 / math.pi) * math.atan(((1.0 / B) * (C - math.hypot(B, C))))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(B, A))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.25e+134)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 4.2e-122)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(1.0 / B) * Float64(C - hypot(B, C)))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(B, A))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.25e+134)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 4.2e-122)
		tmp = (180.0 / pi) * atan(((1.0 / B) * (C - hypot(B, C))));
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(B, A))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.25e+134], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.2e-122], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.24999999999999995e134

   1. Initial program 9.1%

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

   3. Taylor expanded in A around -inf 84.2%

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

      1. associate-*r/ 84.2%

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

   5. Simplified 84.2%

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

   if -1.24999999999999995e134 < A < 4.19999999999999985e-122

   1. Initial program 58.5%

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

   3. Taylor expanded in B around 0 56.9%

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

   5. Simplified 76.5%

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

      1. div-inv 76.6%

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

      2. hypot-undefine 56.9%

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

      3. unpow2 56.9%

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

      4. unpow2 56.9%

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

      5. +-commutative 56.9%

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

      6. associate--l- 58.5%

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

      7. *-commutative 58.5%

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

      8. unpow2 58.5%

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

      9. unpow2 58.5%

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

      10. hypot-define 78.1%

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

   7. Applied egg-rr 78.1%

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

   8. Taylor expanded in A around 0 55.3%

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

      1. unpow2 55.3%

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

      2. unpow2 55.3%

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

      3. hypot-define 74.6%

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

   10. Simplified 74.6%

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

   if 4.19999999999999985e-122 < A

   1. Initial program 78.7%

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

   3. Taylor expanded in B around 0 78.7%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in C around 0 78.6%

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

      1. +-commutative 78.6%

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

      2. unpow2 78.6%

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

      3. unpow2 78.6%

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

      4. hypot-define 92.0%

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

   8. Simplified 92.0%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.25 \cdot 10^{+134}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(C - \mathsf{hypot}\left(B, C\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4 \cdot 10^{+136}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4e+136)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 3.5e-55)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (/ (+ A (hypot B A)) (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4e+136) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 3.5e-55) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4e+136) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 3.5e-55) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(B, A)) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4e+136:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 3.5e-55:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A + math.hypot(B, A)) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4e+136)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 3.5e-55)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4e+136)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 3.5e-55)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4e+136], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.5e-55], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -4.00000000000000023e136

   1. Initial program 9.1%

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

   3. Taylor expanded in A around -inf 84.2%

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

      1. associate-*r/ 84.2%

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

   5. Simplified 84.2%

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

   if -4.00000000000000023e136 < A < 3.50000000000000025e-55

   1. Initial program 60.0%

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

   3. Taylor expanded in A around 0 56.4%

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

      1. unpow2 56.4%

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

      2. unpow2 56.4%

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

      3. hypot-define 75.7%

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

   5. Simplified 75.7%

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

   if 3.50000000000000025e-55 < A

   1. Initial program 78.3%

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

   3. Taylor expanded in C around 0 76.3%

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

      1. mul-1-neg 76.3%

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

      2. distribute-neg-frac2 76.3%

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

      3. +-commutative 76.3%

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

      4. unpow2 76.3%

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

      5. unpow2 76.3%

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

      6. hypot-define 88.8%

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

   5. Simplified 88.8%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4 \cdot 10^{+136}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.2 \cdot 10^{+137}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.28 \cdot 10^{+33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.2e+137)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (<= A 1.28e+33)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (/ 1.0 (/ (/ PI 180.0) (atan (/ (- (- C B) A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.2e+137) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 1.28e+33) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((((C - B) - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.2e+137) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 1.28e+33) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((((C - B) - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.2e+137:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 1.28e+33:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((((C - B) - A) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.2e+137)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 1.28e+33)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(Float64(Float64(C - B) - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.2e+137)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 1.28e+33)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 1.0 / ((pi / 180.0) / atan((((C - B) - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.2e+137], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.28e+33], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.20000000000000019e137

   1. Initial program 9.1%

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

   3. Taylor expanded in A around -inf 84.2%

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

      1. associate-*r/ 84.2%

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

   5. Simplified 84.2%

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

   if -3.20000000000000019e137 < A < 1.28e33

   1. Initial program 62.7%

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

   3. Taylor expanded in A around 0 57.3%

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

      1. unpow2 57.3%

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

      2. unpow2 57.3%

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

      3. hypot-define 75.2%

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

   5. Simplified 75.2%

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

   if 1.28e33 < 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

   4. Applied egg-rr 93.8%

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

      1. inv-pow 93.8%

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

      2. associate-/r* 93.8%

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

   6. Applied egg-rr 93.8%

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

   8. Simplified 93.8%

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

   9. Taylor expanded in B around inf 86.2%

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

       1. mul-1-neg 86.2%

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

       2. unsub-neg 86.2%

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

   11. Simplified 86.2%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.2 \cdot 10^{+137}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.28 \cdot 10^{+33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.3 \cdot 10^{+133}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.3e+133)
   (* 180.0 (/ (atan (/ (* 0.5 B) 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 <= -4.3e+133) {
		tmp = 180.0 * (atan(((0.5 * B) / 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 <= -4.3e+133) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / 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 <= -4.3e+133:
		tmp = 180.0 * (math.atan(((0.5 * B) / 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 <= -4.3e+133)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / 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 <= -4.3e+133)
		tmp = 180.0 * (atan(((0.5 * B) / 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, -4.3e+133], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -4.29999999999999994e133

   1. Initial program 9.1%

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

   3. Taylor expanded in A around -inf 84.2%

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

      1. associate-*r/ 84.2%

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

   5. Simplified 84.2%

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

   if -4.29999999999999994e133 < A

   1. Initial program 66.5%

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

   3. Simplified 83.4%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.3 \cdot 10^{+133}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.16 \cdot 10^{+141}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.16e+141)
   (* 180.0 (/ (atan (/ (* 0.5 B) 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 <= -1.16e+141) {
		tmp = 180.0 * (atan(((0.5 * B) / 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 <= -1.16e+141) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / 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 <= -1.16e+141:
		tmp = 180.0 * (math.atan(((0.5 * B) / 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 <= -1.16e+141)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.16e+141)
		tmp = 180.0 * (atan(((0.5 * B) / 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, -1.16e+141], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.16e141

   1. Initial program 9.1%

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

   3. Taylor expanded in A around -inf 84.2%

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

      1. associate-*r/ 84.2%

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

   5. Simplified 84.2%

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

   if -1.16e141 < A

   1. Initial program 66.5%

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

   3. Simplified 84.4%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.16 \cdot 10^{+141}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{if}\;A \leq -2.45 \cdot 10^{+88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2700000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -2.2 \cdot 10^{-64}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 4.8 \cdot 10^{-271} \lor \neg \left(A \leq 3.7 \cdot 10^{-164}\right) \land A \leq 1.02 \cdot 10^{-131}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI))))
   (if (<= A -2.45e+88)
     (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
     (if (<= A -2700000.0)
       t_0
       (if (<= A -2.2e-64)
         (* 180.0 (/ (atan 1.0) PI))
         (if (or (<= A 4.8e-271) (and (not (<= A 3.7e-164)) (<= A 1.02e-131)))
           t_0
           (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	double tmp;
	if (A <= -2.45e+88) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= -2700000.0) {
		tmp = t_0;
	} else if (A <= -2.2e-64) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if ((A <= 4.8e-271) || (!(A <= 3.7e-164) && (A <= 1.02e-131))) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	double tmp;
	if (A <= -2.45e+88) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= -2700000.0) {
		tmp = t_0;
	} else if (A <= -2.2e-64) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if ((A <= 4.8e-271) || (!(A <= 3.7e-164) && (A <= 1.02e-131))) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	tmp = 0
	if A <= -2.45e+88:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= -2700000.0:
		tmp = t_0
	elif A <= -2.2e-64:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif (A <= 4.8e-271) or (not (A <= 3.7e-164) and (A <= 1.02e-131)):
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi))
	tmp = 0.0
	if (A <= -2.45e+88)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= -2700000.0)
		tmp = t_0;
	elseif (A <= -2.2e-64)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif ((A <= 4.8e-271) || (!(A <= 3.7e-164) && (A <= 1.02e-131)))
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C / B) + -1.0)) / pi);
	tmp = 0.0;
	if (A <= -2.45e+88)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= -2700000.0)
		tmp = t_0;
	elseif (A <= -2.2e-64)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif ((A <= 4.8e-271) || (~((A <= 3.7e-164)) && (A <= 1.02e-131)))
		tmp = t_0;
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -2.45e+88], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2700000.0], t$95$0, If[LessEqual[A, -2.2e-64], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[A, 4.8e-271], And[N[Not[LessEqual[A, 3.7e-164]], $MachinePrecision], LessEqual[A, 1.02e-131]]], t$95$0, N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -2.4500000000000001e88

   1. Initial program 17.3%

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

   3. Taylor expanded in A around -inf 74.5%

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

      1. associate-*r/ 74.5%

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

   5. Simplified 74.5%

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

   if -2.4500000000000001e88 < A < -2.7e6 or -2.2e-64 < A < 4.8000000000000005e-271 or 3.6999999999999999e-164 < A < 1.02000000000000001e-131

   1. Initial program 58.3%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in B around inf 53.1%

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

      1. +-commutative 53.1%

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

   7. Simplified 53.1%

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

   8. Taylor expanded in A around 0 52.4%

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

      1. div-sub 52.4%

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

      2. sub-neg 52.4%

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

      3. *-inverses 52.4%

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

      4. metadata-eval 52.4%

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

   10. Simplified 52.4%

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

   if -2.7e6 < A < -2.2e-64

   1. Initial program 66.1%

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

   3. Taylor expanded in B around -inf 66.0%

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

   if 4.8000000000000005e-271 < A < 3.6999999999999999e-164 or 1.02000000000000001e-131 < A

   1. Initial program 75.5%

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

   3. Taylor expanded in C around 0 70.9%

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

      1. mul-1-neg 70.9%

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

      2. distribute-neg-frac2 70.9%

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

      3. +-commutative 70.9%

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

      4. unpow2 70.9%

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

      5. unpow2 70.9%

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

      6. hypot-define 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in B around -inf 70.0%

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

      1. mul-1-neg 70.0%

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

      2. unsub-neg 70.0%

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

   8. Simplified 70.0%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.45 \cdot 10^{+88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2700000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.2 \cdot 10^{-64}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 4.8 \cdot 10^{-271} \lor \neg \left(A \leq 3.7 \cdot 10^{-164}\right) \land A \leq 1.02 \cdot 10^{-131}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -1.8 \cdot 10^{+88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -2.5 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;A \leq -1 \cdot 10^{-192}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq 8.4 \cdot 10^{-284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq 3.2 \cdot 10^{-55}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (+ 1.0 (/ C B)))))
        (t_1 (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI)))
        (t_2 (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))))
   (if (<= A -1.8e+88)
     t_2
     (if (<= A -2.3e+66)
       t_1
       (if (<= A -2.5e+58)
         t_2
         (if (<= A -1e-192)
           t_0
           (if (<= A 8.4e-284)
             t_1
             (if (<= A 3.2e-55)
               t_0
               (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan((1.0 + (C / B)));
	double t_1 = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	double t_2 = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	double tmp;
	if (A <= -1.8e+88) {
		tmp = t_2;
	} else if (A <= -2.3e+66) {
		tmp = t_1;
	} else if (A <= -2.5e+58) {
		tmp = t_2;
	} else if (A <= -1e-192) {
		tmp = t_0;
	} else if (A <= 8.4e-284) {
		tmp = t_1;
	} else if (A <= 3.2e-55) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan((1.0 + (C / B)));
	double t_1 = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	double t_2 = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	double tmp;
	if (A <= -1.8e+88) {
		tmp = t_2;
	} else if (A <= -2.3e+66) {
		tmp = t_1;
	} else if (A <= -2.5e+58) {
		tmp = t_2;
	} else if (A <= -1e-192) {
		tmp = t_0;
	} else if (A <= 8.4e-284) {
		tmp = t_1;
	} else if (A <= 3.2e-55) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan((1.0 + (C / B)))
	t_1 = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	t_2 = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	tmp = 0
	if A <= -1.8e+88:
		tmp = t_2
	elif A <= -2.3e+66:
		tmp = t_1
	elif A <= -2.5e+58:
		tmp = t_2
	elif A <= -1e-192:
		tmp = t_0
	elif A <= 8.4e-284:
		tmp = t_1
	elif A <= 3.2e-55:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(C / B))))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi))
	t_2 = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi))
	tmp = 0.0
	if (A <= -1.8e+88)
		tmp = t_2;
	elseif (A <= -2.3e+66)
		tmp = t_1;
	elseif (A <= -2.5e+58)
		tmp = t_2;
	elseif (A <= -1e-192)
		tmp = t_0;
	elseif (A <= 8.4e-284)
		tmp = t_1;
	elseif (A <= 3.2e-55)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan((1.0 + (C / B)));
	t_1 = 180.0 * (atan(((C / B) + -1.0)) / pi);
	t_2 = 180.0 * (atan(((0.5 * B) / A)) / pi);
	tmp = 0.0;
	if (A <= -1.8e+88)
		tmp = t_2;
	elseif (A <= -2.3e+66)
		tmp = t_1;
	elseif (A <= -2.5e+58)
		tmp = t_2;
	elseif (A <= -1e-192)
		tmp = t_0;
	elseif (A <= 8.4e-284)
		tmp = t_1;
	elseif (A <= 3.2e-55)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.8e+88], t$95$2, If[LessEqual[A, -2.3e+66], t$95$1, If[LessEqual[A, -2.5e+58], t$95$2, If[LessEqual[A, -1e-192], t$95$0, If[LessEqual[A, 8.4e-284], t$95$1, If[LessEqual[A, 3.2e-55], t$95$0, N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.8000000000000001e88 or -2.3e66 < A < -2.49999999999999993e58

   1. Initial program 18.2%

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

   3. Taylor expanded in A around -inf 76.6%

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

      1. associate-*r/ 76.6%

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

   5. Simplified 76.6%

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

   if -1.8000000000000001e88 < A < -2.3e66 or -1.0000000000000001e-192 < A < 8.39999999999999965e-284

   1. Initial program 66.4%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in B around inf 63.2%

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

      1. +-commutative 63.2%

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

   7. Simplified 63.2%

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

   8. Taylor expanded in A around 0 62.2%

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

      1. div-sub 62.2%

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

      2. sub-neg 62.2%

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

      3. *-inverses 62.2%

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

      4. metadata-eval 62.2%

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

   10. Simplified 62.2%

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

   if -2.49999999999999993e58 < A < -1.0000000000000001e-192 or 8.39999999999999965e-284 < A < 3.2000000000000001e-55

   1. Initial program 61.2%

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

   3. Taylor expanded in B around 0 61.1%

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

   5. Simplified 82.2%

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

      1. div-inv 82.2%

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

      2. hypot-undefine 61.1%

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

      3. unpow2 61.1%

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

      4. unpow2 61.1%

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

      5. +-commutative 61.1%

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

      6. associate--l- 61.2%

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

      7. *-commutative 61.2%

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

      8. unpow2 61.2%

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

      9. unpow2 61.2%

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

      10. hypot-define 82.2%

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

   7. Applied egg-rr 82.2%

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

   8. Taylor expanded in B around -inf 55.6%

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

      1. associate--l+ 55.6%

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

      2. div-sub 55.6%

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

   10. Simplified 55.6%

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

   11. Taylor expanded in C around inf 54.0%

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

   if 3.2000000000000001e-55 < A

   1. Initial program 78.3%

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

   3. Taylor expanded in C around 0 76.3%

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

      1. mul-1-neg 76.3%

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

      2. distribute-neg-frac2 76.3%

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

      3. +-commutative 76.3%

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

      4. unpow2 76.3%

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

      5. unpow2 76.3%

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

      6. hypot-define 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in B around -inf 74.7%

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

      1. mul-1-neg 74.7%

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

      2. unsub-neg 74.7%

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

   8. Simplified 74.7%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+88}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{+66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.5 \cdot 10^{+58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1 \cdot 10^{-192}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{elif}\;A \leq 8.4 \cdot 10^{-284}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -420000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-65} \lor \neg \left(B \leq -1.05 \cdot 10^{-131} \lor \neg \left(B \leq 4.4 \cdot 10^{-194}\right) \land B \leq 5 \cdot 10^{-150}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -420000000.0)
   (* 180.0 (/ (atan (/ (- B A) B)) PI))
   (if (or (<= B -1.6e-65)
           (not
            (or (<= B -1.05e-131) (and (not (<= B 4.4e-194)) (<= B 5e-150)))))
     (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI))
     (* (atan (/ (* 0.5 B) A)) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -420000000.0) {
		tmp = 180.0 * (atan(((B - A) / B)) / ((double) M_PI));
	} else if ((B <= -1.6e-65) || !((B <= -1.05e-131) || (!(B <= 4.4e-194) && (B <= 5e-150)))) {
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / ((double) M_PI));
	} else {
		tmp = atan(((0.5 * B) / A)) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -420000000.0) {
		tmp = 180.0 * (Math.atan(((B - A) / B)) / Math.PI);
	} else if ((B <= -1.6e-65) || !((B <= -1.05e-131) || (!(B <= 4.4e-194) && (B <= 5e-150)))) {
		tmp = 180.0 * (Math.atan(((C - (A + B)) / B)) / Math.PI);
	} else {
		tmp = Math.atan(((0.5 * B) / A)) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -420000000.0:
		tmp = 180.0 * (math.atan(((B - A) / B)) / math.pi)
	elif (B <= -1.6e-65) or not ((B <= -1.05e-131) or (not (B <= 4.4e-194) and (B <= 5e-150))):
		tmp = 180.0 * (math.atan(((C - (A + B)) / B)) / math.pi)
	else:
		tmp = math.atan(((0.5 * B) / A)) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -420000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B - A) / B)) / pi));
	elseif ((B <= -1.6e-65) || !((B <= -1.05e-131) || (!(B <= 4.4e-194) && (B <= 5e-150))))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + B)) / B)) / pi));
	else
		tmp = Float64(atan(Float64(Float64(0.5 * B) / A)) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -420000000.0)
		tmp = 180.0 * (atan(((B - A) / B)) / pi);
	elseif ((B <= -1.6e-65) || ~(((B <= -1.05e-131) || (~((B <= 4.4e-194)) && (B <= 5e-150)))))
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	else
		tmp = atan(((0.5 * B) / A)) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -420000000.0], N[(180.0 * N[(N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, -1.6e-65], N[Not[Or[LessEqual[B, -1.05e-131], And[N[Not[LessEqual[B, 4.4e-194]], $MachinePrecision], LessEqual[B, 5e-150]]]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -4.2e8

   1. Initial program 54.9%

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

   3. Taylor expanded in C around 0 50.1%

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

      1. mul-1-neg 50.1%

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

      2. distribute-neg-frac2 50.1%

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

      3. +-commutative 50.1%

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

      4. unpow2 50.1%

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

      5. unpow2 50.1%

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

      6. hypot-define 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in B around -inf 74.5%

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

      1. mul-1-neg 74.5%

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

      2. unsub-neg 74.5%

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

   8. Simplified 74.5%

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

   if -4.2e8 < B < -1.6e-65 or -1.04999999999999999e-131 < B < 4.4000000000000003e-194 or 4.9999999999999999e-150 < B

   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. Step-by-step derivation

   3. Simplified 77.7%

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

   5. Taylor expanded in B around inf 71.4%

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

      1. +-commutative 71.4%

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

   7. Simplified 71.4%

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

   if -1.6e-65 < B < -1.04999999999999999e-131 or 4.4000000000000003e-194 < B < 4.9999999999999999e-150

   1. Initial program 29.7%

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

   3. Taylor expanded in B around 0 29.0%

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

   5. Simplified 41.7%

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

      1. div-inv 41.7%

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

      2. hypot-undefine 29.0%

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

      3. unpow2 29.0%

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

      4. unpow2 29.0%

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

      5. +-commutative 29.0%

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

      6. associate--l- 29.7%

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

      7. *-commutative 29.7%

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

      8. unpow2 29.7%

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

      9. unpow2 29.7%

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

      10. hypot-define 63.4%

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

   7. Applied egg-rr 63.4%

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

   8. Taylor expanded in A around -inf 67.6%

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

      1. associate-*r/ 67.6%

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

   10. Simplified 67.6%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -420000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.6 \cdot 10^{-65} \lor \neg \left(B \leq -1.05 \cdot 10^{-131} \lor \neg \left(B \leq 4.4 \cdot 10^{-194}\right) \land B \leq 5 \cdot 10^{-150}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.6% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -5.3 \cdot 10^{-39}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -2.65 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.05 \cdot 10^{-210}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-150}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-84}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))
   (if (<= B -5.3e-39)
     t_0
     (if (<= B -2.65e-80)
       (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
       (if (<= B 2.05e-210)
         t_0
         (if (<= B 5e-150)
           (* 180.0 (/ (atan 0.0) PI))
           (if (<= B 3.1e-84)
             (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
             (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	double tmp;
	if (B <= -5.3e-39) {
		tmp = t_0;
	} else if (B <= -2.65e-80) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	} else if (B <= 2.05e-210) {
		tmp = t_0;
	} else if (B <= 5e-150) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (B <= 3.1e-84) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	double tmp;
	if (B <= -5.3e-39) {
		tmp = t_0;
	} else if (B <= -2.65e-80) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else if (B <= 2.05e-210) {
		tmp = t_0;
	} else if (B <= 5e-150) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (B <= 3.1e-84) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	tmp = 0
	if B <= -5.3e-39:
		tmp = t_0
	elif B <= -2.65e-80:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	elif B <= 2.05e-210:
		tmp = t_0
	elif B <= 5e-150:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif B <= 3.1e-84:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi))
	tmp = 0.0
	if (B <= -5.3e-39)
		tmp = t_0;
	elseif (B <= -2.65e-80)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	elseif (B <= 2.05e-210)
		tmp = t_0;
	elseif (B <= 5e-150)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (B <= 3.1e-84)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 - (A / B))) / pi);
	tmp = 0.0;
	if (B <= -5.3e-39)
		tmp = t_0;
	elseif (B <= -2.65e-80)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	elseif (B <= 2.05e-210)
		tmp = t_0;
	elseif (B <= 5e-150)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (B <= 3.1e-84)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	else
		tmp = 180.0 * (atan(((C / B) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -5.3e-39], t$95$0, If[LessEqual[B, -2.65e-80], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.05e-210], t$95$0, If[LessEqual[B, 5e-150], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.1e-84], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -5.30000000000000003e-39 or -2.65000000000000013e-80 < B < 2.04999999999999995e-210

   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 51.5%

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

      1. mul-1-neg 51.5%

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

      2. distribute-neg-frac2 51.5%

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

      3. +-commutative 51.5%

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

      4. unpow2 51.5%

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

      5. unpow2 51.5%

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

      6. hypot-define 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in B around -inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. unsub-neg 59.4%

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

   8. Simplified 59.4%

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

   if -5.30000000000000003e-39 < B < -2.65000000000000013e-80

   1. Initial program 72.9%

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

   3. Taylor expanded in C around -inf 63.8%

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

   if 2.04999999999999995e-210 < B < 4.9999999999999999e-150

   1. Initial program 11.6%

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

      1. +-commutative 11.6%

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

      2. unpow2 11.6%

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

      3. unpow2 11.6%

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

      4. hypot-undefine 63.5%

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

      5. sub-neg 63.5%

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

      6. distribute-lft-in 25.1%

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

      7. hypot-undefine 10.4%

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

      8. unpow2 10.4%

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

      9. unpow2 10.4%

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

      10. +-commutative 10.4%

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

      11. unpow2 10.4%

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

      12. unpow2 10.4%

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

      13. hypot-define 25.1%

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

   4. Applied egg-rr 25.1%

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

   5. Taylor expanded in A around -inf 33.5%

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

      1. distribute-lft1-in 33.5%

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

      2. metadata-eval 33.5%

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

      3. mul0-lft 41.2%

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

   7. Simplified 41.2%

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

   if 4.9999999999999999e-150 < B < 3.10000000000000002e-84

   1. Initial program 65.3%

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

   3. Taylor expanded in A around inf 52.7%

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

   if 3.10000000000000002e-84 < B

   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. Step-by-step derivation

   3. Simplified 85.3%

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

   5. Taylor expanded in B around inf 82.3%

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

      1. +-commutative 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in A around 0 71.5%

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

      1. div-sub 71.5%

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

      2. sub-neg 71.5%

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

      3. *-inverses 71.5%

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

      4. metadata-eval 71.5%

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

   10. Simplified 71.5%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.3 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.65 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.05 \cdot 10^{-210}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-150}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-84}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.9% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{if}\;B \leq -7.2 \cdot 10^{-65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.95 \cdot 10^{-131}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-211}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-150}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - B\right) - A\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (atan (/ (* 0.5 B) A)) (/ 180.0 PI))))
   (if (<= B -7.2e-65)
     (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
     (if (<= B -2.95e-131)
       t_0
       (if (<= B 4.2e-211)
         (* (/ 180.0 PI) (atan (- 1.0 (/ (- A C) B))))
         (if (<= B 7e-150)
           t_0
           (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C B) A))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((0.5 * B) / A)) * (180.0 / ((double) M_PI));
	double tmp;
	if (B <= -7.2e-65) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else if (B <= -2.95e-131) {
		tmp = t_0;
	} else if (B <= 4.2e-211) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 - ((A - C) / B)));
	} else if (B <= 7e-150) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - B) - A))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((0.5 * B) / A)) * (180.0 / Math.PI);
	double tmp;
	if (B <= -7.2e-65) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else if (B <= -2.95e-131) {
		tmp = t_0;
	} else if (B <= 4.2e-211) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 - ((A - C) / B)));
	} else if (B <= 7e-150) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C - B) - A))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((0.5 * B) / A)) * (180.0 / math.pi)
	tmp = 0
	if B <= -7.2e-65:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	elif B <= -2.95e-131:
		tmp = t_0
	elif B <= 4.2e-211:
		tmp = (180.0 / math.pi) * math.atan((1.0 - ((A - C) / B)))
	elif B <= 7e-150:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C - B) - A))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(atan(Float64(Float64(0.5 * B) / A)) * Float64(180.0 / pi))
	tmp = 0.0
	if (B <= -7.2e-65)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	elseif (B <= -2.95e-131)
		tmp = t_0;
	elseif (B <= 4.2e-211)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - Float64(Float64(A - C) / B))));
	elseif (B <= 7e-150)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - B) - A))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((0.5 * B) / A)) * (180.0 / pi);
	tmp = 0.0;
	if (B <= -7.2e-65)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	elseif (B <= -2.95e-131)
		tmp = t_0;
	elseif (B <= 4.2e-211)
		tmp = (180.0 / pi) * atan((1.0 - ((A - C) / B)));
	elseif (B <= 7e-150)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((1.0 / B) * ((C - B) - A))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -7.2e-65], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.95e-131], t$95$0, If[LessEqual[B, 4.2e-211], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7e-150], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -7.1999999999999996e-65

   1. Initial program 60.3%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in B around -inf 80.7%

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

      1. neg-mul-1 80.7%

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

      2. unsub-neg 80.7%

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

   7. Simplified 80.7%

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

   if -7.1999999999999996e-65 < B < -2.94999999999999983e-131 or 4.20000000000000015e-211 < B < 6.9999999999999996e-150

   1. Initial program 27.8%

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

   3. Taylor expanded in B around 0 27.1%

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

   5. Simplified 42.4%

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

      1. div-inv 42.4%

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

      2. hypot-undefine 27.1%

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

      3. unpow2 27.1%

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

      4. unpow2 27.1%

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

      5. +-commutative 27.1%

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

      6. associate--l- 27.8%

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

      7. *-commutative 27.8%

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

      8. unpow2 27.8%

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

      9. unpow2 27.8%

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

      10. hypot-define 66.3%

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

   7. Applied egg-rr 66.3%

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

   8. Taylor expanded in A around -inf 66.2%

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

      1. associate-*r/ 66.2%

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

   10. Simplified 66.2%

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

   if -2.94999999999999983e-131 < B < 4.20000000000000015e-211

   1. Initial program 67.0%

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

   3. Taylor expanded in B around 0 64.0%

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

   5. Simplified 68.7%

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

      1. div-inv 68.7%

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

      2. hypot-undefine 64.0%

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

      3. unpow2 64.0%

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

      4. unpow2 64.0%

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

      5. +-commutative 64.0%

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

      6. associate--l- 67.0%

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

      7. *-commutative 67.0%

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

      8. unpow2 67.0%

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

      9. unpow2 67.0%

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

      10. hypot-define 80.8%

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

   7. Applied egg-rr 80.8%

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

   8. Taylor expanded in B around -inf 57.2%

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

      1. associate--l+ 57.2%

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

      2. div-sub 62.0%

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

   10. Simplified 62.0%

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

   if 6.9999999999999996e-150 < B

   1. Initial program 61.3%

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

   3. Taylor expanded in B around inf 78.8%

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

      1. neg-mul-1 78.8%

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

      2. unsub-neg 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -2.95 \cdot 10^{-131}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-211}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-150}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - B\right) - A\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.9% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{if}\;B \leq -7 \cdot 10^{-64}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.76 \cdot 10^{-128}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-211}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-150}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - B\right) - A\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (atan (/ (* 0.5 B) A)) (/ 180.0 PI))))
   (if (<= B -7e-64)
     (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
     (if (<= B -1.76e-128)
       t_0
       (if (<= B 9e-211)
         (* (/ 180.0 PI) (atan (- 1.0 (/ (- A C) B))))
         (if (<= B 5e-150)
           t_0
           (* (/ 180.0 PI) (atan (* (/ 1.0 B) (- (- C B) A))))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((0.5 * B) / A)) * (180.0 / ((double) M_PI));
	double tmp;
	if (B <= -7e-64) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else if (B <= -1.76e-128) {
		tmp = t_0;
	} else if (B <= 9e-211) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 - ((A - C) / B)));
	} else if (B <= 5e-150) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((1.0 / B) * ((C - B) - A)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((0.5 * B) / A)) * (180.0 / Math.PI);
	double tmp;
	if (B <= -7e-64) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else if (B <= -1.76e-128) {
		tmp = t_0;
	} else if (B <= 9e-211) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 - ((A - C) / B)));
	} else if (B <= 5e-150) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((1.0 / B) * ((C - B) - A)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((0.5 * B) / A)) * (180.0 / math.pi)
	tmp = 0
	if B <= -7e-64:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	elif B <= -1.76e-128:
		tmp = t_0
	elif B <= 9e-211:
		tmp = (180.0 / math.pi) * math.atan((1.0 - ((A - C) / B)))
	elif B <= 5e-150:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan(((1.0 / B) * ((C - B) - A)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(atan(Float64(Float64(0.5 * B) / A)) * Float64(180.0 / pi))
	tmp = 0.0
	if (B <= -7e-64)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	elseif (B <= -1.76e-128)
		tmp = t_0;
	elseif (B <= 9e-211)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - Float64(Float64(A - C) / B))));
	elseif (B <= 5e-150)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(1.0 / B) * Float64(Float64(C - B) - A))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((0.5 * B) / A)) * (180.0 / pi);
	tmp = 0.0;
	if (B <= -7e-64)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	elseif (B <= -1.76e-128)
		tmp = t_0;
	elseif (B <= 9e-211)
		tmp = (180.0 / pi) * atan((1.0 - ((A - C) / B)));
	elseif (B <= 5e-150)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan(((1.0 / B) * ((C - B) - A)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -7e-64], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.76e-128], t$95$0, If[LessEqual[B, 9e-211], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5e-150], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -7.0000000000000006e-64

   1. Initial program 60.3%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in B around -inf 80.7%

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

      1. neg-mul-1 80.7%

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

      2. unsub-neg 80.7%

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

   7. Simplified 80.7%

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

   if -7.0000000000000006e-64 < B < -1.76000000000000002e-128 or 8.9999999999999997e-211 < B < 4.9999999999999999e-150

   1. Initial program 27.8%

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

   3. Taylor expanded in B around 0 27.1%

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

   5. Simplified 42.4%

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

      1. div-inv 42.4%

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

      2. hypot-undefine 27.1%

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

      3. unpow2 27.1%

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

      4. unpow2 27.1%

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

      5. +-commutative 27.1%

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

      6. associate--l- 27.8%

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

      7. *-commutative 27.8%

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

      8. unpow2 27.8%

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

      9. unpow2 27.8%

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

      10. hypot-define 66.3%

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

   7. Applied egg-rr 66.3%

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

   8. Taylor expanded in A around -inf 66.2%

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

      1. associate-*r/ 66.2%

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

   10. Simplified 66.2%

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

   if -1.76000000000000002e-128 < B < 8.9999999999999997e-211

   1. Initial program 67.0%

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

   3. Taylor expanded in B around 0 64.0%

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

   5. Simplified 68.7%

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

      1. div-inv 68.7%

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

      2. hypot-undefine 64.0%

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

      3. unpow2 64.0%

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

      4. unpow2 64.0%

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

      5. +-commutative 64.0%

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

      6. associate--l- 67.0%

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

      7. *-commutative 67.0%

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

      8. unpow2 67.0%

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

      9. unpow2 67.0%

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

      10. hypot-define 80.8%

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

   7. Applied egg-rr 80.8%

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

   8. Taylor expanded in B around -inf 57.2%

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

      1. associate--l+ 57.2%

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

      2. div-sub 62.0%

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

   10. Simplified 62.0%

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

   if 4.9999999999999999e-150 < B

   1. Initial program 61.3%

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

   3. Taylor expanded in B around 0 61.3%

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

   5. Simplified 83.6%

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

      1. div-inv 83.7%

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

      2. hypot-undefine 61.3%

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

      3. unpow2 61.3%

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

      4. unpow2 61.3%

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

      5. +-commutative 61.3%

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

      6. associate--l- 61.3%

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

      7. *-commutative 61.3%

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

      8. unpow2 61.3%

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

      9. unpow2 61.3%

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

      10. hypot-define 83.8%

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

   7. Applied egg-rr 83.8%

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

   8. Taylor expanded in B around inf 78.8%

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

      1. neg-mul-1 78.8%

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

      2. sub-neg 78.8%

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

   10. Simplified 78.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7 \cdot 10^{-64}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.76 \cdot 10^{-128}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-211}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-150}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - B\right) - A\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.9% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{if}\;B \leq -8 \cdot 10^{-66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.76 \cdot 10^{-128}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-210}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-150}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (atan (/ (* 0.5 B) A)) (/ 180.0 PI))))
   (if (<= B -8e-66)
     (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
     (if (<= B -1.76e-128)
       t_0
       (if (<= B 2.8e-210)
         (* (/ 180.0 PI) (atan (- 1.0 (/ (- A C) B))))
         (if (<= B 5e-150)
           t_0
           (/ 1.0 (/ (/ PI 180.0) (atan (/ (- (- C B) A) B))))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((0.5 * B) / A)) * (180.0 / ((double) M_PI));
	double tmp;
	if (B <= -8e-66) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else if (B <= -1.76e-128) {
		tmp = t_0;
	} else if (B <= 2.8e-210) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 - ((A - C) / B)));
	} else if (B <= 5e-150) {
		tmp = t_0;
	} else {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((((C - B) - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((0.5 * B) / A)) * (180.0 / Math.PI);
	double tmp;
	if (B <= -8e-66) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else if (B <= -1.76e-128) {
		tmp = t_0;
	} else if (B <= 2.8e-210) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 - ((A - C) / B)));
	} else if (B <= 5e-150) {
		tmp = t_0;
	} else {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((((C - B) - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((0.5 * B) / A)) * (180.0 / math.pi)
	tmp = 0
	if B <= -8e-66:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	elif B <= -1.76e-128:
		tmp = t_0
	elif B <= 2.8e-210:
		tmp = (180.0 / math.pi) * math.atan((1.0 - ((A - C) / B)))
	elif B <= 5e-150:
		tmp = t_0
	else:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((((C - B) - A) / B)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(atan(Float64(Float64(0.5 * B) / A)) * Float64(180.0 / pi))
	tmp = 0.0
	if (B <= -8e-66)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	elseif (B <= -1.76e-128)
		tmp = t_0;
	elseif (B <= 2.8e-210)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - Float64(Float64(A - C) / B))));
	elseif (B <= 5e-150)
		tmp = t_0;
	else
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(Float64(Float64(C - B) - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((0.5 * B) / A)) * (180.0 / pi);
	tmp = 0.0;
	if (B <= -8e-66)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	elseif (B <= -1.76e-128)
		tmp = t_0;
	elseif (B <= 2.8e-210)
		tmp = (180.0 / pi) * atan((1.0 - ((A - C) / B)));
	elseif (B <= 5e-150)
		tmp = t_0;
	else
		tmp = 1.0 / ((pi / 180.0) / atan((((C - B) - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -8e-66], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.76e-128], t$95$0, If[LessEqual[B, 2.8e-210], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5e-150], t$95$0, N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -7.9999999999999998e-66

   1. Initial program 60.3%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in B around -inf 80.7%

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

      1. neg-mul-1 80.7%

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

      2. unsub-neg 80.7%

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

   7. Simplified 80.7%

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

   if -7.9999999999999998e-66 < B < -1.76000000000000002e-128 or 2.8e-210 < B < 4.9999999999999999e-150

   1. Initial program 27.8%

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

   3. Taylor expanded in B around 0 27.1%

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

   5. Simplified 42.4%

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

      1. div-inv 42.4%

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

      2. hypot-undefine 27.1%

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

      3. unpow2 27.1%

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

      4. unpow2 27.1%

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

      5. +-commutative 27.1%

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

      6. associate--l- 27.8%

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

      7. *-commutative 27.8%

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

      8. unpow2 27.8%

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

      9. unpow2 27.8%

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

      10. hypot-define 66.3%

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

   7. Applied egg-rr 66.3%

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

   8. Taylor expanded in A around -inf 66.2%

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

      1. associate-*r/ 66.2%

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

   10. Simplified 66.2%

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

   if -1.76000000000000002e-128 < B < 2.8e-210

   1. Initial program 67.0%

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

   3. Taylor expanded in B around 0 64.0%

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

   5. Simplified 68.7%

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

      1. div-inv 68.7%

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

      2. hypot-undefine 64.0%

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

      3. unpow2 64.0%

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

      4. unpow2 64.0%

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

      5. +-commutative 64.0%

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

      6. associate--l- 67.0%

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

      7. *-commutative 67.0%

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

      8. unpow2 67.0%

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

      9. unpow2 67.0%

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

      10. hypot-define 80.8%

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

   7. Applied egg-rr 80.8%

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

   8. Taylor expanded in B around -inf 57.2%

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

      1. associate--l+ 57.2%

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

      2. div-sub 62.0%

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

   10. Simplified 62.0%

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

   if 4.9999999999999999e-150 < B

   1. Initial program 61.3%

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

   4. Applied egg-rr 83.7%

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

      1. inv-pow 83.7%

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

      2. associate-/r* 83.8%

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

   6. Applied egg-rr 83.8%

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

   8. Simplified 83.8%

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

   9. Taylor expanded in B around inf 78.8%

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

       1. mul-1-neg 78.8%

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

       2. unsub-neg 78.8%

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

   11. Simplified 78.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8 \cdot 10^{-66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.76 \cdot 10^{-128}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-210}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-150}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.0% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A - C}{B}\\ t_1 := \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{if}\;B \leq -1.05 \cdot 10^{-65}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \left(1 + \left(-1 - t\_0\right)\right)\right)\\ \mathbf{elif}\;B \leq -3.9 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-211}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - t\_0\right)\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- A C) B)) (t_1 (* (atan (/ (* 0.5 B) A)) (/ 180.0 PI))))
   (if (<= B -1.05e-65)
     (* (/ 180.0 PI) (atan (+ 1.0 (+ 1.0 (- -1.0 t_0)))))
     (if (<= B -3.9e-126)
       t_1
       (if (<= B 1.9e-211)
         (* (/ 180.0 PI) (atan (- 1.0 t_0)))
         (if (<= B 5e-150)
           t_1
           (/ 1.0 (/ (/ PI 180.0) (atan (/ (- (- C B) A) B))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double t_1 = atan(((0.5 * B) / A)) * (180.0 / ((double) M_PI));
	double tmp;
	if (B <= -1.05e-65) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + (1.0 + (-1.0 - t_0))));
	} else if (B <= -3.9e-126) {
		tmp = t_1;
	} else if (B <= 1.9e-211) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 - t_0));
	} else if (B <= 5e-150) {
		tmp = t_1;
	} else {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((((C - B) - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (A - C) / B;
	double t_1 = Math.atan(((0.5 * B) / A)) * (180.0 / Math.PI);
	double tmp;
	if (B <= -1.05e-65) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + (1.0 + (-1.0 - t_0))));
	} else if (B <= -3.9e-126) {
		tmp = t_1;
	} else if (B <= 1.9e-211) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 - t_0));
	} else if (B <= 5e-150) {
		tmp = t_1;
	} else {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((((C - B) - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (A - C) / B
	t_1 = math.atan(((0.5 * B) / A)) * (180.0 / math.pi)
	tmp = 0
	if B <= -1.05e-65:
		tmp = (180.0 / math.pi) * math.atan((1.0 + (1.0 + (-1.0 - t_0))))
	elif B <= -3.9e-126:
		tmp = t_1
	elif B <= 1.9e-211:
		tmp = (180.0 / math.pi) * math.atan((1.0 - t_0))
	elif B <= 5e-150:
		tmp = t_1
	else:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((((C - B) - A) / B)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(A - C) / B)
	t_1 = Float64(atan(Float64(Float64(0.5 * B) / A)) * Float64(180.0 / pi))
	tmp = 0.0
	if (B <= -1.05e-65)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(1.0 + Float64(-1.0 - t_0)))));
	elseif (B <= -3.9e-126)
		tmp = t_1;
	elseif (B <= 1.9e-211)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - t_0)));
	elseif (B <= 5e-150)
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(Float64(Float64(C - B) - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (A - C) / B;
	t_1 = atan(((0.5 * B) / A)) * (180.0 / pi);
	tmp = 0.0;
	if (B <= -1.05e-65)
		tmp = (180.0 / pi) * atan((1.0 + (1.0 + (-1.0 - t_0))));
	elseif (B <= -3.9e-126)
		tmp = t_1;
	elseif (B <= 1.9e-211)
		tmp = (180.0 / pi) * atan((1.0 - t_0));
	elseif (B <= 5e-150)
		tmp = t_1;
	else
		tmp = 1.0 / ((pi / 180.0) / atan((((C - B) - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$1 = N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.05e-65], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(1.0 + N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.9e-126], t$95$1, If[LessEqual[B, 1.9e-211], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 - t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5e-150], t$95$1, N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.05000000000000001e-65

   1. Initial program 60.3%

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

   3. Taylor expanded in B around 0 60.4%

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

   5. Simplified 82.3%

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

      1. div-inv 82.3%

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

      2. hypot-undefine 60.4%

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

      3. unpow2 60.4%

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

      4. unpow2 60.4%

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

      5. +-commutative 60.4%

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

      6. associate--l- 60.3%

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

      7. *-commutative 60.3%

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

      8. unpow2 60.3%

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

      9. unpow2 60.3%

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

      10. hypot-define 82.2%

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

   7. Applied egg-rr 82.2%

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

   8. Taylor expanded in B around -inf 80.7%

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

      1. associate--l+ 80.7%

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

      2. div-sub 80.7%

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

   10. Simplified 80.7%

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

       1. expm1-log1p-u 80.3%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{C - A}{B}\right)\right)}\right) \]

       2. log1p-define 80.3%

          \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \mathsf{expm1}\left(\color{blue}{\log \left(1 + \frac{C - A}{B}\right)}\right)\right) \]

       3. expm1-undefine 80.3%

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

       4. add-exp-log 80.7%

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

   12. Applied egg-rr 80.7%

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

       1. associate--l+ 80.7%

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

   14. Simplified 80.7%

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

   if -1.05000000000000001e-65 < B < -3.8999999999999998e-126 or 1.90000000000000006e-211 < B < 4.9999999999999999e-150

   1. Initial program 27.8%

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

   3. Taylor expanded in B around 0 27.1%

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

   5. Simplified 42.4%

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

      1. div-inv 42.4%

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

      2. hypot-undefine 27.1%

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

      3. unpow2 27.1%

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

      4. unpow2 27.1%

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

      5. +-commutative 27.1%

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

      6. associate--l- 27.8%

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

      7. *-commutative 27.8%

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

      8. unpow2 27.8%

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

      9. unpow2 27.8%

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

      10. hypot-define 66.3%

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

   7. Applied egg-rr 66.3%

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

   8. Taylor expanded in A around -inf 66.2%

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

      1. associate-*r/ 66.2%

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

   10. Simplified 66.2%

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

   if -3.8999999999999998e-126 < B < 1.90000000000000006e-211

   1. Initial program 67.0%

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

   3. Taylor expanded in B around 0 64.0%

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

   5. Simplified 68.7%

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

      1. div-inv 68.7%

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

      2. hypot-undefine 64.0%

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

      3. unpow2 64.0%

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

      4. unpow2 64.0%

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

      5. +-commutative 64.0%

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

      6. associate--l- 67.0%

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

      7. *-commutative 67.0%

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

      8. unpow2 67.0%

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

      9. unpow2 67.0%

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

      10. hypot-define 80.8%

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

   7. Applied egg-rr 80.8%

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

   8. Taylor expanded in B around -inf 57.2%

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

      1. associate--l+ 57.2%

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

      2. div-sub 62.0%

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

   10. Simplified 62.0%

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

   if 4.9999999999999999e-150 < B

   1. Initial program 61.3%

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

   4. Applied egg-rr 83.7%

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

      1. inv-pow 83.7%

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

      2. associate-/r* 83.8%

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

   6. Applied egg-rr 83.8%

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

   8. Simplified 83.8%

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

   9. Taylor expanded in B around inf 78.8%

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

       1. mul-1-neg 78.8%

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

       2. unsub-neg 78.8%

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

   11. Simplified 78.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.05 \cdot 10^{-65}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \left(1 + \left(-1 - \frac{A - C}{B}\right)\right)\right)\\ \mathbf{elif}\;B \leq -3.9 \cdot 10^{-126}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-211}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-150}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 64.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -8 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq -5.1 \cdot 10^{-126}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-150}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (atan (/ (* 0.5 B) A)) (/ 180.0 PI)))
        (t_1 (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))))
   (if (<= B -8e-66)
     t_1
     (if (<= B -5.1e-126)
       t_0
       (if (<= B 2.8e-210)
         t_1
         (if (<= B 5e-150)
           t_0
           (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((0.5 * B) / A)) * (180.0 / ((double) M_PI));
	double t_1 = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	double tmp;
	if (B <= -8e-66) {
		tmp = t_1;
	} else if (B <= -5.1e-126) {
		tmp = t_0;
	} else if (B <= 2.8e-210) {
		tmp = t_1;
	} else if (B <= 5e-150) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((0.5 * B) / A)) * (180.0 / Math.PI);
	double t_1 = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	double tmp;
	if (B <= -8e-66) {
		tmp = t_1;
	} else if (B <= -5.1e-126) {
		tmp = t_0;
	} else if (B <= 2.8e-210) {
		tmp = t_1;
	} else if (B <= 5e-150) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + B)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((0.5 * B) / A)) * (180.0 / math.pi)
	t_1 = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	tmp = 0
	if B <= -8e-66:
		tmp = t_1
	elif B <= -5.1e-126:
		tmp = t_0
	elif B <= 2.8e-210:
		tmp = t_1
	elif B <= 5e-150:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((C - (A + B)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(atan(Float64(Float64(0.5 * B) / A)) * Float64(180.0 / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi))
	tmp = 0.0
	if (B <= -8e-66)
		tmp = t_1;
	elseif (B <= -5.1e-126)
		tmp = t_0;
	elseif (B <= 2.8e-210)
		tmp = t_1;
	elseif (B <= 5e-150)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + B)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((0.5 * B) / A)) * (180.0 / pi);
	t_1 = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	tmp = 0.0;
	if (B <= -8e-66)
		tmp = t_1;
	elseif (B <= -5.1e-126)
		tmp = t_0;
	elseif (B <= 2.8e-210)
		tmp = t_1;
	elseif (B <= 5e-150)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -8e-66], t$95$1, If[LessEqual[B, -5.1e-126], t$95$0, If[LessEqual[B, 2.8e-210], t$95$1, If[LessEqual[B, 5e-150], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -7.9999999999999998e-66 or -5.10000000000000002e-126 < B < 2.8e-210

   1. Initial program 63.3%

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

   3. Simplified 76.3%

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

   5. Taylor expanded in B around -inf 72.4%

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

      1. neg-mul-1 72.4%

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

      2. unsub-neg 72.4%

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

   7. Simplified 72.4%

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

   if -7.9999999999999998e-66 < B < -5.10000000000000002e-126 or 2.8e-210 < B < 4.9999999999999999e-150

   1. Initial program 27.8%

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

   3. Taylor expanded in B around 0 27.1%

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

   5. Simplified 42.4%

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

      1. div-inv 42.4%

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

      2. hypot-undefine 27.1%

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

      3. unpow2 27.1%

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

      4. unpow2 27.1%

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

      5. +-commutative 27.1%

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

      6. associate--l- 27.8%

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

      7. *-commutative 27.8%

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

      8. unpow2 27.8%

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

      9. unpow2 27.8%

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

      10. hypot-define 66.3%

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

   7. Applied egg-rr 66.3%

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

   8. Taylor expanded in A around -inf 66.2%

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

      1. associate-*r/ 66.2%

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

   10. Simplified 66.2%

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

   if 4.9999999999999999e-150 < B

   1. Initial program 61.3%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in B around inf 78.8%

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

      1. +-commutative 78.8%

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

   7. Simplified 78.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8 \cdot 10^{-66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5.1 \cdot 10^{-126}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-210}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-150}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 64.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{if}\;B \leq -8 \cdot 10^{-66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.4 \cdot 10^{-126}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-210}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-150}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (atan (/ (* 0.5 B) A)) (/ 180.0 PI))))
   (if (<= B -8e-66)
     (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
     (if (<= B -8.4e-126)
       t_0
       (if (<= B 3.7e-210)
         (* (/ 180.0 PI) (atan (- 1.0 (/ (- A C) B))))
         (if (<= B 5e-150)
           t_0
           (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((0.5 * B) / A)) * (180.0 / ((double) M_PI));
	double tmp;
	if (B <= -8e-66) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else if (B <= -8.4e-126) {
		tmp = t_0;
	} else if (B <= 3.7e-210) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 - ((A - C) / B)));
	} else if (B <= 5e-150) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((0.5 * B) / A)) * (180.0 / Math.PI);
	double tmp;
	if (B <= -8e-66) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else if (B <= -8.4e-126) {
		tmp = t_0;
	} else if (B <= 3.7e-210) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 - ((A - C) / B)));
	} else if (B <= 5e-150) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + B)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((0.5 * B) / A)) * (180.0 / math.pi)
	tmp = 0
	if B <= -8e-66:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	elif B <= -8.4e-126:
		tmp = t_0
	elif B <= 3.7e-210:
		tmp = (180.0 / math.pi) * math.atan((1.0 - ((A - C) / B)))
	elif B <= 5e-150:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((C - (A + B)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(atan(Float64(Float64(0.5 * B) / A)) * Float64(180.0 / pi))
	tmp = 0.0
	if (B <= -8e-66)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	elseif (B <= -8.4e-126)
		tmp = t_0;
	elseif (B <= 3.7e-210)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - Float64(Float64(A - C) / B))));
	elseif (B <= 5e-150)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + B)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((0.5 * B) / A)) * (180.0 / pi);
	tmp = 0.0;
	if (B <= -8e-66)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	elseif (B <= -8.4e-126)
		tmp = t_0;
	elseif (B <= 3.7e-210)
		tmp = (180.0 / pi) * atan((1.0 - ((A - C) / B)));
	elseif (B <= 5e-150)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -8e-66], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.4e-126], t$95$0, If[LessEqual[B, 3.7e-210], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5e-150], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -7.9999999999999998e-66

   1. Initial program 60.3%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in B around -inf 80.7%

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

      1. neg-mul-1 80.7%

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

      2. unsub-neg 80.7%

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

   7. Simplified 80.7%

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

   if -7.9999999999999998e-66 < B < -8.3999999999999994e-126 or 3.7000000000000003e-210 < B < 4.9999999999999999e-150

   1. Initial program 27.8%

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

   3. Taylor expanded in B around 0 27.1%

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

   5. Simplified 42.4%

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

      1. div-inv 42.4%

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

      2. hypot-undefine 27.1%

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

      3. unpow2 27.1%

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

      4. unpow2 27.1%

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

      5. +-commutative 27.1%

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

      6. associate--l- 27.8%

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

      7. *-commutative 27.8%

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

      8. unpow2 27.8%

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

      9. unpow2 27.8%

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

      10. hypot-define 66.3%

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

   7. Applied egg-rr 66.3%

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

   8. Taylor expanded in A around -inf 66.2%

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

      1. associate-*r/ 66.2%

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

   10. Simplified 66.2%

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

   if -8.3999999999999994e-126 < B < 3.7000000000000003e-210

   1. Initial program 67.0%

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

   3. Taylor expanded in B around 0 64.0%

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

   5. Simplified 68.7%

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

      1. div-inv 68.7%

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

      2. hypot-undefine 64.0%

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

      3. unpow2 64.0%

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

      4. unpow2 64.0%

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

      5. +-commutative 64.0%

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

      6. associate--l- 67.0%

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

      7. *-commutative 67.0%

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

      8. unpow2 67.0%

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

      9. unpow2 67.0%

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

      10. hypot-define 80.8%

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

   7. Applied egg-rr 80.8%

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

   8. Taylor expanded in B around -inf 57.2%

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

      1. associate--l+ 57.2%

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

      2. div-sub 62.0%

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

   10. Simplified 62.0%

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

   if 4.9999999999999999e-150 < B

   1. Initial program 61.3%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in B around inf 78.8%

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

      1. +-commutative 78.8%

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

   7. Simplified 78.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8 \cdot 10^{-66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.4 \cdot 10^{-126}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-210}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A - C}{B}\right)\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-150}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 47.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -31000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-210}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-150}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -31000.0)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.85e-210)
     (* 180.0 (/ (atan (/ C B)) PI))
     (if (<= B 7e-150)
       (* 180.0 (/ (atan 0.0) PI))
       (if (<= B 8.5e-63)
         (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
         (* 180.0 (/ (atan -1.0) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -31000.0) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.85e-210) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= 7e-150) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (B <= 8.5e-63) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((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 <= -31000.0) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.85e-210) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= 7e-150) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (B <= 8.5e-63) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -31000.0:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.85e-210:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= 7e-150:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif B <= 8.5e-63:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / 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 <= -31000.0)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.85e-210)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= 7e-150)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (B <= 8.5e-63)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / 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 <= -31000.0)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.85e-210)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= 7e-150)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (B <= 8.5e-63)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -31000.0], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.85e-210], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7e-150], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.5e-63], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -31000

   1. Initial program 55.5%

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

   3. Taylor expanded in B around -inf 67.6%

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

   if -31000 < B < 1.8500000000000001e-210

   1. Initial program 66.7%

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

   3. Simplified 69.0%

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

   5. Taylor expanded in B around inf 57.3%

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

      1. +-commutative 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in C around inf 40.2%

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

   if 1.8500000000000001e-210 < B < 6.9999999999999996e-150

   1. Initial program 11.6%

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

      1. +-commutative 11.6%

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

      2. unpow2 11.6%

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

      3. unpow2 11.6%

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

      4. hypot-undefine 63.5%

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

      5. sub-neg 63.5%

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

      6. distribute-lft-in 25.1%

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

      7. hypot-undefine 10.4%

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

      8. unpow2 10.4%

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

      9. unpow2 10.4%

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

      10. +-commutative 10.4%

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

      11. unpow2 10.4%

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

      12. unpow2 10.4%

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

      13. hypot-define 25.1%

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

   4. Applied egg-rr 25.1%

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

   5. Taylor expanded in A around -inf 33.5%

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

      1. distribute-lft1-in 33.5%

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

      2. metadata-eval 33.5%

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

      3. mul0-lft 41.2%

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

   7. Simplified 41.2%

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

   if 6.9999999999999996e-150 < B < 8.49999999999999969e-63

   1. Initial program 67.6%

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

   3. Taylor expanded in A around inf 55.9%

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

   if 8.49999999999999969e-63 < B

   1. Initial program 59.9%

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

   3. Taylor expanded in B around inf 58.2%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -31000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-210}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-150}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 47.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -30000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-210}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-150}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -30000.0)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.8e-210)
     (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
     (if (<= B 6e-150)
       (* 180.0 (/ (atan 0.0) PI))
       (if (<= B 3.5e-60)
         (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
         (* 180.0 (/ (atan -1.0) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -30000.0) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.8e-210) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	} else if (B <= 6e-150) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (B <= 3.5e-60) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((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 <= -30000.0) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.8e-210) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else if (B <= 6e-150) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (B <= 3.5e-60) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -30000.0:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.8e-210:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	elif B <= 6e-150:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif B <= 3.5e-60:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / 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 <= -30000.0)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.8e-210)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	elseif (B <= 6e-150)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (B <= 3.5e-60)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / 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 <= -30000.0)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.8e-210)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	elseif (B <= 6e-150)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (B <= 3.5e-60)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -30000.0], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.8e-210], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6e-150], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.5e-60], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -3e4

   1. Initial program 55.5%

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

   3. Taylor expanded in B around -inf 67.6%

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

   if -3e4 < B < 1.7999999999999999e-210

   1. Initial program 66.7%

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

   3. Taylor expanded in C around -inf 40.2%

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

   if 1.7999999999999999e-210 < B < 6.0000000000000003e-150

   1. Initial program 11.6%

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

      1. +-commutative 11.6%

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

      2. unpow2 11.6%

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

      3. unpow2 11.6%

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

      4. hypot-undefine 63.5%

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

      5. sub-neg 63.5%

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

      6. distribute-lft-in 25.1%

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

      7. hypot-undefine 10.4%

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

      8. unpow2 10.4%

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

      9. unpow2 10.4%

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

      10. +-commutative 10.4%

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

      11. unpow2 10.4%

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

      12. unpow2 10.4%

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

      13. hypot-define 25.1%

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

   4. Applied egg-rr 25.1%

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

   5. Taylor expanded in A around -inf 33.5%

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

      1. distribute-lft1-in 33.5%

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

      2. metadata-eval 33.5%

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

      3. mul0-lft 41.2%

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

   7. Simplified 41.2%

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

   if 6.0000000000000003e-150 < B < 3.49999999999999976e-60

   1. Initial program 67.6%

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

   3. Taylor expanded in A around inf 55.9%

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

   if 3.49999999999999976e-60 < B

   1. Initial program 59.9%

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

   3. Taylor expanded in B around inf 58.2%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -30000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-210}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;B \leq 6 \cdot 10^{-150}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 47.7% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3900000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-212}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-150}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 1.12 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3900000.0)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.4e-212)
     (* 180.0 (/ (atan (/ C B)) PI))
     (if (<= B 8.5e-150)
       (* 180.0 (/ (atan 0.0) PI))
       (if (<= B 1.12e-63)
         (* 180.0 (/ (atan (/ A (- B))) PI))
         (* 180.0 (/ (atan -1.0) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3900000.0) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.4e-212) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= 8.5e-150) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (B <= 1.12e-63) {
		tmp = 180.0 * (atan((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 <= -3900000.0) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.4e-212) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= 8.5e-150) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (B <= 1.12e-63) {
		tmp = 180.0 * (Math.atan((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 <= -3900000.0:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.4e-212:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= 8.5e-150:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif B <= 1.12e-63:
		tmp = 180.0 * (math.atan((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 <= -3900000.0)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.4e-212)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= 8.5e-150)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (B <= 1.12e-63)
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-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 <= -3900000.0)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.4e-212)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= 8.5e-150)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (B <= 1.12e-63)
		tmp = 180.0 * (atan((A / -B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3900000.0], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.4e-212], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.5e-150], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.12e-63], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -3.9e6

   1. Initial program 55.5%

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

   3. Taylor expanded in B around -inf 67.6%

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

   if -3.9e6 < B < 2.39999999999999989e-212

   1. Initial program 66.7%

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

   3. Simplified 69.0%

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

   5. Taylor expanded in B around inf 57.3%

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

      1. +-commutative 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in C around inf 40.2%

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

   if 2.39999999999999989e-212 < B < 8.4999999999999997e-150

   1. Initial program 11.6%

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

      1. +-commutative 11.6%

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

      2. unpow2 11.6%

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

      3. unpow2 11.6%

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

      4. hypot-undefine 63.5%

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

      5. sub-neg 63.5%

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

      6. distribute-lft-in 25.1%

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

      7. hypot-undefine 10.4%

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

      8. unpow2 10.4%

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

      9. unpow2 10.4%

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

      10. +-commutative 10.4%

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

      11. unpow2 10.4%

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

      12. unpow2 10.4%

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

      13. hypot-define 25.1%

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

   4. Applied egg-rr 25.1%

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

   5. Taylor expanded in A around -inf 33.5%

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

      1. distribute-lft1-in 33.5%

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

      2. metadata-eval 33.5%

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

      3. mul0-lft 41.2%

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

   7. Simplified 41.2%

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

   if 8.4999999999999997e-150 < B < 1.12000000000000002e-63

   1. Initial program 67.6%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in B around inf 63.5%

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

      1. +-commutative 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in A around inf 55.8%

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

      1. associate-*r/ 55.8%

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

      2. mul-1-neg 55.8%

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

   10. Simplified 55.8%

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

   if 1.12000000000000002e-63 < B

   1. Initial program 59.9%

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

   3. Taylor expanded in B around inf 58.2%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3900000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-212}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-150}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 1.12 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 47.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -30000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7.4 \cdot 10^{-211}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 270000000000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ C B)) PI))))
   (if (<= B -30000.0)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 7.4e-211)
       t_0
       (if (<= B 2.55e-132)
         (* 180.0 (/ (atan 0.0) PI))
         (if (<= B 270000000000.0) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double tmp;
	if (B <= -30000.0) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 7.4e-211) {
		tmp = t_0;
	} else if (B <= 2.55e-132) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (B <= 270000000000.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double tmp;
	if (B <= -30000.0) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 7.4e-211) {
		tmp = t_0;
	} else if (B <= 2.55e-132) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (B <= 270000000000.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((C / B)) / math.pi)
	tmp = 0
	if B <= -30000.0:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 7.4e-211:
		tmp = t_0
	elif B <= 2.55e-132:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif B <= 270000000000.0:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	tmp = 0.0
	if (B <= -30000.0)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 7.4e-211)
		tmp = t_0;
	elseif (B <= 2.55e-132)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (B <= 270000000000.0)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((C / B)) / pi);
	tmp = 0.0;
	if (B <= -30000.0)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 7.4e-211)
		tmp = t_0;
	elseif (B <= 2.55e-132)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (B <= 270000000000.0)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -30000.0], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.4e-211], t$95$0, If[LessEqual[B, 2.55e-132], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 270000000000.0], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -3e4

   1. Initial program 55.5%

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

   3. Taylor expanded in B around -inf 67.6%

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

   if -3e4 < B < 7.3999999999999996e-211 or 2.55000000000000003e-132 < B < 2.7e11

   1. Initial program 66.7%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in B around inf 58.3%

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

      1. +-commutative 58.3%

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

   7. Simplified 58.3%

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

   8. Taylor expanded in C around inf 38.8%

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

   if 7.3999999999999996e-211 < B < 2.55000000000000003e-132

   1. Initial program 24.2%

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

      1. +-commutative 24.2%

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

      2. unpow2 24.2%

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

      3. unpow2 24.2%

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

      4. hypot-undefine 67.0%

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

      5. sub-neg 67.0%

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

      6. distribute-lft-in 33.7%

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

      7. hypot-undefine 23.1%

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

      8. unpow2 23.1%

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

      9. unpow2 23.1%

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

      10. +-commutative 23.1%

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

      11. unpow2 23.1%

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

      12. unpow2 23.1%

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

      13. hypot-define 33.7%

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

   4. Applied egg-rr 33.7%

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

   5. Taylor expanded in A around -inf 24.0%

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

      1. distribute-lft1-in 24.0%

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

      2. metadata-eval 24.0%

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

      3. mul0-lft 36.4%

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

   7. Simplified 36.4%

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

   if 2.7e11 < B

   1. Initial program 60.6%

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

   3. Taylor expanded in B around inf 63.9%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -30000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7.4 \cdot 10^{-211}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.55 \cdot 10^{-132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;B \leq 270000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 55.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{if}\;B \leq -8.5 \cdot 10^{-66}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -1.55 \cdot 10^{-136}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq -2.7 \cdot 10^{-284}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + B}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (+ 1.0 (/ C B))))))
   (if (<= B -8.5e-66)
     t_0
     (if (<= B -1.55e-136)
       (* (atan (/ (* 0.5 B) A)) (/ 180.0 PI))
       (if (<= B -2.7e-284) t_0 (* 180.0 (/ (atan (/ (+ A B) (- B))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan((1.0 + (C / B)));
	double tmp;
	if (B <= -8.5e-66) {
		tmp = t_0;
	} else if (B <= -1.55e-136) {
		tmp = atan(((0.5 * B) / A)) * (180.0 / ((double) M_PI));
	} else if (B <= -2.7e-284) {
		tmp = t_0;
	} 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 t_0 = (180.0 / Math.PI) * Math.atan((1.0 + (C / B)));
	double tmp;
	if (B <= -8.5e-66) {
		tmp = t_0;
	} else if (B <= -1.55e-136) {
		tmp = Math.atan(((0.5 * B) / A)) * (180.0 / Math.PI);
	} else if (B <= -2.7e-284) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((A + B) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan((1.0 + (C / B)))
	tmp = 0
	if B <= -8.5e-66:
		tmp = t_0
	elif B <= -1.55e-136:
		tmp = math.atan(((0.5 * B) / A)) * (180.0 / math.pi)
	elif B <= -2.7e-284:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((A + B) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(C / B))))
	tmp = 0.0
	if (B <= -8.5e-66)
		tmp = t_0;
	elseif (B <= -1.55e-136)
		tmp = Float64(atan(Float64(Float64(0.5 * B) / A)) * Float64(180.0 / pi));
	elseif (B <= -2.7e-284)
		tmp = t_0;
	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)
	t_0 = (180.0 / pi) * atan((1.0 + (C / B)));
	tmp = 0.0;
	if (B <= -8.5e-66)
		tmp = t_0;
	elseif (B <= -1.55e-136)
		tmp = atan(((0.5 * B) / A)) * (180.0 / pi);
	elseif (B <= -2.7e-284)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((A + B) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -8.5e-66], t$95$0, If[LessEqual[B, -1.55e-136], N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.7e-284], t$95$0, 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 < -8.49999999999999966e-66 or -1.55e-136 < B < -2.69999999999999984e-284

   1. Initial program 59.5%

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

   3. Taylor expanded in B around 0 58.8%

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

   5. Simplified 75.0%

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

      1. div-inv 75.0%

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

      2. hypot-undefine 58.8%

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

      3. unpow2 58.8%

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

      4. unpow2 58.8%

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

      5. +-commutative 58.8%

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

      6. associate--l- 59.5%

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

      7. *-commutative 59.5%

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

      8. unpow2 59.5%

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

      9. unpow2 59.5%

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

      10. hypot-define 78.9%

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

   7. Applied egg-rr 78.9%

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

   8. Taylor expanded in B around -inf 69.5%

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

      1. associate--l+ 69.5%

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

      2. div-sub 71.2%

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

   10. Simplified 71.2%

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

   11. Taylor expanded in C around inf 61.5%

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

   if -8.49999999999999966e-66 < B < -1.55e-136

   1. Initial program 49.4%

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

   3. Taylor expanded in B around 0 48.8%

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

   5. Simplified 56.4%

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

      1. div-inv 56.4%

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

      2. hypot-undefine 48.8%

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

      3. unpow2 48.8%

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

      4. unpow2 48.8%

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

      5. +-commutative 48.8%

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

      6. associate--l- 49.4%

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

      7. *-commutative 49.4%

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

      8. unpow2 49.4%

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

      9. unpow2 49.4%

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

      10. hypot-define 71.8%

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

   7. Applied egg-rr 71.8%

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

   8. Taylor expanded in A around -inf 57.1%

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

      1. associate-*r/ 57.1%

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

   10. Simplified 57.1%

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

   if -2.69999999999999984e-284 < B

   1. Initial program 59.8%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in B around inf 72.8%

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

      1. +-commutative 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in C around 0 64.8%

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

      1. mul-1-neg 64.8%

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

      2. distribute-neg-frac2 64.8%

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

   10. Simplified 64.8%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{elif}\;B \leq -1.55 \cdot 10^{-136}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq -2.7 \cdot 10^{-284}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + B}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 46.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-75}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-75)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.7e-132)
     (* 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 <= -5e-75) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.7e-132) {
		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 <= -5e-75) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.7e-132) {
		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 <= -5e-75:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.7e-132:
		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 <= -5e-75)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.7e-132)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5e-75)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.7e-132)
		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, -5e-75], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.7e-132], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -4.99999999999999979e-75

   1. Initial program 60.1%

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

   3. Taylor expanded in B around -inf 58.3%

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

   if -4.99999999999999979e-75 < B < 2.6999999999999999e-132

   1. Initial program 55.8%

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

      1. +-commutative 55.8%

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

      2. unpow2 55.8%

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

      3. unpow2 55.8%

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

      4. hypot-undefine 77.1%

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

      5. sub-neg 77.1%

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

      6. distribute-lft-in 54.3%

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

      7. hypot-undefine 50.9%

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

      8. unpow2 50.9%

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

      9. unpow2 50.9%

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

      10. +-commutative 50.9%

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

      11. unpow2 50.9%

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

      12. unpow2 50.9%

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

      13. hypot-define 54.3%

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

   4. Applied egg-rr 54.3%

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

   5. Taylor expanded in A around -inf 15.3%

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

      1. distribute-lft1-in 15.3%

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

      2. metadata-eval 15.3%

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

      3. mul0-lft 25.9%

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

   7. Simplified 25.9%

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

   if 2.6999999999999999e-132 < B

   1. Initial program 62.0%

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

   3. Taylor expanded in B around inf 53.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-75}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 51.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -38000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -38000.0)
   (* 180.0 (/ (atan 1.0) PI))
   (* 180.0 (/ (atan (+ (/ C B) -1.0)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -38000.0) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C / B) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -38000.0) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C / B) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -38000.0:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C / B) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -38000.0)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -38000.0)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(((C / B) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -38000.0], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -38000

   1. Initial program 55.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf 67.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -38000 < B

   1. Initial program 60.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

   3. Simplified 73.2%

      \[\leadsto \color{blue}{180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around inf 64.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(A + B\right)}}{B}\right)}{\pi} \]
   6. Step-by-step derivation

      1. +-commutative 64.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(B + A\right)}}{B}\right)}{\pi} \]

   7. Simplified 64.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C - \color{blue}{\left(B + A\right)}}{B}\right)}{\pi} \]

   8. Taylor expanded in A around 0 50.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C - B}{B}\right)}}{\pi} \]
   9. Step-by-step derivation

      1. div-sub 50.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B} - \frac{B}{B}\right)}}{\pi} \]

      2. sub-neg 50.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B} + \left(-\frac{B}{B}\right)\right)}}{\pi} \]

      3. *-inverses 50.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-\color{blue}{1}\right)\right)}{\pi} \]

      4. metadata-eval 50.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \color{blue}{-1}\right)}{\pi} \]

   10. Simplified 50.1%

       \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B} + -1\right)}}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -38000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.1 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.1e-129) (* 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 <= 1.1e-129) {
		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 <= 1.1e-129) {
		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 <= 1.1e-129:
		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 <= 1.1e-129)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 1.1e-129)
		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, 1.1e-129], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 1.10000000000000001e-129

   1. Initial program 57.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 57.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}\right)\right)}{\pi} \]

      2. unpow2 57.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}\right)\right)}{\pi} \]

      3. unpow2 57.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}\right)\right)}{\pi} \]

      4. hypot-undefine 79.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}\right)\right)}{\pi} \]

      5. sub-neg 79.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) + \left(-\mathsf{hypot}\left(B, A - C\right)\right)\right)}\right)}{\pi} \]

      6. distribute-lft-in 67.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\mathsf{hypot}\left(B, A - C\right)\right)\right)}}{\pi} \]

      7. hypot-undefine 55.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}\right)\right)}{\pi} \]

      8. unpow2 55.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\color{blue}{{B}^{2}} + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)}{\pi} \]

      9. unpow2 55.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{{B}^{2} + \color{blue}{{\left(A - C\right)}^{2}}}\right)\right)}{\pi} \]

      10. +-commutative 55.3%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\color{blue}{{\left(A - C\right)}^{2} + {B}^{2}}}\right)\right)}{\pi} \]

      11. unpow2 55.3%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\color{blue}{\left(A - C\right) \cdot \left(A - C\right)} + {B}^{2}}\right)\right)}{\pi} \]

      12. unpow2 55.3%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

      13. hypot-define 67.1%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\color{blue}{\mathsf{hypot}\left(A - C, B\right)}\right)\right)}{\pi} \]

   4. Applied egg-rr 67.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(-\mathsf{hypot}\left(A - C, B\right)\right)\right)}}{\pi} \]

   5. Taylor expanded in A around -inf 9.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{C}{B} + \frac{C}{B}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. distribute-lft1-in 9.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(-1 + 1\right) \cdot \frac{C}{B}\right)}}{\pi} \]

      2. metadata-eval 9.7%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\color{blue}{0} \cdot \frac{C}{B}\right)}{\pi} \]

      3. mul0-lft 15.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   7. Simplified 15.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   if 1.10000000000000001e-129 < B

   1. Initial program 62.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around inf 53.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.1 \cdot 10^{-129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 21.7% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ 180 \cdot \frac{\tan^{-1} -1}{\pi} \end{array} \]

FPCore

(FPCore (A B C) :precision binary64 (* 180.0 (/ (atan -1.0) PI)))

C

double code(double A, double B, double C) {
	return 180.0 * (atan(-1.0) / ((double) M_PI));
}

Java

public static double code(double A, double B, double C) {
	return 180.0 * (Math.atan(-1.0) / Math.PI);
}

Python

def code(A, B, C):
	return 180.0 * (math.atan(-1.0) / math.pi)

Julia

function code(A, B, C)
	return Float64(180.0 * Float64(atan(-1.0) / pi))
end

MATLAB

function tmp = code(A, B, C)
	tmp = 180.0 * (atan(-1.0) / pi);
end

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 59.1%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
2. Add Preprocessing

3. Taylor expanded in B around inf 20.2%

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]

4. Final simplification 20.2%

   \[\leadsto 180 \cdot \frac{\tan^{-1} -1}{\pi} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024053 
(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)))