ABCF->ab-angle angle

Percentage Accurate: 53.3% → 81.4%

Time: 18.8s

Alternatives: 31

Speedup: 3.7×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+120}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.5e+120)
   (* (atan (/ (* B 0.5) A)) (/ 180.0 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 <= -1.5e+120) {
		tmp = atan(((B * 0.5) / A)) * (180.0 / ((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 <= -1.5e+120) {
		tmp = Math.atan(((B * 0.5) / A)) * (180.0 / 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 <= -1.5e+120:
		tmp = math.atan(((B * 0.5) / A)) * (180.0 / 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 <= -1.5e+120)
		tmp = Float64(atan(Float64(Float64(B * 0.5) / A)) * Float64(180.0 / 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 <= -1.5e+120)
		tmp = atan(((B * 0.5) / A)) * (180.0 / 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, -1.5e+120], N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * N[(180.0 / 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 < -1.5e120

   1. Initial program 15.7%

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

   3. Taylor expanded in A around -inf 75.8%

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

      1. associate-*r/ 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in B around 0 75.8%

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

      1. associate-*r/ 76.1%

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

      2. *-commutative 76.1%

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

      3. associate-/l* 76.3%

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

      4. *-commutative 76.3%

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

      5. associate-*l/ 76.3%

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

   8. Simplified 76.3%

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

   if -1.5e120 < A

   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. Step-by-step derivation

      1. associate-*l/ 62.7%

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

      2. *-lft-identity 62.7%

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

      3. +-commutative 62.7%

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

      4. unpow2 62.7%

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

      5. unpow2 62.7%

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

      6. hypot-define 82.9%

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

   3. Simplified 82.9%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+120}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8 \cdot 10^{+118}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8e+118)
   (* (atan (/ (* B 0.5) A)) (/ 180.0 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 <= -8e+118) {
		tmp = atan(((B * 0.5) / A)) * (180.0 / ((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 <= -8e+118) {
		tmp = Math.atan(((B * 0.5) / A)) * (180.0 / 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 <= -8e+118:
		tmp = math.atan(((B * 0.5) / A)) * (180.0 / 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 <= -8e+118)
		tmp = Float64(atan(Float64(Float64(B * 0.5) / A)) * Float64(180.0 / 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 <= -8e+118)
		tmp = atan(((B * 0.5) / A)) * (180.0 / 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, -8e+118], N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * N[(180.0 / 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 < -7.99999999999999973e118

   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 76.5%

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

      1. associate-*r/ 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in B around 0 76.5%

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

      1. associate-*r/ 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-/l* 77.0%

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

      4. *-commutative 77.0%

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

      5. associate-*l/ 77.0%

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

   8. Simplified 77.0%

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

   if -7.99999999999999973e118 < A

   1. Initial program 62.6%

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

   3. Simplified 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
3. Recombined 2 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8 \cdot 10^{+118}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 4.2 \cdot 10^{+173}:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot {\left(\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 4.2e+173)
   (* 180.0 (/ 1.0 (/ PI (atan (- 1.0 (/ (- A C) B))))))
   (* 180.0 (pow (/ PI (atan (* 0.5 (/ B A)))) -1.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 4.2e+173) {
		tmp = 180.0 * (1.0 / (((double) M_PI) / atan((1.0 - ((A - C) / B)))));
	} else {
		tmp = 180.0 * pow((((double) M_PI) / atan((0.5 * (B / A)))), -1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 4.2e+173) {
		tmp = 180.0 * (1.0 / (Math.PI / Math.atan((1.0 - ((A - C) / B)))));
	} else {
		tmp = 180.0 * Math.pow((Math.PI / Math.atan((0.5 * (B / A)))), -1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 4.2e+173:
		tmp = 180.0 * (1.0 / (math.pi / math.atan((1.0 - ((A - C) / B)))))
	else:
		tmp = 180.0 * math.pow((math.pi / math.atan((0.5 * (B / A)))), -1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 4.2e+173)
		tmp = Float64(180.0 * Float64(1.0 / Float64(pi / atan(Float64(1.0 - Float64(Float64(A - C) / B))))));
	else
		tmp = Float64(180.0 * (Float64(pi / atan(Float64(0.5 * Float64(B / A)))) ^ -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 4.2e+173)
		tmp = 180.0 * (1.0 / (pi / atan((1.0 - ((A - C) / B)))));
	else
		tmp = 180.0 * ((pi / atan((0.5 * (B / A)))) ^ -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 4.2e+173], N[(180.0 * N[(1.0 / N[(Pi / N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[Power[N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 4.2e173

   1. Initial program 60.5%

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

   3. Taylor expanded in B around -inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. div-sub 56.3%

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

   5. Simplified 56.3%

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

      1. clear-num 56.3%

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

      2. inv-pow 56.3%

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

      3. +-commutative 56.3%

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

   7. Applied egg-rr 56.3%

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

      1. unpow-1 56.3%

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

      2. +-commutative 56.3%

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

   9. Simplified 56.3%

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

   if 4.2e173 < C

   1. Initial program 9.2%

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

   3. Taylor expanded in A around -inf 22.2%

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

      1. associate-*r/ 22.2%

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

   5. Simplified 22.2%

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

      1. clear-num 34.4%

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

      2. inv-pow 34.4%

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

      3. associate-/l* 34.4%

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

   7. Applied egg-rr 34.4%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 4.2 \cdot 10^{+173}:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot {\left(\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}\right)}^{-1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.7%

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

   1. associate-*r/ 56.7%

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

   2. associate-*l/ 56.7%

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

   3. *-un-lft-identity 56.7%

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

   4. unpow2 56.7%

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

   5. unpow2 56.7%

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

   6. hypot-define 78.2%

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

4. Applied egg-rr 78.2%

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

5. Final simplification 78.2%

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

Alternative 5: 63.4% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.7%

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

   1. associate-*r/ 56.7%

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

   2. associate-*l/ 56.7%

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

   3. *-un-lft-identity 56.7%

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

   4. unpow2 56.7%

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

   5. unpow2 56.7%

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

   6. hypot-define 78.2%

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

4. Applied egg-rr 78.2%

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

   1. clear-num 78.2%

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

   2. inv-pow 78.2%

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

   3. associate--l- 75.8%

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

6. Applied egg-rr 75.8%

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

8. Simplified 78.1%

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

9. Taylor expanded in C around 0 47.7%

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

    1. associate-*r/ 47.7%

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

    2. mul-1-neg 47.7%

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

    3. +-commutative 47.7%

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

    4. unpow2 47.7%

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

    5. unpow2 47.7%

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

    6. hypot-undefine 63.8%

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

    7. distribute-neg-frac 63.8%

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

    8. distribute-neg-frac2 63.8%

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

11. Simplified 63.8%

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

    1. frac-2neg 63.8%

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

    2. metadata-eval 63.8%

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

    3. div-inv 63.8%

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

    4. distribute-neg-frac2 63.8%

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

    5. add-sqr-sqrt 29.9%

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

    6. sqrt-unprod 20.0%

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

    7. sqr-neg 20.0%

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

    8. sqrt-prod 4.2%

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

    9. add-sqr-sqrt 6.2%

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

    10. atan-neg 6.2%

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

    11. distribute-frac-neg2 6.2%

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

    12. clear-num 6.2%

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

13. Applied egg-rr 63.8%

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

    1. neg-mul-1 63.8%

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

    2. distribute-rgt-neg-in 63.8%

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

    3. hypot-undefine 47.7%

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

    4. unpow2 47.7%

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

    5. unpow2 47.7%

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

    6. +-commutative 47.7%

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

    7. unpow2 47.7%

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

    8. unpow2 47.7%

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

    9. hypot-define 63.8%

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

    10. distribute-neg-frac 63.8%

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

    11. metadata-eval 63.8%

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

15. Simplified 63.8%

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

16. Final simplification 63.8%

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

Alternative 6: 59.7% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 6400:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot \left(B \cdot \frac{B}{C}\right) + A \cdot 0}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 6400.0)
   (* 180.0 (/ 1.0 (/ PI (atan (- 1.0 (/ (- A C) B))))))
   (/ (* 180.0 (atan (/ (+ (* -0.5 (* B (/ B C))) (* A 0.0)) B))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 6400.0) {
		tmp = 180.0 * (1.0 / (((double) M_PI) / atan((1.0 - ((A - C) / B)))));
	} else {
		tmp = (180.0 * atan((((-0.5 * (B * (B / C))) + (A * 0.0)) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 6400.0) {
		tmp = 180.0 * (1.0 / (Math.PI / Math.atan((1.0 - ((A - C) / B)))));
	} else {
		tmp = (180.0 * Math.atan((((-0.5 * (B * (B / C))) + (A * 0.0)) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 6400.0:
		tmp = 180.0 * (1.0 / (math.pi / math.atan((1.0 - ((A - C) / B)))))
	else:
		tmp = (180.0 * math.atan((((-0.5 * (B * (B / C))) + (A * 0.0)) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 6400.0)
		tmp = Float64(180.0 * Float64(1.0 / Float64(pi / atan(Float64(1.0 - Float64(Float64(A - C) / B))))));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(-0.5 * Float64(B * Float64(B / C))) + Float64(A * 0.0)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 6400.0)
		tmp = 180.0 * (1.0 / (pi / atan((1.0 - ((A - C) / B)))));
	else
		tmp = (180.0 * atan((((-0.5 * (B * (B / C))) + (A * 0.0)) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 6400.0], N[(180.0 * N[(1.0 / N[(Pi / N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(N[(-0.5 * N[(B * N[(B / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(A * 0.0), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 6400

   1. Initial program 63.7%

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

   3. Taylor expanded in B around -inf 59.4%

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

      1. associate--l+ 59.4%

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

      2. div-sub 60.4%

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

   5. Simplified 60.4%

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

      1. clear-num 60.4%

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

      2. inv-pow 60.4%

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

      3. +-commutative 60.4%

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

   7. Applied egg-rr 60.4%

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

      1. unpow-1 60.4%

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

      2. +-commutative 60.4%

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

   9. Simplified 60.4%

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

   if 6400 < C

   1. Initial program 30.4%

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

      1. associate-*r/ 30.4%

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

      2. associate-*l/ 30.4%

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

      3. *-un-lft-identity 30.4%

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

      4. unpow2 30.4%

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

      5. unpow2 30.4%

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

      6. hypot-define 59.4%

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

   4. Applied egg-rr 59.4%

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

   5. Taylor expanded in C around inf 65.9%

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

      1. distribute-rgt1-in 65.9%

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

      2. metadata-eval 65.9%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot \frac{{B}^{2}}{C} - \color{blue}{0} \cdot A}{B}\right)}{\pi} \]

   7. Simplified 65.9%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{-0.5 \cdot \frac{{B}^{2}}{C} - 0 \cdot A}}{B}\right)}{\pi} \]
   8. Step-by-step derivation

      1. unpow2 65.9%

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

      2. *-un-lft-identity 65.9%

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

      3. times-frac 69.3%

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

   9. Applied egg-rr 69.3%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot \color{blue}{\left(\frac{B}{1} \cdot \frac{B}{C}\right)} - 0 \cdot A}{B}\right)}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 6400:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot \left(B \cdot \frac{B}{C}\right) + A \cdot 0}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 7500:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A - A}{B} + -0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 7500.0)
   (* 180.0 (/ 1.0 (/ PI (atan (- 1.0 (/ (- A C) B))))))
   (* 180.0 (/ (atan (+ (/ (- A A) B) (* -0.5 (/ B C)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 7500.0) {
		tmp = 180.0 * (1.0 / (((double) M_PI) / atan((1.0 - ((A - C) / B)))));
	} else {
		tmp = 180.0 * (atan((((A - A) / B) + (-0.5 * (B / C)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 7500.0) {
		tmp = 180.0 * (1.0 / (Math.PI / Math.atan((1.0 - ((A - C) / B)))));
	} else {
		tmp = 180.0 * (Math.atan((((A - A) / B) + (-0.5 * (B / C)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 7500.0:
		tmp = 180.0 * (1.0 / (math.pi / math.atan((1.0 - ((A - C) / B)))))
	else:
		tmp = 180.0 * (math.atan((((A - A) / B) + (-0.5 * (B / C)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 7500.0)
		tmp = Float64(180.0 * Float64(1.0 / Float64(pi / atan(Float64(1.0 - Float64(Float64(A - C) / B))))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(A - A) / B) + Float64(-0.5 * Float64(B / C)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 7500.0)
		tmp = 180.0 * (1.0 / (pi / atan((1.0 - ((A - C) / B)))));
	else
		tmp = 180.0 * (atan((((A - A) / B) + (-0.5 * (B / C)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 7500.0], N[(180.0 * N[(1.0 / N[(Pi / N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(A - A), $MachinePrecision] / B), $MachinePrecision] + N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 7500

   1. Initial program 63.7%

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

   3. Taylor expanded in B around -inf 59.4%

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

      1. associate--l+ 59.4%

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

      2. div-sub 60.4%

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

   5. Simplified 60.4%

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

      1. clear-num 60.4%

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

      2. inv-pow 60.4%

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

      3. +-commutative 60.4%

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

   7. Applied egg-rr 60.4%

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

      1. unpow-1 60.4%

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

      2. +-commutative 60.4%

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

   9. Simplified 60.4%

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

   if 7500 < C

   1. Initial program 30.4%

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

   3. Taylor expanded in C around inf 68.6%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 7500:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A - A}{B} + -0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 6800:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{A - A}{B} + -0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 6800.0)
   (* 180.0 (/ 1.0 (/ PI (atan (- 1.0 (/ (- A C) B))))))
   (/ (* 180.0 (atan (+ (/ (- A A) B) (* -0.5 (/ B C))))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 6800.0) {
		tmp = 180.0 * (1.0 / (((double) M_PI) / atan((1.0 - ((A - C) / B)))));
	} else {
		tmp = (180.0 * atan((((A - A) / B) + (-0.5 * (B / C))))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 6800.0) {
		tmp = 180.0 * (1.0 / (Math.PI / Math.atan((1.0 - ((A - C) / B)))));
	} else {
		tmp = (180.0 * Math.atan((((A - A) / B) + (-0.5 * (B / C))))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 6800.0:
		tmp = 180.0 * (1.0 / (math.pi / math.atan((1.0 - ((A - C) / B)))))
	else:
		tmp = (180.0 * math.atan((((A - A) / B) + (-0.5 * (B / C))))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 6800.0)
		tmp = Float64(180.0 * Float64(1.0 / Float64(pi / atan(Float64(1.0 - Float64(Float64(A - C) / B))))));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(A - A) / B) + Float64(-0.5 * Float64(B / C))))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 6800.0)
		tmp = 180.0 * (1.0 / (pi / atan((1.0 - ((A - C) / B)))));
	else
		tmp = (180.0 * atan((((A - A) / B) + (-0.5 * (B / C))))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 6800.0], N[(180.0 * N[(1.0 / N[(Pi / N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(N[(A - A), $MachinePrecision] / B), $MachinePrecision] + N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 6800

   1. Initial program 63.7%

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

   3. Taylor expanded in B around -inf 59.4%

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

      1. associate--l+ 59.4%

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

      2. div-sub 60.4%

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

   5. Simplified 60.4%

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

      1. clear-num 60.4%

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

      2. inv-pow 60.4%

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

      3. +-commutative 60.4%

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

   7. Applied egg-rr 60.4%

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

      1. unpow-1 60.4%

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

      2. +-commutative 60.4%

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

   9. Simplified 60.4%

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

   if 6800 < C

   1. Initial program 30.4%

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

      1. associate-*r/ 30.4%

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

      2. associate-*l/ 30.4%

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

      3. *-un-lft-identity 30.4%

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

      4. unpow2 30.4%

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

      5. unpow2 30.4%

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

      6. hypot-define 59.4%

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

   4. Applied egg-rr 59.4%

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

   5. Taylor expanded in C around inf 68.5%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 6800:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{A - A}{B} + -0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.3 \cdot 10^{-154}:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.3e-154)
   (* 180.0 (/ 1.0 (/ PI (atan (- 1.0 (/ (- A C) B))))))
   (/ (* 180.0 (atan (+ (/ C B) (- -1.0 (/ A B))))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.3e-154) {
		tmp = 180.0 * (1.0 / (((double) M_PI) / atan((1.0 - ((A - C) / B)))));
	} else {
		tmp = (180.0 * atan(((C / B) + (-1.0 - (A / B))))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.3e-154) {
		tmp = 180.0 * (1.0 / (Math.PI / Math.atan((1.0 - ((A - C) / B)))));
	} else {
		tmp = (180.0 * Math.atan(((C / B) + (-1.0 - (A / B))))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 1.3e-154:
		tmp = 180.0 * (1.0 / (math.pi / math.atan((1.0 - ((A - C) / B)))))
	else:
		tmp = (180.0 * math.atan(((C / B) + (-1.0 - (A / B))))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 1.3e-154)
		tmp = Float64(180.0 * Float64(1.0 / Float64(pi / atan(Float64(1.0 - Float64(Float64(A - C) / B))))));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B))))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 1.3e-154)
		tmp = 180.0 * (1.0 / (pi / atan((1.0 - ((A - C) / B)))));
	else
		tmp = (180.0 * atan(((C / B) + (-1.0 - (A / B))))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 1.3e-154], N[(180.0 * N[(1.0 / N[(Pi / N[ArcTan[N[(1.0 - N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 1.3e-154

   1. Initial program 55.9%

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

   3. Taylor expanded in B around -inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. div-sub 66.8%

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

   5. Simplified 66.8%

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

      1. clear-num 66.8%

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

      2. inv-pow 66.8%

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

      3. +-commutative 66.8%

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

   7. Applied egg-rr 66.8%

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

      1. unpow-1 66.8%

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

      2. +-commutative 66.8%

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

   9. Simplified 66.8%

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

   if 1.3e-154 < B

   1. Initial program 57.9%

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

      1. associate-*r/ 58.0%

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

      2. associate-*l/ 58.0%

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

      3. *-un-lft-identity 58.0%

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

      4. unpow2 58.0%

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

      5. unpow2 58.0%

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

      6. hypot-define 81.2%

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

   4. Applied egg-rr 81.2%

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

   5. Taylor expanded in B around inf 75.7%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.3 \cdot 10^{-154}:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(1 - \frac{A - C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.4% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 4.6 \cdot 10^{-282}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + B}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 4.6e-282)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (* 180.0 (/ (atan (/ (+ A B) (- B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 4.6e-282) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A + B) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 4.6e-282) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A + B) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 4.6e-282:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A + B) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 4.6e-282)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + B) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 4.6e-282)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan(((A + B) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 4.6e-282], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A + B), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 4.5999999999999998e-282

   1. Initial program 56.3%

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

   3. Taylor expanded in B around -inf 69.7%

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

      1. associate--l+ 69.7%

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

      2. div-sub 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in C around inf 61.6%

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

   if 4.5999999999999998e-282 < B

   1. Initial program 57.1%

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

   3. Taylor expanded in C around 0 51.0%

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

      1. mul-1-neg 51.0%

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

      2. distribute-neg-frac2 51.0%

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

      3. +-commutative 51.0%

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

      4. unpow2 51.0%

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

      5. unpow2 51.0%

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

      6. hypot-define 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in A around 0 60.4%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 4.6 \cdot 10^{-282}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + B}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.8% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.4 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.4e-101)
   (* 180.0 (/ (atan 1.0) PI))
   (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.4e-101) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.4e-101) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5.4e-101:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5.4e-101)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5.4e-101)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5.4e-101], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -5.4000000000000003e-101

   1. Initial program 50.5%

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

   3. Taylor expanded in B around -inf 53.6%

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

   if -5.4000000000000003e-101 < B

   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 A around inf 27.1%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.4 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 33.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.5 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.5e-302)
   (* 180.0 (/ (atan 1.0) PI))
   (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.5e-302) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.5e-302) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -6.5e-302:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -6.5e-302)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -6.5e-302)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -6.5e-302], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -6.4999999999999995e-302

   1. Initial program 55.3%

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

   3. Taylor expanded in B around -inf 44.9%

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

   if -6.4999999999999995e-302 < B

   1. Initial program 58.0%

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

      1. associate-*r/ 58.0%

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

      2. associate-*l/ 58.0%

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

      3. *-un-lft-identity 58.0%

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

      4. unpow2 58.0%

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

      5. unpow2 58.0%

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

      6. hypot-define 80.8%

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

   4. Applied egg-rr 80.8%

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

   5. Taylor expanded in C around inf 28.2%

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

   6. Taylor expanded in A around inf 28.2%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.5 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.0% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.7 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.7e-85)
   (* 180.0 (/ (atan 1.0) PI))
   (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.7e-85) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.7e-85) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.7e-85:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.7e-85)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.7e-85)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.7e-85], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.7e-85

   1. Initial program 50.5%

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

   3. Taylor expanded in B around -inf 54.5%

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

   if -1.7e-85 < B

   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 C around -inf 27.2%

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

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.7 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 5.5 \cdot 10^{-283}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 5.5e-283)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (* (/ 180.0 PI) (atan (- -1.0 (/ A B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.5e-283) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.5e-283) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 5.5e-283:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 5.5e-283)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 5.5e-283)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 5.5e-283], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 5.49999999999999953e-283

   1. Initial program 56.3%

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

   3. Taylor expanded in B around -inf 69.7%

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

      1. associate--l+ 69.7%

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

      2. div-sub 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in C around inf 61.6%

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

   if 5.49999999999999953e-283 < B

   1. Initial program 57.1%

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

   3. Taylor expanded in C around 0 51.0%

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

      1. mul-1-neg 51.0%

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

      2. distribute-neg-frac2 51.0%

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

      3. +-commutative 51.0%

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

      4. unpow2 51.0%

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

      5. unpow2 51.0%

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

      6. hypot-define 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in A around 0 60.4%

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

   7. Taylor expanded in A around 0 60.4%

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

      1. associate-*r/ 60.4%

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

      2. neg-mul-1 60.4%

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

      3. distribute-frac-neg2 60.4%

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

      4. *-commutative 60.4%

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

      5. associate-/l* 60.4%

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

      6. distribute-frac-neg2 60.4%

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

      7. distribute-neg-frac 60.4%

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

      8. +-commutative 60.4%

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

      9. distribute-neg-in 60.4%

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

      10. unsub-neg 60.4%

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

      11. div-sub 60.4%

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

      12. distribute-frac-neg 60.4%

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

      13. *-inverses 60.4%

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

      14. metadata-eval 60.4%

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

   9. Simplified 60.4%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 5.5 \cdot 10^{-283}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 3.3 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 3.3e-109)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (* (atan (/ (* B 0.5) A)) (/ 180.0 PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 3.3e-109) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = atan(((B * 0.5) / A)) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 3.3e-109) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = Math.atan(((B * 0.5) / A)) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 3.3e-109:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = math.atan(((B * 0.5) / A)) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 3.3e-109)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(atan(Float64(Float64(B * 0.5) / A)) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 3.3e-109)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = atan(((B * 0.5) / A)) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 3.3e-109], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 3.2999999999999999e-109

   1. Initial program 57.3%

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

   3. Taylor expanded in C around 0 46.4%

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

      1. mul-1-neg 46.4%

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

      2. distribute-neg-frac2 46.4%

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

      3. +-commutative 46.4%

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

      4. unpow2 46.4%

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

      5. unpow2 46.4%

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

      6. hypot-define 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in B around -inf 54.9%

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

      1. mul-1-neg 54.9%

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

      2. unsub-neg 54.9%

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

   8. Simplified 54.9%

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

   if 3.2999999999999999e-109 < B

   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 A around -inf 23.6%

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

      1. associate-*r/ 23.6%

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

   5. Simplified 23.6%

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

   6. Taylor expanded in B around 0 23.6%

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

      1. associate-*r/ 23.7%

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

      2. *-commutative 23.7%

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

      3. associate-/l* 23.7%

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

      4. *-commutative 23.7%

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

      5. associate-*l/ 23.7%

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

   8. Simplified 23.7%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 3.3 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 41.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 3.7 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 3.7e-109)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 3.7e-109) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 3.7e-109) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 3.7e-109:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 3.7e-109)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 3.7e-109)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 3.7e-109], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 3.69999999999999981e-109

   1. Initial program 57.3%

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

   3. Taylor expanded in C around 0 46.4%

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

      1. mul-1-neg 46.4%

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

      2. distribute-neg-frac2 46.4%

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

      3. +-commutative 46.4%

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

      4. unpow2 46.4%

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

      5. unpow2 46.4%

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

      6. hypot-define 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in B around -inf 54.9%

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

      1. mul-1-neg 54.9%

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

      2. unsub-neg 54.9%

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

   8. Simplified 54.9%

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

   if 3.69999999999999981e-109 < B

   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. Step-by-step derivation

      1. associate-*r/ 55.6%

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

      2. associate-*l/ 55.6%

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

      3. *-un-lft-identity 55.6%

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

      4. unpow2 55.6%

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

      5. unpow2 55.6%

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

      6. hypot-define 81.9%

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

   4. Applied egg-rr 81.9%

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

      1. clear-num 81.9%

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

      2. inv-pow 81.9%

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

      3. associate--l- 79.9%

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

   6. Applied egg-rr 79.9%

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

   8. Simplified 81.9%

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

   9. Taylor expanded in A around -inf 23.7%

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

       1. associate-*r/ 23.7%

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

   11. Simplified 23.7%

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

       1. associate-/r/ 23.7%

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

       2. clear-num 23.7%

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

       3. associate-/l* 23.7%

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

   13. Applied egg-rr 23.7%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 3.7 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 41.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 8.2 \cdot 10^{-283}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 8.2e-283)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (* (/ 180.0 PI) (atan (* B (/ -0.5 C))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 8.2e-283) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / C)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 8.2e-283) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / C)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 8.2e-283:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / C)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 8.2e-283)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / C))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 8.2e-283)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = (180.0 / pi) * atan((B * (-0.5 / C)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 8.2e-283], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 8.19999999999999973e-283

   1. Initial program 56.3%

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

   3. Taylor expanded in B around -inf 69.7%

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

      1. associate--l+ 69.7%

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

      2. div-sub 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in C around inf 61.6%

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

   if 8.19999999999999973e-283 < B

   1. Initial program 57.1%

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

      1. associate-*r/ 57.1%

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

      2. associate-*l/ 57.1%

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

      3. *-un-lft-identity 57.1%

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

      4. unpow2 57.1%

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

      5. unpow2 57.1%

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

      6. hypot-define 80.0%

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

   4. Applied egg-rr 80.0%

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

   5. Taylor expanded in C around inf 29.2%

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

   6. Taylor expanded in A around 0 29.2%

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

   8. Simplified 29.1%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 8.2 \cdot 10^{-283}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 41.5% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 5.5 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 5.5e-281)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (/ 180.0 (/ PI (atan (* -0.5 (/ B C)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.5e-281) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((-0.5 * (B / C))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.5e-281) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((-0.5 * (B / C))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 5.5e-281:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((-0.5 * (B / C))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 5.5e-281)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-0.5 * Float64(B / C)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 5.5e-281)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 / (pi / atan((-0.5 * (B / C))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 5.5e-281], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 5.5000000000000003e-281

   1. Initial program 56.3%

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

   3. Taylor expanded in B around -inf 69.7%

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

      1. associate--l+ 69.7%

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

      2. div-sub 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in C around inf 61.6%

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

   if 5.5000000000000003e-281 < B

   1. Initial program 57.1%

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

      1. associate-*r/ 57.1%

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

      2. associate-*l/ 57.1%

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

      3. *-un-lft-identity 57.1%

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

      4. unpow2 57.1%

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

      5. unpow2 57.1%

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

      6. hypot-define 80.0%

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

   4. Applied egg-rr 80.0%

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

   5. Taylor expanded in C around inf 25.4%

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

      1. distribute-rgt1-in 25.4%

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

      2. metadata-eval 25.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot \frac{{B}^{2}}{C} - \color{blue}{0} \cdot A}{B}\right)}{\pi} \]

   7. Simplified 25.4%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{-0.5 \cdot \frac{{B}^{2}}{C} - 0 \cdot A}}{B}\right)}{\pi} \]
   8. Step-by-step derivation

      1. clear-num 25.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{\pi}{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot \frac{{B}^{2}}{C} - 0 \cdot A}{B}\right)}}} \]

      2. inv-pow 25.4%

         \[\leadsto \color{blue}{{\left(\frac{\pi}{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot \frac{{B}^{2}}{C} - 0 \cdot A}{B}\right)}\right)}^{-1}} \]

   9. Applied egg-rr 25.4%

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

       1. unpow-1 25.4%

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

       2. associate-/r* 25.4%

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

       3. metadata-eval 25.4%

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

       4. associate-/l/ 24.5%

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

       5. unpow2 24.5%

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

       6. times-frac 29.8%

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

       7. *-inverses 29.8%

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

       8. *-lft-identity 29.8%

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

   11. Simplified 29.8%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 5.5 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 41.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 3.6 \cdot 10^{-280}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 3.6e-280)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (/ (* 180.0 (atan (* B (/ -0.5 C)))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 3.6e-280) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((B * (-0.5 / C)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 3.6e-280) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((B * (-0.5 / C)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 3.6e-280:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = (180.0 * math.atan((B * (-0.5 / C)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 3.6e-280)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(B * Float64(-0.5 / C)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 3.6e-280)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = (180.0 * atan((B * (-0.5 / C)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 3.6e-280], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 3.59999999999999994e-280

   1. Initial program 56.3%

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

   3. Taylor expanded in B around -inf 69.7%

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

      1. associate--l+ 69.7%

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

      2. div-sub 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in C around inf 61.6%

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

   if 3.59999999999999994e-280 < B

   1. Initial program 57.1%

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

      1. associate-*r/ 57.1%

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

      2. associate-*l/ 57.1%

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

      3. *-un-lft-identity 57.1%

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

      4. unpow2 57.1%

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

      5. unpow2 57.1%

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

      6. hypot-define 80.0%

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

   4. Applied egg-rr 80.0%

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

   5. Taylor expanded in C around inf 29.2%

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

   6. Taylor expanded in A around inf 29.2%

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

      1. associate-*r/ 29.2%

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

      2. *-commutative 29.2%

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

      3. associate-/l* 29.2%

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

   8. Simplified 29.2%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 3.6 \cdot 10^{-280}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 41.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 5.4 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 5.4e-281)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (/ (* 180.0 (atan (/ (* B -0.5) C))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.4e-281) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((B * -0.5) / C))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.4e-281) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((B * -0.5) / C))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 5.4e-281:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = (180.0 * math.atan(((B * -0.5) / C))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 5.4e-281)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / C))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 5.4e-281)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = (180.0 * atan(((B * -0.5) / C))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 5.4e-281], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 5.39999999999999979e-281

   1. Initial program 56.3%

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

   3. Taylor expanded in B around -inf 69.7%

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

      1. associate--l+ 69.7%

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

      2. div-sub 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in C around inf 61.6%

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

   if 5.39999999999999979e-281 < B

   1. Initial program 57.1%

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

      1. associate-*r/ 57.1%

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

      2. associate-*l/ 57.1%

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

      3. *-un-lft-identity 57.1%

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

      4. unpow2 57.1%

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

      5. unpow2 57.1%

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

      6. hypot-define 80.0%

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

   4. Applied egg-rr 80.0%

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

   5. Taylor expanded in C around inf 25.4%

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

      1. distribute-rgt1-in 25.4%

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

      2. metadata-eval 25.4%

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-0.5 \cdot \frac{{B}^{2}}{C} - \color{blue}{0} \cdot A}{B}\right)}{\pi} \]

   7. Simplified 25.4%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{-0.5 \cdot \frac{{B}^{2}}{C} - 0 \cdot A}}{B}\right)}{\pi} \]

   8. Taylor expanded in B around 0 29.2%

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

      1. associate-*r/ 29.2%

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

   10. Simplified 29.2%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 5.4 \cdot 10^{-281}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 41.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 4.8 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 4.8e-109)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (/ (* 180.0 (atan (/ (* B 0.5) A))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 4.8e-109) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((B * 0.5) / A))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 4.8e-109) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((B * 0.5) / A))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 4.8e-109:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = (180.0 * math.atan(((B * 0.5) / A))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 4.8e-109)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * 0.5) / A))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 4.8e-109)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = (180.0 * atan(((B * 0.5) / A))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 4.8e-109], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 4.79999999999999977e-109

   1. Initial program 57.3%

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

   3. Taylor expanded in C around 0 46.4%

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

      1. mul-1-neg 46.4%

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

      2. distribute-neg-frac2 46.4%

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

      3. +-commutative 46.4%

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

      4. unpow2 46.4%

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

      5. unpow2 46.4%

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

      6. hypot-define 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in B around -inf 54.9%

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

      1. mul-1-neg 54.9%

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

      2. unsub-neg 54.9%

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

   8. Simplified 54.9%

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

   if 4.79999999999999977e-109 < B

   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. Step-by-step derivation

      1. associate-*r/ 55.6%

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

      2. associate-*l/ 55.6%

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

      3. *-un-lft-identity 55.6%

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

      4. unpow2 55.6%

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

      5. unpow2 55.6%

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

      6. hypot-define 81.9%

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

   4. Applied egg-rr 81.9%

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

   5. Taylor expanded in A around -inf 23.7%

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

      1. associate-*r/ 23.7%

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

   7. Simplified 23.7%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 4.8 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 47.2% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq 6.5 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A 6.5e+25)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (/ (* 180.0 (atan (/ (* A -2.0) B))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= 6.5e+25) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((A * -2.0) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= 6.5e+25) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((A * -2.0) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= 6.5e+25:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = (180.0 * math.atan(((A * -2.0) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= 6.5e+25)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(A * -2.0) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= 6.5e+25)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = (180.0 * atan(((A * -2.0) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, 6.5e+25], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < 6.50000000000000005e25

   1. Initial program 49.0%

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

   3. Taylor expanded in B around -inf 42.4%

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

      1. associate--l+ 42.4%

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

      2. div-sub 43.5%

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

   5. Simplified 43.5%

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

   6. Taylor expanded in C around inf 41.8%

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

   if 6.50000000000000005e25 < A

   1. Initial program 79.1%

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

      1. associate-*r/ 79.2%

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

      2. associate-*l/ 79.2%

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

      3. *-un-lft-identity 79.2%

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

      4. unpow2 79.2%

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

      5. unpow2 79.2%

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

      6. hypot-define 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in A around inf 72.4%

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

      1. *-commutative 72.4%

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

   7. Simplified 72.4%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq 6.5 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 35.7% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.2 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.2e-101)
   (* 180.0 (/ (atan 1.0) PI))
   (* 180.0 (/ (atan (- (/ A B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.2e-101) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-(A / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.2e-101) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-(A / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -6.2e-101:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-(A / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -6.2e-101)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -6.2e-101)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-(A / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -6.2e-101], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[(-N[(A / B), $MachinePrecision])], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -6.19999999999999946e-101

   1. Initial program 50.5%

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

   3. Taylor expanded in B around -inf 53.6%

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

   if -6.19999999999999946e-101 < B

   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 C around 0 49.5%

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

      1. mul-1-neg 49.5%

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

      2. distribute-neg-frac2 49.5%

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

      3. +-commutative 49.5%

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

      4. unpow2 49.5%

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

      5. unpow2 49.5%

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

      6. hypot-define 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in A around 0 54.6%

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

   7. Taylor expanded in A around inf 26.9%

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

      1. associate-*r/ 26.9%

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

      2. mul-1-neg 26.9%

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

   9. Simplified 26.9%

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

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.2 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 50.6% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.7%

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

3. Taylor expanded in B around -inf 51.1%

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

   1. associate--l+ 51.1%

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

   2. div-sub 52.7%

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

5. Simplified 52.7%

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

   1. clear-num 52.7%

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

   2. inv-pow 52.7%

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

   3. +-commutative 52.7%

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

7. Applied egg-rr 52.7%

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

   1. unpow-1 52.7%

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

   2. +-commutative 52.7%

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

9. Simplified 52.7%

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

10. Final simplification 52.7%

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

Alternative 25: 28.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.4 \cdot 10^{-201}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.4e-201)
   (* 180.0 (/ (atan 1.0) PI))
   (* 180.0 (/ (atan (/ 0.0 B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.4e-201) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.4e-201) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5.4e-201:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5.4e-201)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5.4e-201)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5.4e-201], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -5.40000000000000011e-201

   1. Initial program 53.4%

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

   3. Taylor expanded in B around -inf 48.1%

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

   if -5.40000000000000011e-201 < B

   1. Initial program 59.2%

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

   3. Taylor expanded in C around inf 15.5%

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

      1. associate-*r/ 15.5%

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

      2. distribute-rgt1-in 15.5%

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

      3. metadata-eval 15.5%

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

      4. mul0-lft 15.5%

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

      5. metadata-eval 15.5%

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

   5. Simplified 15.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.4 \cdot 10^{-201}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 28.5% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.7 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.7e-203)
   (* 180.0 (/ (atan 1.0) PI))
   (/ (* 180.0 (atan (/ 0.0 B))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.7e-203) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((0.0 / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.7e-203) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((0.0 / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.7e-203:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = (180.0 * math.atan((0.0 / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.7e-203)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(0.0 / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.7e-203)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = (180.0 * atan((0.0 / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.7e-203], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -3.70000000000000002e-203

   1. Initial program 53.4%

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

   3. Taylor expanded in B around -inf 48.1%

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

   if -3.70000000000000002e-203 < B

   1. Initial program 59.2%

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

      1. associate-*r/ 59.2%

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

      2. associate-*l/ 59.2%

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

      3. *-un-lft-identity 59.2%

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

      4. unpow2 59.2%

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

      5. unpow2 59.2%

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

      6. hypot-define 80.9%

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

   4. Applied egg-rr 80.9%

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

   5. Taylor expanded in C around inf 15.5%

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

      1. distribute-rgt1-in 15.5%

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

      2. metadata-eval 15.5%

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

      3. mul0-lft 15.5%

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

      4. metadata-eval 15.5%

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

   7. Simplified 15.5%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.7 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 50.6% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.7%

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

3. Taylor expanded in B around -inf 51.1%

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

   1. associate--l+ 51.1%

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

   2. div-sub 52.7%

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

5. Simplified 52.7%

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

6. Final simplification 52.7%

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

Alternative 28: 20.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 9.2 \cdot 10^{-205}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 9.2e-205) (* 180.0 (/ (atan -1.0) PI)) (* 180.0 (/ (atan 1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 9.2e-205) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 9.2e-205) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 9.2e-205:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 9.2e-205)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 9.2e-205)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan(1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 9.2e-205], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 9.1999999999999997e-205

   1. Initial program 66.0%

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

   3. Taylor expanded in B around inf 27.0%

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

   if 9.1999999999999997e-205 < C

   1. Initial program 41.6%

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

   3. Taylor expanded in B around -inf 22.4%

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

4. Final simplification 25.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 9.2 \cdot 10^{-205}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 20.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 3.05 \cdot 10^{-204}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 3.05e-204)
   (* 180.0 (/ (atan -1.0) PI))
   (/ (* 180.0 (atan 1.0)) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 3.05e-204) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(1.0)) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 3.05e-204) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(1.0)) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 3.05e-204:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = (180.0 * math.atan(1.0)) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 3.05e-204)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(1.0)) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 3.05e-204)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = (180.0 * atan(1.0)) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 3.05e-204], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 3.04999999999999987e-204

   1. Initial program 66.0%

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

   3. Taylor expanded in B around inf 27.0%

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

   if 3.04999999999999987e-204 < C

   1. Initial program 41.6%

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

      1. associate-*r/ 41.7%

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

      2. associate-*l/ 41.7%

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

      3. *-un-lft-identity 41.7%

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

      4. unpow2 41.7%

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

      5. unpow2 41.7%

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

      6. hypot-define 65.9%

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

   4. Applied egg-rr 65.9%

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

   5. Taylor expanded in B around -inf 22.4%

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

4. Final simplification 25.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 3.05 \cdot 10^{-204}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 39.6% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.7%

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

3. Taylor expanded in B around -inf 51.1%

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

   1. associate--l+ 51.1%

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

   2. div-sub 52.7%

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

5. Simplified 52.7%

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

6. Taylor expanded in C around inf 40.7%

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

7. Final simplification 40.7%

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

Alternative 31: 20.8% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.7%

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

3. Taylor expanded in B around inf 22.6%

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

4. Final simplification 22.6%

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

Reproduce

herbie shell --seed 2024066 
(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)))