ABCF->ab-angle angle

Percentage Accurate: 54.5% → 81.1%

Time: 23.5s

Alternatives: 20

Speedup: 3.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 2.5 \cdot 10^{+111}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - \mathsf{hypot}\left(B, A - C\right)\right) - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 2.5e+111)
   (* 180.0 (/ (atan (/ (- (- C (hypot B (- A C))) A) B)) PI))
   (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.5e+111) {
		tmp = 180.0 * (atan((((C - hypot(B, (A - C))) - A) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.5e+111) {
		tmp = 180.0 * (Math.atan((((C - Math.hypot(B, (A - C))) - A) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 2.5e+111:
		tmp = 180.0 * (math.atan((((C - math.hypot(B, (A - C))) - A) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 2.5e+111)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - hypot(B, Float64(A - C))) - A) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 2.5e+111)
		tmp = 180.0 * (atan((((C - hypot(B, (A - C))) - A) / B)) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 2.5e+111], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 2.4999999999999998e111

   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 79.1%

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

   5. Taylor expanded in C around -inf 84.2%

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

   if 2.4999999999999998e111 < C

   1. Initial program 8.4%

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

   3. Taylor expanded in C around inf 56.3%

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

   4. Taylor expanded in B around inf 80.4%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 2.5 \cdot 10^{+111}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - \mathsf{hypot}\left(B, A - C\right)\right) - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := A + \mathsf{hypot}\left(B, A\right)\\ \mathbf{if}\;C \leq -1 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - t\_0}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.5 \cdot 10^{+135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_0 \cdot \frac{-1}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (+ A (hypot B A))))
   (if (<= C -1e-80)
     (* 180.0 (/ (atan (/ (- C t_0) B)) PI))
     (if (<= C 1.5e+135)
       (* 180.0 (/ (atan (* t_0 (/ -1.0 B))) PI))
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = A + hypot(B, A);
	double tmp;
	if (C <= -1e-80) {
		tmp = 180.0 * (atan(((C - t_0) / B)) / ((double) M_PI));
	} else if (C <= 1.5e+135) {
		tmp = 180.0 * (atan((t_0 * (-1.0 / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = A + Math.hypot(B, A);
	double tmp;
	if (C <= -1e-80) {
		tmp = 180.0 * (Math.atan(((C - t_0) / B)) / Math.PI);
	} else if (C <= 1.5e+135) {
		tmp = 180.0 * (Math.atan((t_0 * (-1.0 / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = A + math.hypot(B, A)
	tmp = 0
	if C <= -1e-80:
		tmp = 180.0 * (math.atan(((C - t_0) / B)) / math.pi)
	elif C <= 1.5e+135:
		tmp = 180.0 * (math.atan((t_0 * (-1.0 / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(A + hypot(B, A))
	tmp = 0.0
	if (C <= -1e-80)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - t_0) / B)) / pi));
	elseif (C <= 1.5e+135)
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 * Float64(-1.0 / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = A + hypot(B, A);
	tmp = 0.0;
	if (C <= -1e-80)
		tmp = 180.0 * (atan(((C - t_0) / B)) / pi);
	elseif (C <= 1.5e+135)
		tmp = 180.0 * (atan((t_0 * (-1.0 / B))) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1e-80], N[(180.0 * N[(N[ArcTan[N[(N[(C - t$95$0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.5e+135], N[(180.0 * N[(N[ArcTan[N[(t$95$0 * N[(-1.0 / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if C < -9.99999999999999961e-81

   1. Initial program 76.8%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in C around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. unpow2 76.8%

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

      3. unpow2 76.8%

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

      4. hypot-def 92.6%

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

   7. Simplified 92.6%

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

   if -9.99999999999999961e-81 < C < 1.5e135

   1. Initial program 52.7%

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

   3. Taylor expanded in C around 0 51.4%

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

      1. mul-1-neg 51.4%

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

      2. +-commutative 51.4%

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

      3. unpow2 51.4%

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

      4. unpow2 51.4%

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

      5. hypot-def 76.4%

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

   5. Simplified 76.4%

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

   if 1.5e135 < C

   1. Initial program 5.0%

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

   3. Taylor expanded in C around inf 56.6%

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

   4. Taylor expanded in B around inf 84.1%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.5 \cdot 10^{+135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(A + \mathsf{hypot}\left(B, A\right)\right) \cdot \frac{-1}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.35 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.3 \cdot 10^{+135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(A + \mathsf{hypot}\left(B, A\right)\right) \cdot \frac{-1}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.35e-80)
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))
   (if (<= C 2.3e+135)
     (* 180.0 (/ (atan (* (+ A (hypot B A)) (/ -1.0 B))) PI))
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.35e-80) {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	} else if (C <= 2.3e+135) {
		tmp = 180.0 * (atan(((A + hypot(B, A)) * (-1.0 / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.35e-80) {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	} else if (C <= 2.3e+135) {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(B, A)) * (-1.0 / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.35e-80:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	elif C <= 2.3e+135:
		tmp = 180.0 * (math.atan(((A + math.hypot(B, A)) * (-1.0 / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.35e-80)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	elseif (C <= 2.3e+135)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) * Float64(-1.0 / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.35e-80)
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	elseif (C <= 2.3e+135)
		tmp = 180.0 * (atan(((A + hypot(B, A)) * (-1.0 / B))) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.35e-80], 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], If[LessEqual[C, 2.3e+135], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] * N[(-1.0 / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.3500000000000001e-80

   1. Initial program 76.8%

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

   3. Simplified 92.9%

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

   if -1.3500000000000001e-80 < C < 2.3000000000000001e135

   1. Initial program 52.7%

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

   3. Taylor expanded in C around 0 51.4%

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

      1. mul-1-neg 51.4%

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

      2. +-commutative 51.4%

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

      3. unpow2 51.4%

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

      4. unpow2 51.4%

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

      5. hypot-def 76.4%

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

   5. Simplified 76.4%

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

   if 2.3000000000000001e135 < C

   1. Initial program 5.0%

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

   3. Taylor expanded in C around inf 56.6%

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

   4. Taylor expanded in B around inf 84.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.35 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.3 \cdot 10^{+135}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(A + \mathsf{hypot}\left(B, A\right)\right) \cdot \frac{-1}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -850000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{+131}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -850000000000.0)
   (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
   (if (<= C 9.5e+131)
     (* 180.0 (/ (atan (/ (- (+ A (hypot B A))) B)) PI))
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -850000000000.0) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else if (C <= 9.5e+131) {
		tmp = 180.0 * (atan((-(A + hypot(B, A)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -850000000000.0) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else if (C <= 9.5e+131) {
		tmp = 180.0 * (Math.atan((-(A + Math.hypot(B, A)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -850000000000.0:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	elif C <= 9.5e+131:
		tmp = 180.0 * (math.atan((-(A + math.hypot(B, A)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -850000000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	elseif (C <= 9.5e+131)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-Float64(A + hypot(B, A))) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -850000000000.0)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	elseif (C <= 9.5e+131)
		tmp = 180.0 * (atan((-(A + hypot(B, A)) / B)) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -850000000000.0], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 9.5e+131], N[(180.0 * N[(N[ArcTan[N[((-N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -8.5e11

   1. Initial program 80.8%

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

   3. Taylor expanded in A around 0 80.8%

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

      1. unpow2 80.8%

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

      2. unpow2 80.8%

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

      3. hypot-def 95.0%

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

   5. Simplified 95.0%

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

   if -8.5e11 < C < 9.50000000000000015e131

   1. Initial program 54.0%

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

   3. Taylor expanded in C around 0 51.7%

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

      1. associate-*r/ 51.7%

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

      2. mul-1-neg 51.7%

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

      3. +-commutative 51.7%

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

      4. unpow2 51.7%

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

      5. unpow2 51.7%

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

      6. hypot-def 76.7%

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

   5. Simplified 76.7%

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

   if 9.50000000000000015e131 < C

   1. Initial program 5.0%

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

   3. Taylor expanded in C around inf 56.6%

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

   4. Taylor expanded in B around inf 84.1%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -850000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 9.5 \cdot 10^{+131}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := A + \mathsf{hypot}\left(B, A\right)\\ \mathbf{if}\;C \leq -8.2 \cdot 10^{-81}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - t\_0}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.5 \cdot 10^{+131}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-t\_0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (+ A (hypot B A))))
   (if (<= C -8.2e-81)
     (* 180.0 (/ (atan (/ (- C t_0) B)) PI))
     (if (<= C 8.5e+131)
       (* 180.0 (/ (atan (/ (- t_0) B)) PI))
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = A + hypot(B, A);
	double tmp;
	if (C <= -8.2e-81) {
		tmp = 180.0 * (atan(((C - t_0) / B)) / ((double) M_PI));
	} else if (C <= 8.5e+131) {
		tmp = 180.0 * (atan((-t_0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = A + Math.hypot(B, A);
	double tmp;
	if (C <= -8.2e-81) {
		tmp = 180.0 * (Math.atan(((C - t_0) / B)) / Math.PI);
	} else if (C <= 8.5e+131) {
		tmp = 180.0 * (Math.atan((-t_0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = A + math.hypot(B, A)
	tmp = 0
	if C <= -8.2e-81:
		tmp = 180.0 * (math.atan(((C - t_0) / B)) / math.pi)
	elif C <= 8.5e+131:
		tmp = 180.0 * (math.atan((-t_0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(A + hypot(B, A))
	tmp = 0.0
	if (C <= -8.2e-81)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - t_0) / B)) / pi));
	elseif (C <= 8.5e+131)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-t_0) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = A + hypot(B, A);
	tmp = 0.0;
	if (C <= -8.2e-81)
		tmp = 180.0 * (atan(((C - t_0) / B)) / pi);
	elseif (C <= 8.5e+131)
		tmp = 180.0 * (atan((-t_0 / B)) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -8.2e-81], N[(180.0 * N[(N[ArcTan[N[(N[(C - t$95$0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 8.5e+131], N[(180.0 * N[(N[ArcTan[N[((-t$95$0) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if C < -8.19999999999999968e-81

   1. Initial program 76.8%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in C around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. unpow2 76.8%

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

      3. unpow2 76.8%

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

      4. hypot-def 92.6%

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

   7. Simplified 92.6%

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

   if -8.19999999999999968e-81 < C < 8.50000000000000063e131

   1. Initial program 52.7%

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

   3. Taylor expanded in C around 0 51.4%

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

      1. associate-*r/ 51.4%

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

      2. mul-1-neg 51.4%

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

      3. +-commutative 51.4%

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

      4. unpow2 51.4%

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

      5. unpow2 51.4%

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

      6. hypot-def 76.4%

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

   5. Simplified 76.4%

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

   if 8.50000000000000063e131 < C

   1. Initial program 5.0%

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

   3. Taylor expanded in C around inf 56.6%

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

   4. Taylor expanded in B around inf 84.1%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -8.2 \cdot 10^{-81}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.5 \cdot 10^{+131}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-\left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.4 \cdot 10^{+154}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{+164}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.4e+154)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (if (<= A 1.55e+164)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.4e+154) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= 1.55e+164) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.4e+154) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= 1.55e+164) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.4e+154:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= 1.55e+164:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.4e+154)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= 1.55e+164)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.4e+154)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= 1.55e+164)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.4e+154], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.55e+164], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.40000000000000015e154

   1. Initial program 8.3%

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

   3. Taylor expanded in A around -inf 54.9%

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

   4. Taylor expanded in B around 0 82.9%

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

      1. associate-*r/ 82.9%

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

   6. Simplified 82.9%

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

   if -2.40000000000000015e154 < A < 1.5500000000000001e164

   1. Initial program 54.8%

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

   3. Taylor expanded in A around 0 49.9%

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

      1. unpow2 49.9%

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

      2. unpow2 49.9%

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

      3. hypot-def 74.2%

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

   5. Simplified 74.2%

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

   if 1.5500000000000001e164 < A

   1. Initial program 90.2%

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

   3. Taylor expanded in C around 0 90.2%

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

      1. mul-1-neg 90.2%

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

      2. +-commutative 90.2%

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

      3. unpow2 90.2%

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

      4. unpow2 90.2%

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

      5. hypot-def 96.7%

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

   5. Simplified 96.7%

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

   6. Taylor expanded in B around -inf 95.0%

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

      1. mul-1-neg 95.0%

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

      2. unsub-neg 95.0%

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

   8. Simplified 95.0%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.4 \cdot 10^{+154}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{+164}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.5% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1450000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.35 \cdot 10^{-219}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 1.1 \cdot 10^{-48}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.6 \cdot 10^{+38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.8 \cdot 10^{+92}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))
   (if (<= C -1450000000000.0)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= C 2.35e-219)
       t_0
       (if (<= C 1.1e-48)
         (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
         (if (<= C 6.6e+38)
           (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
           (if (<= C 2.8e+92)
             t_0
             (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	double tmp;
	if (C <= -1450000000000.0) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= 2.35e-219) {
		tmp = t_0;
	} else if (C <= 1.1e-48) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else if (C <= 6.6e+38) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (C <= 2.8e+92) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	double tmp;
	if (C <= -1450000000000.0) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= 2.35e-219) {
		tmp = t_0;
	} else if (C <= 1.1e-48) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else if (C <= 6.6e+38) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (C <= 2.8e+92) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	tmp = 0
	if C <= -1450000000000.0:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= 2.35e-219:
		tmp = t_0
	elif C <= 1.1e-48:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	elif C <= 6.6e+38:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif C <= 2.8e+92:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi))
	tmp = 0.0
	if (C <= -1450000000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= 2.35e-219)
		tmp = t_0;
	elseif (C <= 1.1e-48)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	elseif (C <= 6.6e+38)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (C <= 2.8e+92)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 - (A / B))) / pi);
	tmp = 0.0;
	if (C <= -1450000000000.0)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= 2.35e-219)
		tmp = t_0;
	elseif (C <= 1.1e-48)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	elseif (C <= 6.6e+38)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (C <= 2.8e+92)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1450000000000.0], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.35e-219], t$95$0, If[LessEqual[C, 1.1e-48], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.6e+38], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.8e+92], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -1.45e12

   1. Initial program 80.8%

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

   3. Taylor expanded in C around -inf 75.6%

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

   if -1.45e12 < C < 2.35e-219 or 6.5999999999999998e38 < C < 2.80000000000000001e92

   1. Initial program 57.5%

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

   3. Taylor expanded in C around 0 55.6%

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

      1. mul-1-neg 55.6%

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

      2. +-commutative 55.6%

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

      3. unpow2 55.6%

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

      4. unpow2 55.6%

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

      5. hypot-def 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in B around -inf 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   8. Simplified 58.5%

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

   if 2.35e-219 < C < 1.10000000000000006e-48

   1. Initial program 57.2%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in B around inf 63.2%

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

      1. +-commutative 63.2%

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

   7. Simplified 63.2%

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

   8. Taylor expanded in C around 0 62.8%

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

      1. associate-*r/ 62.8%

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

      2. distribute-lft-in 62.8%

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

      3. mul-1-neg 62.8%

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

      4. sub-neg 62.8%

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

      5. mul-1-neg 62.8%

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

   10. Simplified 62.8%

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

   11. Taylor expanded in A around 0 62.8%

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

       1. mul-1-neg 62.8%

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

       2. distribute-neg-frac 62.8%

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

       3. distribute-neg-out 62.8%

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

       4. neg-mul-1 62.8%

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

       5. sub-neg 62.8%

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

       6. sub-neg 62.8%

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

       7. neg-mul-1 62.8%

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

       8. distribute-neg-out 62.8%

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

       9. +-commutative 62.8%

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

       10. distribute-neg-out 62.8%

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

       11. mul-1-neg 62.8%

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

       12. sub-neg 62.8%

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

       13. div-sub 62.8%

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

       14. mul-1-neg 62.8%

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

       15. distribute-frac-neg 62.8%

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

       16. *-inverses 62.8%

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

       17. metadata-eval 62.8%

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

   13. Simplified 62.8%

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

   if 1.10000000000000006e-48 < C < 6.5999999999999998e38

   1. Initial program 37.9%

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

   3. Taylor expanded in A around -inf 51.1%

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

      1. associate-*r/ 51.1%

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

   5. Simplified 51.1%

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

   if 2.80000000000000001e92 < C

   1. Initial program 10.5%

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

   3. Taylor expanded in C around inf 55.4%

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

   4. Taylor expanded in B around inf 79.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1450000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.35 \cdot 10^{-219}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.1 \cdot 10^{-48}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.6 \cdot 10^{+38}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.8 \cdot 10^{+92}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.9% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.45 \cdot 10^{-58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.85 \cdot 10^{-221}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 3.3 \cdot 10^{-43}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.3 \cdot 10^{+39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.1 \cdot 10^{+93}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))
   (if (<= C -1.45e-58)
     (* 180.0 (/ (atan (/ (- C B) B)) PI))
     (if (<= C 3.85e-221)
       t_0
       (if (<= C 3.3e-43)
         (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
         (if (<= C 2.3e+39)
           (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
           (if (<= C 1.1e+93)
             t_0
             (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	double tmp;
	if (C <= -1.45e-58) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (C <= 3.85e-221) {
		tmp = t_0;
	} else if (C <= 3.3e-43) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else if (C <= 2.3e+39) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (C <= 1.1e+93) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	double tmp;
	if (C <= -1.45e-58) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (C <= 3.85e-221) {
		tmp = t_0;
	} else if (C <= 3.3e-43) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else if (C <= 2.3e+39) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (C <= 1.1e+93) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	tmp = 0
	if C <= -1.45e-58:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif C <= 3.85e-221:
		tmp = t_0
	elif C <= 3.3e-43:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	elif C <= 2.3e+39:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif C <= 1.1e+93:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi))
	tmp = 0.0
	if (C <= -1.45e-58)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (C <= 3.85e-221)
		tmp = t_0;
	elseif (C <= 3.3e-43)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	elseif (C <= 2.3e+39)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (C <= 1.1e+93)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 - (A / B))) / pi);
	tmp = 0.0;
	if (C <= -1.45e-58)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (C <= 3.85e-221)
		tmp = t_0;
	elseif (C <= 3.3e-43)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	elseif (C <= 2.3e+39)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (C <= 1.1e+93)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.45e-58], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.85e-221], t$95$0, If[LessEqual[C, 3.3e-43], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.3e+39], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.1e+93], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -1.44999999999999995e-58

   1. Initial program 75.4%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in B around inf 78.5%

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

      1. +-commutative 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in A around 0 78.2%

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

   if -1.44999999999999995e-58 < C < 3.84999999999999996e-221 or 2.30000000000000012e39 < C < 1.10000000000000011e93

   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 0 57.0%

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

      1. mul-1-neg 57.0%

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

      2. +-commutative 57.0%

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

      3. unpow2 57.0%

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

      4. unpow2 57.0%

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

      5. hypot-def 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in B around -inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. unsub-neg 61.1%

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

   8. Simplified 61.1%

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

   if 3.84999999999999996e-221 < C < 3.30000000000000016e-43

   1. Initial program 57.2%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in B around inf 63.2%

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

      1. +-commutative 63.2%

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

   7. Simplified 63.2%

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

   8. Taylor expanded in C around 0 62.8%

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

      1. associate-*r/ 62.8%

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

      2. distribute-lft-in 62.8%

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

      3. mul-1-neg 62.8%

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

      4. sub-neg 62.8%

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

      5. mul-1-neg 62.8%

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

   10. Simplified 62.8%

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

   11. Taylor expanded in A around 0 62.8%

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

       1. mul-1-neg 62.8%

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

       2. distribute-neg-frac 62.8%

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

       3. distribute-neg-out 62.8%

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

       4. neg-mul-1 62.8%

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

       5. sub-neg 62.8%

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

       6. sub-neg 62.8%

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

       7. neg-mul-1 62.8%

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

       8. distribute-neg-out 62.8%

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

       9. +-commutative 62.8%

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

       10. distribute-neg-out 62.8%

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

       11. mul-1-neg 62.8%

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

       12. sub-neg 62.8%

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

       13. div-sub 62.8%

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

       14. mul-1-neg 62.8%

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

       15. distribute-frac-neg 62.8%

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

       16. *-inverses 62.8%

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

       17. metadata-eval 62.8%

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

   13. Simplified 62.8%

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

   if 3.30000000000000016e-43 < C < 2.30000000000000012e39

   1. Initial program 37.9%

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

   3. Taylor expanded in A around -inf 51.1%

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

      1. associate-*r/ 51.1%

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

   5. Simplified 51.1%

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

   if 1.10000000000000011e93 < C

   1. Initial program 10.5%

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

   3. Taylor expanded in C around inf 55.4%

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

   4. Taylor expanded in B around inf 79.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.45 \cdot 10^{-58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.85 \cdot 10^{-221}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.3 \cdot 10^{-43}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.3 \cdot 10^{+39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.1 \cdot 10^{+93}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.9% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -7 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.9 \cdot 10^{-220}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{-43}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.2 \cdot 10^{+91}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))
   (if (<= C -7e-54)
     (* 180.0 (/ (atan (/ (- C B) B)) PI))
     (if (<= C 3.9e-220)
       t_0
       (if (<= C 3.5e-43)
         (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
         (if (<= C 2.2e+40)
           (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
           (if (<= C 5.2e+91)
             t_0
             (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	double tmp;
	if (C <= -7e-54) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (C <= 3.9e-220) {
		tmp = t_0;
	} else if (C <= 3.5e-43) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else if (C <= 2.2e+40) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (C <= 5.2e+91) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	double tmp;
	if (C <= -7e-54) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (C <= 3.9e-220) {
		tmp = t_0;
	} else if (C <= 3.5e-43) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else if (C <= 2.2e+40) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (C <= 5.2e+91) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	tmp = 0
	if C <= -7e-54:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif C <= 3.9e-220:
		tmp = t_0
	elif C <= 3.5e-43:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	elif C <= 2.2e+40:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif C <= 5.2e+91:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi))
	tmp = 0.0
	if (C <= -7e-54)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (C <= 3.9e-220)
		tmp = t_0;
	elseif (C <= 3.5e-43)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	elseif (C <= 2.2e+40)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (C <= 5.2e+91)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 - (A / B))) / pi);
	tmp = 0.0;
	if (C <= -7e-54)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (C <= 3.9e-220)
		tmp = t_0;
	elseif (C <= 3.5e-43)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	elseif (C <= 2.2e+40)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (C <= 5.2e+91)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -7e-54], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.9e-220], t$95$0, If[LessEqual[C, 3.5e-43], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.2e+40], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 5.2e+91], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -6.99999999999999964e-54

   1. Initial program 75.4%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in B around inf 78.5%

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

      1. +-commutative 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in A around 0 78.2%

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

   if -6.99999999999999964e-54 < C < 3.90000000000000003e-220 or 2.1999999999999999e40 < C < 5.2000000000000001e91

   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 0 57.0%

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

      1. mul-1-neg 57.0%

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

      2. +-commutative 57.0%

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

      3. unpow2 57.0%

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

      4. unpow2 57.0%

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

      5. hypot-def 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in B around -inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. unsub-neg 61.1%

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

   8. Simplified 61.1%

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

   if 3.90000000000000003e-220 < C < 3.49999999999999997e-43

   1. Initial program 57.2%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in B around inf 63.2%

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

      1. +-commutative 63.2%

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

   7. Simplified 63.2%

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

   8. Taylor expanded in C around 0 62.8%

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

      1. associate-*r/ 62.8%

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

      2. distribute-lft-in 62.8%

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

      3. mul-1-neg 62.8%

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

      4. sub-neg 62.8%

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

      5. mul-1-neg 62.8%

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

   10. Simplified 62.8%

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

   11. Taylor expanded in A around 0 62.8%

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

       1. mul-1-neg 62.8%

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

       2. distribute-neg-frac 62.8%

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

       3. distribute-neg-out 62.8%

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

       4. neg-mul-1 62.8%

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

       5. sub-neg 62.8%

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

       6. sub-neg 62.8%

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

       7. neg-mul-1 62.8%

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

       8. distribute-neg-out 62.8%

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

       9. +-commutative 62.8%

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

       10. distribute-neg-out 62.8%

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

       11. mul-1-neg 62.8%

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

       12. sub-neg 62.8%

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

       13. div-sub 62.8%

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

       14. mul-1-neg 62.8%

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

       15. distribute-frac-neg 62.8%

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

       16. *-inverses 62.8%

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

       17. metadata-eval 62.8%

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

   13. Simplified 62.8%

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

   if 3.49999999999999997e-43 < C < 2.1999999999999999e40

   1. Initial program 37.9%

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

   3. Taylor expanded in A around -inf 48.1%

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

   4. Taylor expanded in B around 0 51.1%

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

      1. associate-*r/ 51.3%

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

   6. Simplified 51.3%

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

   if 5.2000000000000001e91 < C

   1. Initial program 10.5%

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

   3. Taylor expanded in C around inf 55.4%

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

   4. Taylor expanded in B around inf 79.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -7 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.9 \cdot 10^{-220}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.5 \cdot 10^{-43}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.2 \cdot 10^{+91}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;C \leq -500000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.6 \cdot 10^{-92}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq -1.9 \cdot 10^{-231}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.9 \cdot 10^{-227}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan 1.0) PI))))
   (if (<= C -500000000000.0)
     (* 180.0 (/ (atan (/ C B)) PI))
     (if (<= C -2.6e-92)
       t_0
       (if (<= C -1.9e-231)
         (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
         (if (<= C 2.9e-227) t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(1.0) / ((double) M_PI));
	double tmp;
	if (C <= -500000000000.0) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (C <= -2.6e-92) {
		tmp = t_0;
	} else if (C <= -1.9e-231) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (C <= 2.9e-227) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(1.0) / Math.PI);
	double tmp;
	if (C <= -500000000000.0) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (C <= -2.6e-92) {
		tmp = t_0;
	} else if (C <= -1.9e-231) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (C <= 2.9e-227) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(1.0) / math.pi)
	tmp = 0
	if C <= -500000000000.0:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif C <= -2.6e-92:
		tmp = t_0
	elif C <= -1.9e-231:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif C <= 2.9e-227:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(1.0) / pi))
	tmp = 0.0
	if (C <= -500000000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (C <= -2.6e-92)
		tmp = t_0;
	elseif (C <= -1.9e-231)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (C <= 2.9e-227)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(1.0) / pi);
	tmp = 0.0;
	if (C <= -500000000000.0)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (C <= -2.6e-92)
		tmp = t_0;
	elseif (C <= -1.9e-231)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (C <= 2.9e-227)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -500000000000.0], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -2.6e-92], t$95$0, If[LessEqual[C, -1.9e-231], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.9e-227], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -5e11

   1. Initial program 80.8%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in B around inf 85.6%

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

      1. +-commutative 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in C around inf 75.2%

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

   if -5e11 < C < -2.6e-92 or -1.90000000000000007e-231 < C < 2.90000000000000011e-227

   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 44.8%

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

   if -2.6e-92 < C < -1.90000000000000007e-231

   1. Initial program 58.3%

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

   3. Taylor expanded in A around inf 45.0%

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

   if 2.90000000000000011e-227 < C

   1. Initial program 35.8%

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

   3. Taylor expanded in C around inf 33.3%

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

   4. Taylor expanded in B around inf 53.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -500000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.6 \cdot 10^{-92}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq -1.9 \cdot 10^{-231}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.9 \cdot 10^{-227}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;C \leq -880000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -7.8 \cdot 10^{-92}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq -6.1 \cdot 10^{-232}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.36 \cdot 10^{-227}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan 1.0) PI))))
   (if (<= C -880000000000.0)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= C -7.8e-92)
       t_0
       (if (<= C -6.1e-232)
         (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
         (if (<= C 1.36e-227)
           t_0
           (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(1.0) / ((double) M_PI));
	double tmp;
	if (C <= -880000000000.0) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= -7.8e-92) {
		tmp = t_0;
	} else if (C <= -6.1e-232) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if (C <= 1.36e-227) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(1.0) / Math.PI);
	double tmp;
	if (C <= -880000000000.0) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= -7.8e-92) {
		tmp = t_0;
	} else if (C <= -6.1e-232) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if (C <= 1.36e-227) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(1.0) / math.pi)
	tmp = 0
	if C <= -880000000000.0:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= -7.8e-92:
		tmp = t_0
	elif C <= -6.1e-232:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif C <= 1.36e-227:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(1.0) / pi))
	tmp = 0.0
	if (C <= -880000000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= -7.8e-92)
		tmp = t_0;
	elseif (C <= -6.1e-232)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif (C <= 1.36e-227)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(1.0) / pi);
	tmp = 0.0;
	if (C <= -880000000000.0)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= -7.8e-92)
		tmp = t_0;
	elseif (C <= -6.1e-232)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif (C <= 1.36e-227)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -880000000000.0], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -7.8e-92], t$95$0, If[LessEqual[C, -6.1e-232], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.36e-227], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -8.8e11

   1. Initial program 80.8%

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

   3. Taylor expanded in C around -inf 75.6%

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

   if -8.8e11 < C < -7.7999999999999993e-92 or -6.1000000000000001e-232 < C < 1.35999999999999996e-227

   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 44.8%

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

   if -7.7999999999999993e-92 < C < -6.1000000000000001e-232

   1. Initial program 58.3%

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

   3. Taylor expanded in A around inf 45.0%

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

   if 1.35999999999999996e-227 < C

   1. Initial program 35.8%

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

   3. Taylor expanded in C around inf 33.3%

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

   4. Taylor expanded in B around inf 53.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -880000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -7.8 \cdot 10^{-92}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq -6.1 \cdot 10^{-232}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.36 \cdot 10^{-227}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -1.05 \cdot 10^{+44}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -6.2 \cdot 10^{-290}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 1.12 \cdot 10^{-231}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 5.7 \cdot 10^{-58}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))
   (if (<= C -1.05e+44)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= C -6.2e-290)
       t_0
       (if (<= C 1.12e-231)
         (* 180.0 (/ (atan 1.0) PI))
         (if (<= C 5.7e-58) t_0 (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	double tmp;
	if (C <= -1.05e+44) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= -6.2e-290) {
		tmp = t_0;
	} else if (C <= 1.12e-231) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (C <= 5.7e-58) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	double tmp;
	if (C <= -1.05e+44) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= -6.2e-290) {
		tmp = t_0;
	} else if (C <= 1.12e-231) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (C <= 5.7e-58) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	tmp = 0
	if C <= -1.05e+44:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= -6.2e-290:
		tmp = t_0
	elif C <= 1.12e-231:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif C <= 5.7e-58:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi))
	tmp = 0.0
	if (C <= -1.05e+44)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= -6.2e-290)
		tmp = t_0;
	elseif (C <= 1.12e-231)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (C <= 5.7e-58)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((-1.0 - (A / B))) / pi);
	tmp = 0.0;
	if (C <= -1.05e+44)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= -6.2e-290)
		tmp = t_0;
	elseif (C <= 1.12e-231)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (C <= 5.7e-58)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.05e+44], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -6.2e-290], t$95$0, If[LessEqual[C, 1.12e-231], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 5.7e-58], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.04999999999999993e44

   1. Initial program 82.2%

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

   3. Taylor expanded in C around -inf 80.1%

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

   if -1.04999999999999993e44 < C < -6.1999999999999998e-290 or 1.11999999999999997e-231 < C < 5.70000000000000032e-58

   1. Initial program 61.0%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in B around inf 57.9%

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

      1. +-commutative 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in C around 0 54.9%

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

      1. associate-*r/ 54.9%

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

      2. distribute-lft-in 54.9%

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

      3. mul-1-neg 54.9%

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

      4. sub-neg 54.9%

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

      5. mul-1-neg 54.9%

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

   10. Simplified 54.9%

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

   11. Taylor expanded in A around 0 54.9%

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

       1. mul-1-neg 54.9%

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

       2. distribute-neg-frac 54.9%

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

       3. distribute-neg-out 54.9%

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

       4. neg-mul-1 54.9%

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

       5. sub-neg 54.9%

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

       6. sub-neg 54.9%

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

       7. neg-mul-1 54.9%

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

       8. distribute-neg-out 54.9%

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

       9. +-commutative 54.9%

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

       10. distribute-neg-out 54.9%

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

       11. mul-1-neg 54.9%

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

       12. sub-neg 54.9%

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

       13. div-sub 54.9%

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

       14. mul-1-neg 54.9%

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

       15. distribute-frac-neg 54.9%

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

       16. *-inverses 54.9%

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

       17. metadata-eval 54.9%

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

   13. Simplified 54.9%

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

   if -6.1999999999999998e-290 < C < 1.11999999999999997e-231

   1. Initial program 51.5%

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

   3. Taylor expanded in B around -inf 50.7%

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

   if 5.70000000000000032e-58 < C

   1. Initial program 24.0%

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

   3. Taylor expanded in C around inf 42.5%

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

   4. Taylor expanded in B around inf 60.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.05 \cdot 10^{+44}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -6.2 \cdot 10^{-290}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.12 \cdot 10^{-231}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 5.7 \cdot 10^{-58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.9% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -3 \cdot 10^{-40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5 \cdot 10^{-203}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))))
   (if (<= B -3e-40)
     t_0
     (if (<= B -4e-101)
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
       (if (<= B -5e-203) t_0 (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	double tmp;
	if (B <= -3e-40) {
		tmp = t_0;
	} else if (B <= -4e-101) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= -5e-203) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	double tmp;
	if (B <= -3e-40) {
		tmp = t_0;
	} else if (B <= -4e-101) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= -5e-203) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + B)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	tmp = 0
	if B <= -3e-40:
		tmp = t_0
	elif B <= -4e-101:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= -5e-203:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((C - (A + B)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi))
	tmp = 0.0
	if (B <= -3e-40)
		tmp = t_0;
	elseif (B <= -4e-101)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= -5e-203)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + B)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	tmp = 0.0;
	if (B <= -3e-40)
		tmp = t_0;
	elseif (B <= -4e-101)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= -5e-203)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3e-40], t$95$0, If[LessEqual[B, -4e-101], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -5e-203], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.0000000000000002e-40 or -4.00000000000000021e-101 < B < -5.0000000000000002e-203

   1. Initial program 52.8%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in B around -inf 77.5%

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

      1. neg-mul-1 77.5%

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

      2. unsub-neg 77.5%

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

   7. Simplified 77.5%

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

   if -3.0000000000000002e-40 < B < -4.00000000000000021e-101

   1. Initial program 22.9%

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

   3. Taylor expanded in C around inf 35.1%

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

   4. Taylor expanded in B around inf 54.9%

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

   if -5.0000000000000002e-203 < B

   1. Initial program 57.7%

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

   3. Simplified 71.7%

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

   5. Taylor expanded in B around inf 64.8%

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

      1. +-commutative 64.8%

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

   7. Simplified 64.8%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3 \cdot 10^{-40}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.9% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.6 \cdot 10^{-40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-198}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))))
   (if (<= B -1.6e-40)
     t_0
     (if (<= B -4e-101)
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
       (if (<= B -1e-198) t_0 (/ (* 180.0 (atan (/ (- C (+ A B)) B))) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	double tmp;
	if (B <= -1.6e-40) {
		tmp = t_0;
	} else if (B <= -4e-101) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else if (B <= -1e-198) {
		tmp = t_0;
	} else {
		tmp = (180.0 * atan(((C - (A + B)) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	double tmp;
	if (B <= -1.6e-40) {
		tmp = t_0;
	} else if (B <= -4e-101) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else if (B <= -1e-198) {
		tmp = t_0;
	} else {
		tmp = (180.0 * Math.atan(((C - (A + B)) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	tmp = 0
	if B <= -1.6e-40:
		tmp = t_0
	elif B <= -4e-101:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	elif B <= -1e-198:
		tmp = t_0
	else:
		tmp = (180.0 * math.atan(((C - (A + B)) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi))
	tmp = 0.0
	if (B <= -1.6e-40)
		tmp = t_0;
	elseif (B <= -4e-101)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	elseif (B <= -1e-198)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - Float64(A + B)) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	tmp = 0.0;
	if (B <= -1.6e-40)
		tmp = t_0;
	elseif (B <= -4e-101)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	elseif (B <= -1e-198)
		tmp = t_0;
	else
		tmp = (180.0 * atan(((C - (A + B)) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.6e-40], t$95$0, If[LessEqual[B, -4e-101], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1e-198], t$95$0, N[(N[(180.0 * N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.60000000000000001e-40 or -4.00000000000000021e-101 < B < -9.9999999999999991e-199

   1. Initial program 52.8%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in B around -inf 77.5%

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

      1. neg-mul-1 77.5%

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

      2. unsub-neg 77.5%

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

   7. Simplified 77.5%

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

   if -1.60000000000000001e-40 < B < -4.00000000000000021e-101

   1. Initial program 22.9%

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

   3. Taylor expanded in C around inf 35.1%

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

   4. Taylor expanded in B around inf 54.9%

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

   if -9.9999999999999991e-199 < B

   1. Initial program 57.7%

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

   3. Simplified 71.7%

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

   5. Taylor expanded in B around inf 64.8%

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

      1. +-commutative 64.8%

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

   7. Simplified 64.8%

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

      1. associate-*r/ 64.8%

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

      2. +-commutative 64.8%

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

   9. Applied egg-rr 64.8%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.6 \cdot 10^{-40}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-198}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.8% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1250000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.5 \cdot 10^{-217}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1250000000000.0)
   (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
   (if (<= C 5.5e-217)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (if (<= C 1.6e-57)
       (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
       (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1250000000000.0) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= 5.5e-217) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (C <= 1.6e-57) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1250000000000.0) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= 5.5e-217) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (C <= 1.6e-57) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1250000000000.0:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= 5.5e-217:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif C <= 1.6e-57:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1250000000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= 5.5e-217)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (C <= 1.6e-57)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1250000000000.0)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= 5.5e-217)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (C <= 1.6e-57)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1250000000000.0], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 5.5e-217], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.6e-57], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.25e12

   1. Initial program 80.8%

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

   3. Taylor expanded in C around -inf 75.6%

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

   if -1.25e12 < C < 5.49999999999999975e-217

   1. Initial program 57.5%

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

   3. Taylor expanded in C around 0 55.5%

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

      1. mul-1-neg 55.5%

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

      2. +-commutative 55.5%

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

      3. unpow2 55.5%

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

      4. unpow2 55.5%

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

      5. hypot-def 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in B around -inf 58.2%

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

      1. mul-1-neg 58.2%

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

      2. unsub-neg 58.2%

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

   8. Simplified 58.2%

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

   if 5.49999999999999975e-217 < C < 1.6e-57

   1. Initial program 62.8%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in B around inf 69.6%

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

      1. +-commutative 69.6%

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

   7. Simplified 69.6%

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

   8. Taylor expanded in C around 0 68.9%

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

      1. associate-*r/ 68.9%

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

      2. distribute-lft-in 68.9%

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

      3. mul-1-neg 68.9%

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

      4. sub-neg 68.9%

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

      5. mul-1-neg 68.9%

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

   10. Simplified 68.9%

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

   11. Taylor expanded in A around 0 68.9%

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

       1. mul-1-neg 68.9%

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

       2. distribute-neg-frac 68.9%

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

       3. distribute-neg-out 68.9%

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

       4. neg-mul-1 68.9%

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

       5. sub-neg 68.9%

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

       6. sub-neg 68.9%

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

       7. neg-mul-1 68.9%

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

       8. distribute-neg-out 68.9%

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

       9. +-commutative 68.9%

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

       10. distribute-neg-out 68.9%

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

       11. mul-1-neg 68.9%

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

       12. sub-neg 68.9%

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

       13. div-sub 68.9%

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

       14. mul-1-neg 68.9%

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

       15. distribute-frac-neg 68.9%

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

       16. *-inverses 68.9%

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

       17. metadata-eval 68.9%

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

   13. Simplified 68.9%

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

   if 1.6e-57 < C

   1. Initial program 24.0%

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

   3. Taylor expanded in C around inf 42.5%

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

   4. Taylor expanded in B around inf 60.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)}}{\pi} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1250000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 5.5 \cdot 10^{-217}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 63.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.8 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.8e-39)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (if (<= B -8.5e-102)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.8e-39) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= -8.5e-102) {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.8e-39) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= -8.5e-102) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + B)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.8e-39:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= -8.5e-102:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (A + B)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.8e-39)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= -8.5e-102)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + B)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.8e-39)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= -8.5e-102)
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	else
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.8e-39], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.5e-102], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.8000000000000002e-39

   1. Initial program 51.8%

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

   3. Taylor expanded in C around 0 47.5%

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

      1. mul-1-neg 47.5%

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

      2. +-commutative 47.5%

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

      3. unpow2 47.5%

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

      4. unpow2 47.5%

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

      5. hypot-def 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in B around -inf 74.2%

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

      1. mul-1-neg 74.2%

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

      2. unsub-neg 74.2%

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

   8. Simplified 74.2%

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

   if -3.8000000000000002e-39 < B < -8.49999999999999973e-102

   1. Initial program 22.9%

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

   3. Taylor expanded in C around inf 35.1%

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

   4. Taylor expanded in B around inf 54.9%

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

   if -8.49999999999999973e-102 < B

   1. Initial program 57.7%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in B around inf 63.1%

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

      1. +-commutative 63.1%

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

   7. Simplified 63.1%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.8 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.6% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.2 \cdot 10^{-49}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.2e-49)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 6.0)
     (* 180.0 (/ (atan (/ C B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.2e-49) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 6.0) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.2e-49) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 6.0) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.2e-49:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 6.0:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.2e-49)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 6.0)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.2e-49)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 6.0)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.2e-49], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.0], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.20000000000000002e-49

   1. Initial program 50.0%

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

   3. Taylor expanded in B around -inf 59.5%

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

   if -3.20000000000000002e-49 < B < 6

   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. Step-by-step derivation

   3. Simplified 62.4%

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

   5. Taylor expanded in B around inf 48.5%

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

      1. +-commutative 48.5%

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

   7. Simplified 48.5%

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

   8. Taylor expanded in C around inf 32.9%

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

   if 6 < B

   1. Initial program 55.2%

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

   3. Taylor expanded in B around inf 69.0%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.2 \cdot 10^{-49}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 6:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 44.6% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7 \cdot 10^{-175}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7e-175)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.4e-16)
     (* 180.0 (/ (atan 0.0) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7e-175) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.4e-16) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -7e-175) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.4e-16) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7e-175:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.4e-16:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -7e-175)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.4e-16)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -7e-175)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.4e-16)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7e-175], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.4e-16], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -6.99999999999999997e-175

   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 50.5%

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

   if -6.99999999999999997e-175 < B < 1.4000000000000001e-16

   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-*l/ 59.2%

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

      2. *-un-lft-identity 59.2%

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

      3. div-sub 53.4%

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

      4. unpow2 53.4%

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

      5. unpow2 53.4%

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

      6. hypot-def 54.9%

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

   4. Applied egg-rr 54.9%

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

   5. Taylor expanded in C around inf 9.4%

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

      1. distribute-lft1-in 9.4%

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

      2. metadata-eval 9.4%

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

      3. mul0-lft 25.1%

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

      4. metadata-eval 25.1%

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

   7. Simplified 25.1%

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

   if 1.4000000000000001e-16 < B

   1. Initial program 54.1%

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

   3. Taylor expanded in B around inf 64.1%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7 \cdot 10^{-175}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.2% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.4 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.4e-16) (* 180.0 (/ (atan 0.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.4e-16) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.4e-16) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 1.4e-16:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 1.4e-16)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 1.4e-16)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 1.4e-16], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 1.4000000000000001e-16

   1. Initial program 53.8%

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

      1. associate-*l/ 53.8%

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

      2. *-un-lft-identity 53.8%

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

      3. div-sub 51.0%

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

      4. unpow2 51.0%

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

      5. unpow2 51.0%

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

      6. hypot-def 64.3%

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

   4. Applied egg-rr 64.3%

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

   5. Taylor expanded in C around inf 7.8%

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

      1. distribute-lft1-in 7.8%

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

      2. metadata-eval 7.8%

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

      3. mul0-lft 15.6%

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

      4. metadata-eval 15.6%

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

   7. Simplified 15.6%

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

   if 1.4000000000000001e-16 < B

   1. Initial program 54.1%

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

   3. Taylor expanded in B around inf 64.1%

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

4. Final simplification 27.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.4 \cdot 10^{-16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 21.4% 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 53.9%

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

3. Taylor expanded in B around inf 19.5%

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

4. Final simplification 19.5%

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

Reproduce

herbie shell --seed 2024027 
(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)))