ABCF->ab-angle angle

Percentage Accurate: 53.1% → 80.4%

Time: 19.8s

Alternatives: 11

Speedup: 3.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.6 \cdot 10^{+91}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.6e+91)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.6e+91) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.6e+91) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.6e+91:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.6e+91)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.6e+91)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.6e+91], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -5.5999999999999997e91

   1. Initial program 11.3%

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

   2. Taylor expanded in A around -inf 80.0%

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

   if -5.5999999999999997e91 < A

   1. Initial program 61.3%

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

   3. Simplified 82.9%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.6 \cdot 10^{+91}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 2: 54.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -1.4 \cdot 10^{+89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.2 \cdot 10^{-197}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-35}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))))
   (if (<= A -1.4e+89)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (if (<= A -4.2e-197)
       t_0
       (if (<= A -5.5e-269)
         (* 180.0 (/ (atan -1.0) PI))
         (if (<= A 1.5e-35) t_0 (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	double tmp;
	if (A <= -1.4e+89) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= -4.2e-197) {
		tmp = t_0;
	} else if (A <= -5.5e-269) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 1.5e-35) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	double tmp;
	if (A <= -1.4e+89) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= -4.2e-197) {
		tmp = t_0;
	} else if (A <= -5.5e-269) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 1.5e-35) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	tmp = 0
	if A <= -1.4e+89:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= -4.2e-197:
		tmp = t_0
	elif A <= -5.5e-269:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 1.5e-35:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi))
	tmp = 0.0
	if (A <= -1.4e+89)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= -4.2e-197)
		tmp = t_0;
	elseif (A <= -5.5e-269)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 1.5e-35)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 + (C / B))) / pi);
	tmp = 0.0;
	if (A <= -1.4e+89)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= -4.2e-197)
		tmp = t_0;
	elseif (A <= -5.5e-269)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 1.5e-35)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.4e+89], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -4.2e-197], t$95$0, If[LessEqual[A, -5.5e-269], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.5e-35], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.3999999999999999e89

   1. Initial program 11.3%

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

   2. Taylor expanded in A around -inf 80.0%

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

   if -1.3999999999999999e89 < A < -4.2e-197 or -5.5000000000000001e-269 < A < 1.49999999999999994e-35

   1. Initial program 55.4%

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

   2. Taylor expanded in B around -inf 54.3%

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

      1. associate--l+ 54.3%

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

      2. div-sub 55.7%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in C around inf 53.0%

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

   if -4.2e-197 < A < -5.5000000000000001e-269

   1. Initial program 37.4%

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

   2. Taylor expanded in B around inf 48.0%

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

   if 1.49999999999999994e-35 < A

   1. Initial program 80.2%

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

   2. Taylor expanded in A around inf 72.2%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.4 \cdot 10^{+89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.2 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-35}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \]

Alternative 3: 56.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -1.4 \cdot 10^{+89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.2 \cdot 10^{-201}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{-33}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))))
   (if (<= A -1.4e+89)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (if (<= A -4.2e-201)
       t_0
       (if (<= A -5.5e-269)
         (* 180.0 (/ (atan -1.0) PI))
         (if (<= A 4.4e-33) t_0 (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	double tmp;
	if (A <= -1.4e+89) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= -4.2e-201) {
		tmp = t_0;
	} else if (A <= -5.5e-269) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 4.4e-33) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	double tmp;
	if (A <= -1.4e+89) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= -4.2e-201) {
		tmp = t_0;
	} else if (A <= -5.5e-269) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 4.4e-33) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	tmp = 0
	if A <= -1.4e+89:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= -4.2e-201:
		tmp = t_0
	elif A <= -5.5e-269:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 4.4e-33:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi))
	tmp = 0.0
	if (A <= -1.4e+89)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= -4.2e-201)
		tmp = t_0;
	elseif (A <= -5.5e-269)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 4.4e-33)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 + (C / B))) / pi);
	tmp = 0.0;
	if (A <= -1.4e+89)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= -4.2e-201)
		tmp = t_0;
	elseif (A <= -5.5e-269)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 4.4e-33)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.4e+89], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -4.2e-201], t$95$0, If[LessEqual[A, -5.5e-269], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.4e-33], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.3999999999999999e89

   1. Initial program 11.3%

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

   2. Taylor expanded in A around -inf 80.0%

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

   if -1.3999999999999999e89 < A < -4.20000000000000024e-201 or -5.5000000000000001e-269 < A < 4.40000000000000011e-33

   1. Initial program 55.4%

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

   2. Taylor expanded in B around -inf 54.3%

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

      1. associate--l+ 54.3%

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

      2. div-sub 55.7%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in C around inf 53.0%

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

   if -4.20000000000000024e-201 < A < -5.5000000000000001e-269

   1. Initial program 37.4%

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

   2. Taylor expanded in B around inf 48.0%

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

   if 4.40000000000000011e-33 < A

   1. Initial program 80.2%

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

      1. associate-*l/ 80.2%

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

      2. *-un-lft-identity 80.2%

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

      3. +-commutative 80.2%

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

      4. unpow2 80.2%

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

      5. unpow2 80.2%

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

      6. hypot-udef 93.4%

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

      7. div-sub 88.2%

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

      8. hypot-udef 78.4%

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

      9. unpow2 78.4%

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

      10. unpow2 78.4%

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

      11. +-commutative 78.4%

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

      12. unpow2 78.4%

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

      13. unpow2 78.4%

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

      14. hypot-def 88.2%

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

   3. Applied egg-rr 88.2%

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

   4. Taylor expanded in C around 0 87.5%

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

      1. mul-1-neg 87.5%

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

      2. distribute-neg-frac 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in B around inf 76.6%

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

   8. Taylor expanded in A around inf 76.6%

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

      1. neg-sub0 76.6%

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

      2. associate--r+ 76.6%

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

      3. metadata-eval 76.6%

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

   10. Simplified 76.6%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.4 \cdot 10^{+89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.2 \cdot 10^{-201}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 4.4 \cdot 10^{-33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 61.0% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.2 \cdot 10^{-189}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{+19}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B -1.2e-189)
     t_0
     (if (<= B -1.25e-294)
       (* 180.0 (/ (atan (/ (* A 0.0) B)) PI))
       (if (<= B 3.2e+19) t_0 (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (B <= -1.2e-189) {
		tmp = t_0;
	} else if (B <= -1.25e-294) {
		tmp = 180.0 * (atan(((A * 0.0) / B)) / ((double) M_PI));
	} else if (B <= 3.2e+19) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= -1.2e-189) {
		tmp = t_0;
	} else if (B <= -1.25e-294) {
		tmp = 180.0 * (Math.atan(((A * 0.0) / B)) / Math.PI);
	} else if (B <= 3.2e+19) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= -1.2e-189:
		tmp = t_0
	elif B <= -1.25e-294:
		tmp = 180.0 * (math.atan(((A * 0.0) / B)) / math.pi)
	elif B <= 3.2e+19:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= -1.2e-189)
		tmp = t_0;
	elseif (B <= -1.25e-294)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * 0.0) / B)) / pi));
	elseif (B <= 3.2e+19)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= -1.2e-189)
		tmp = t_0;
	elseif (B <= -1.25e-294)
		tmp = 180.0 * (atan(((A * 0.0) / B)) / pi);
	elseif (B <= 3.2e+19)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.2e-189], t$95$0, If[LessEqual[B, -1.25e-294], N[(180.0 * N[(N[ArcTan[N[(N[(A * 0.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.2e+19], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.1999999999999999e-189 or -1.2500000000000001e-294 < B < 3.2e19

   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. Taylor expanded in B around -inf 63.0%

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

      1. associate--l+ 63.0%

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

      2. div-sub 65.2%

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

   4. Simplified 65.2%

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

   if -1.1999999999999999e-189 < B < -1.2500000000000001e-294

   1. Initial program 34.6%

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

   2. Taylor expanded in C around inf 55.2%

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

      1. associate-*r/ 55.2%

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

      2. distribute-rgt1-in 55.2%

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

      3. associate-*r* 55.2%

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

      4. metadata-eval 55.2%

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

      5. metadata-eval 55.2%

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

      6. metadata-eval 55.2%

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

      7. *-commutative 55.2%

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

      8. metadata-eval 55.2%

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

   4. Simplified 55.2%

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

   if 3.2e19 < B

   1. Initial program 40.0%

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

      1. associate-*l/ 40.0%

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

      2. *-un-lft-identity 40.0%

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

      3. +-commutative 40.0%

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

      4. unpow2 40.0%

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

      5. unpow2 40.0%

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

      6. hypot-udef 77.5%

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

      7. div-sub 77.5%

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

      8. hypot-udef 40.0%

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

      9. unpow2 40.0%

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

      10. unpow2 40.0%

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

      11. +-commutative 40.0%

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

      12. unpow2 40.0%

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

      13. unpow2 40.0%

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

      14. hypot-def 77.5%

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

   3. Applied egg-rr 77.5%

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

   4. Taylor expanded in C around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. distribute-neg-frac 76.2%

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

   6. Simplified 76.2%

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

   7. Taylor expanded in B around inf 72.6%

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

   8. Taylor expanded in A around inf 72.6%

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

      1. neg-sub0 72.6%

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

      2. associate--r+ 72.6%

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

      3. metadata-eval 72.6%

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

   10. Simplified 72.6%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.2 \cdot 10^{-189}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 64.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-143}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + -0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.6e-143)
   (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
   (if (<= B -1.5e-294)
     (* 180.0 (/ (atan (+ (/ (* A 0.0) B) (* -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 <= -2.6e-143) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else if (B <= -1.5e-294) {
		tmp = 180.0 * (atan((((A * 0.0) / B) + (-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 <= -2.6e-143) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else if (B <= -1.5e-294) {
		tmp = 180.0 * (Math.atan((((A * 0.0) / B) + (-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 <= -2.6e-143:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	elif B <= -1.5e-294:
		tmp = 180.0 * (math.atan((((A * 0.0) / B) + (-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 <= -2.6e-143)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	elseif (B <= -1.5e-294)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(A * 0.0) / B) + 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 <= -2.6e-143)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	elseif (B <= -1.5e-294)
		tmp = 180.0 * (atan((((A * 0.0) / B) + (-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, -2.6e-143], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.5e-294], N[(180.0 * N[(N[ArcTan[N[(N[(N[(A * 0.0), $MachinePrecision] / B), $MachinePrecision] + N[(-0.5 * N[(B / C), $MachinePrecision]), $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 < -2.59999999999999987e-143

   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. Step-by-step derivation

   3. Simplified 75.6%

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

   4. Taylor expanded in B around -inf 72.3%

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

      1. mul-1-neg 72.3%

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

   6. Simplified 72.3%

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

   if -2.59999999999999987e-143 < B < -1.4999999999999999e-294

   1. Initial program 29.5%

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

   2. Taylor expanded in C around inf 27.8%

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

      1. associate-*r/ 27.8%

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

      2. distribute-rgt1-in 27.8%

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

      3. associate-*r* 27.8%

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

      4. metadata-eval 27.8%

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

      5. metadata-eval 27.8%

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

      6. metadata-eval 27.8%

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

      7. *-commutative 27.8%

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

      8. metadata-eval 27.8%

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

      9. associate-*r/ 27.8%

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

      10. +-commutative 27.8%

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

      11. associate--l+ 29.9%

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

      12. mul-1-neg 29.9%

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

   4. Simplified 29.9%

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

   5. Taylor expanded in B around 0 57.2%

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

   if -1.4999999999999999e-294 < B

   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. Step-by-step derivation

   3. Simplified 72.1%

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

   4. Taylor expanded in B around inf 68.0%

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

      1. +-commutative 68.0%

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

   6. Simplified 68.0%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-143}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.5 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + -0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 6: 65.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.6 \cdot 10^{-190}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.6e-190)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= B -1.25e-294)
     (* 180.0 (/ (atan (/ (* A 0.0) B)) PI))
     (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.6e-190) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= -1.25e-294) {
		tmp = 180.0 * (atan(((A * 0.0) / B)) / ((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 <= -4.6e-190) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= -1.25e-294) {
		tmp = 180.0 * (Math.atan(((A * 0.0) / B)) / 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 <= -4.6e-190:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= -1.25e-294:
		tmp = 180.0 * (math.atan(((A * 0.0) / B)) / 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 <= -4.6e-190)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= -1.25e-294)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * 0.0) / B)) / 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 <= -4.6e-190)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= -1.25e-294)
		tmp = 180.0 * (atan(((A * 0.0) / B)) / pi);
	else
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.6e-190], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.25e-294], N[(180.0 * N[(N[ArcTan[N[(N[(A * 0.0), $MachinePrecision] / B), $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 < -4.59999999999999984e-190

   1. Initial program 53.0%

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

   2. Taylor expanded in B around -inf 69.7%

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

      1. associate--l+ 69.7%

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

      2. div-sub 70.6%

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

   4. Simplified 70.6%

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

   if -4.59999999999999984e-190 < B < -1.2500000000000001e-294

   1. Initial program 34.6%

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

   2. Taylor expanded in C around inf 55.2%

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

      1. associate-*r/ 55.2%

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

      2. distribute-rgt1-in 55.2%

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

      3. associate-*r* 55.2%

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

      4. metadata-eval 55.2%

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

      5. metadata-eval 55.2%

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

      6. metadata-eval 55.2%

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

      7. *-commutative 55.2%

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

      8. metadata-eval 55.2%

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

   4. Simplified 55.2%

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

   if -1.2500000000000001e-294 < B

   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. Step-by-step derivation

   3. Simplified 72.1%

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

   4. Taylor expanded in B around inf 68.0%

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

      1. +-commutative 68.0%

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

   6. Simplified 68.0%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.6 \cdot 10^{-190}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 65.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.4 \cdot 10^{-190}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.4e-190)
   (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
   (if (<= B -1.4e-294)
     (* 180.0 (/ (atan (/ (* A 0.0) B)) PI))
     (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.4e-190) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else if (B <= -1.4e-294) {
		tmp = 180.0 * (atan(((A * 0.0) / B)) / ((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 <= -4.4e-190) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else if (B <= -1.4e-294) {
		tmp = 180.0 * (Math.atan(((A * 0.0) / B)) / 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 <= -4.4e-190:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	elif B <= -1.4e-294:
		tmp = 180.0 * (math.atan(((A * 0.0) / B)) / 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 <= -4.4e-190)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	elseif (B <= -1.4e-294)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * 0.0) / B)) / 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 <= -4.4e-190)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	elseif (B <= -1.4e-294)
		tmp = 180.0 * (atan(((A * 0.0) / B)) / pi);
	else
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.4e-190], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.4e-294], N[(180.0 * N[(N[ArcTan[N[(N[(A * 0.0), $MachinePrecision] / B), $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 < -4.40000000000000008e-190

   1. Initial program 53.0%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in B around -inf 70.7%

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

      1. mul-1-neg 70.7%

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

   6. Simplified 70.7%

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

   if -4.40000000000000008e-190 < B < -1.39999999999999995e-294

   1. Initial program 34.6%

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

   2. Taylor expanded in C around inf 55.2%

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

      1. associate-*r/ 55.2%

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

      2. distribute-rgt1-in 55.2%

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

      3. associate-*r* 55.2%

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

      4. metadata-eval 55.2%

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

      5. metadata-eval 55.2%

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

      6. metadata-eval 55.2%

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

      7. *-commutative 55.2%

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

      8. metadata-eval 55.2%

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

   4. Simplified 55.2%

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

   if -1.39999999999999995e-294 < B

   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. Step-by-step derivation

   3. Simplified 72.1%

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

   4. Taylor expanded in B around inf 68.0%

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

      1. +-commutative 68.0%

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

   6. Simplified 68.0%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.4 \cdot 10^{-190}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{-294}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 48.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{-271}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.7 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.9e-271)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 1.7e-32)
     (* 180.0 (/ (atan 1.0) PI))
     (* 180.0 (/ (atan (* (/ A B) -2.0)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-271) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 1.7e-32) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-271) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 1.7e-32) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.9e-271:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 1.7e-32:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.9e-271)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 1.7e-32)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.9e-271)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 1.7e-32)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.9e-271], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.7e-32], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.90000000000000005e-271

   1. Initial program 36.4%

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

   2. Taylor expanded in A around -inf 53.5%

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

   if -1.90000000000000005e-271 < A < 1.69999999999999989e-32

   1. Initial program 56.2%

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

   2. Taylor expanded in B around -inf 38.8%

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

   if 1.69999999999999989e-32 < A

   1. Initial program 80.2%

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

   2. Taylor expanded in A around inf 72.2%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{-271}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.7 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \]

Alternative 9: 46.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6900:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6900.0)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.8e+19)
     (* 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 <= -6900.0) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.8e+19) {
		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 <= -6900.0) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.8e+19) {
		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 <= -6900.0:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.8e+19:
		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 <= -6900.0)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.8e+19)
		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 <= -6900.0)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.8e+19)
		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, -6900.0], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.8e+19], 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 < -6900

   1. Initial program 52.2%

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

   2. Taylor expanded in B around -inf 59.4%

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

   if -6900 < B < 4.8e19

   1. Initial program 56.8%

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

      1. associate-*l/ 56.8%

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

      2. *-un-lft-identity 56.8%

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

      3. +-commutative 56.8%

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

      4. unpow2 56.8%

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

      5. unpow2 56.8%

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

      6. hypot-udef 72.2%

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

      7. div-sub 54.2%

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

      8. hypot-udef 51.4%

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

      9. unpow2 51.4%

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

      10. unpow2 51.4%

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

      11. +-commutative 51.4%

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

      12. unpow2 51.4%

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

      13. unpow2 51.4%

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

      14. hypot-def 54.2%

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

   3. Applied egg-rr 54.2%

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

   4. Taylor expanded in C around 0 52.8%

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

      1. mul-1-neg 52.8%

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

      2. distribute-neg-frac 52.8%

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

   6. Simplified 52.8%

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

   7. Taylor expanded in C around -inf 33.4%

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

   if 4.8e19 < B

   1. Initial program 40.0%

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

   2. Taylor expanded in B around inf 65.6%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6900:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 10: 40.1% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.999999999999994e-310

   1. Initial program 51.0%

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

   2. Taylor expanded in B around -inf 40.9%

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

   if -1.999999999999994e-310 < B

   1. Initial program 52.0%

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

   2. Taylor expanded in B around inf 40.4%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11: 21.2% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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. Taylor expanded in B around inf 20.4%

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

3. Final simplification 20.4%

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

Reproduce

herbie shell --seed 2023336 
(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)))