ABCF->ab-angle angle

Percentage Accurate: 53.7% → 78.3%

Time: 19.8s

Alternatives: 15

Speedup: 2.4×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.7% 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: 78.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -0.5 \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (or (<= t_0 -0.5) (not (<= t_0 0.0)))
     (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))
     (* (atan (* B (/ 0.5 A))) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -0.5) || !(t_0 <= 0.0)) {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	} else {
		tmp = atan((B * (0.5 / A))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -0.5) || !(t_0 <= 0.0)) {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	} else {
		tmp = Math.atan((B * (0.5 / A))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if (t_0 <= -0.5) or not (t_0 <= 0.0):
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	else:
		tmp = math.atan((B * (0.5 / A))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if ((t_0 <= -0.5) || !(t_0 <= 0.0))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	else
		tmp = Float64(atan(Float64(B * Float64(0.5 / A))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if ((t_0 <= -0.5) || ~((t_0 <= 0.0)))
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	else
		tmp = atan((B * (0.5 / A))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, If[Or[LessEqual[t$95$0, -0.5], N[Not[LessEqual[t$95$0, 0.0]], $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], N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.5 or -0.0 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 60.5%

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

   3. Simplified 85.9%

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

   if -0.5 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.0

   1. Initial program 13.1%

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

   2. Taylor expanded in A around -inf 48.3%

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

      1. associate-*r/ 48.3%

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

   4. Simplified 48.3%

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

      1. add-exp-log 15.8%

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

      2. associate-/l* 15.8%

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

   6. Applied egg-rr 15.8%

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

   7. Taylor expanded in A around 0 48.3%

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

      1. associate-*r/ 48.4%

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

      2. associate-*l/ 48.4%

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

      3. *-commutative 48.4%

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

      4. associate-*r/ 48.4%

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

      5. associate-*l/ 48.3%

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

      6. *-commutative 48.3%

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

   9. Simplified 48.3%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.5 \lor \neg \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A}\right) \cdot \frac{180}{\pi}\\ \end{array} \]

Alternative 2: 74.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ t_1 := \tan^{-1} \left(B \cdot \frac{0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{if}\;A \leq -5.9 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -8.8 \cdot 10^{+46}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.2 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 50000000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI)))
        (t_1 (* (atan (* B (/ 0.5 A))) (/ 180.0 PI))))
   (if (<= A -5.9e+140)
     t_1
     (if (<= A -8.8e+46)
       t_0
       (if (<= A -2.2e+27)
         t_1
         (if (<= A 50000000000000.0)
           t_0
           (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	double t_1 = atan((B * (0.5 / A))) * (180.0 / ((double) M_PI));
	double tmp;
	if (A <= -5.9e+140) {
		tmp = t_1;
	} else if (A <= -8.8e+46) {
		tmp = t_0;
	} else if (A <= -2.2e+27) {
		tmp = t_1;
	} else if (A <= 50000000000000.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	double t_1 = Math.atan((B * (0.5 / A))) * (180.0 / Math.PI);
	double tmp;
	if (A <= -5.9e+140) {
		tmp = t_1;
	} else if (A <= -8.8e+46) {
		tmp = t_0;
	} else if (A <= -2.2e+27) {
		tmp = t_1;
	} else if (A <= 50000000000000.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	t_1 = math.atan((B * (0.5 / A))) * (180.0 / math.pi)
	tmp = 0
	if A <= -5.9e+140:
		tmp = t_1
	elif A <= -8.8e+46:
		tmp = t_0
	elif A <= -2.2e+27:
		tmp = t_1
	elif A <= 50000000000000.0:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi))
	t_1 = Float64(atan(Float64(B * Float64(0.5 / A))) * Float64(180.0 / pi))
	tmp = 0.0
	if (A <= -5.9e+140)
		tmp = t_1;
	elseif (A <= -8.8e+46)
		tmp = t_0;
	elseif (A <= -2.2e+27)
		tmp = t_1;
	elseif (A <= 50000000000000.0)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	t_1 = atan((B * (0.5 / A))) * (180.0 / pi);
	tmp = 0.0;
	if (A <= -5.9e+140)
		tmp = t_1;
	elseif (A <= -8.8e+46)
		tmp = t_0;
	elseif (A <= -2.2e+27)
		tmp = t_1;
	elseif (A <= 50000000000000.0)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -5.9e+140], t$95$1, If[LessEqual[A, -8.8e+46], t$95$0, If[LessEqual[A, -2.2e+27], t$95$1, If[LessEqual[A, 50000000000000.0], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.9000000000000003e140 or -8.8000000000000001e46 < A < -2.1999999999999999e27

   1. Initial program 13.8%

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

   2. Taylor expanded in A around -inf 73.7%

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

      1. associate-*r/ 73.7%

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

   4. Simplified 73.7%

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

      1. add-exp-log 47.4%

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

      2. associate-/l* 47.4%

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

   6. Applied egg-rr 47.4%

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

   7. Taylor expanded in A around 0 73.7%

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

      1. associate-*r/ 73.7%

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

      2. associate-*l/ 73.7%

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

      3. *-commutative 73.7%

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

      4. associate-*r/ 73.7%

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

      5. associate-*l/ 73.7%

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

      6. *-commutative 73.7%

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

   9. Simplified 73.7%

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

   if -5.9000000000000003e140 < A < -8.8000000000000001e46 or -2.1999999999999999e27 < A < 5e13

   1. Initial program 57.0%

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

   2. Taylor expanded in A around 0 53.8%

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

      1. unpow2 53.8%

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

      2. unpow2 53.8%

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

      3. hypot-def 78.4%

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

   4. Simplified 78.4%

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

   if 5e13 < A

   1. Initial program 73.6%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in B around inf 75.6%

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

      1. +-commutative 75.6%

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

   6. Simplified 75.6%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.9 \cdot 10^{+140}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq -8.8 \cdot 10^{+46}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.2 \cdot 10^{+27}:\\ \;\;\;\;\tan^{-1} \left(B \cdot \frac{0.5}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 50000000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3: 72.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -3.3 \cdot 10^{+37}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{+165}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -3.3e+37)
   (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
   (if (<= C 6.2e+165)
     (/ (* -180.0 (atan (/ (+ A (hypot A B)) B))) PI)
     (* 180.0 (/ (atan (/ 0.0 B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.3e+37) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else if (C <= 6.2e+165) {
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.3e+37) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else if (C <= 6.2e+165) {
		tmp = (-180.0 * Math.atan(((A + Math.hypot(A, B)) / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -3.3e+37:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	elif C <= 6.2e+165:
		tmp = (-180.0 * math.atan(((A + math.hypot(A, B)) / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -3.3e+37)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	elseif (C <= 6.2e+165)
		tmp = Float64(Float64(-180.0 * atan(Float64(Float64(A + hypot(A, B)) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -3.3e+37)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	elseif (C <= 6.2e+165)
		tmp = (-180.0 * atan(((A + hypot(A, B)) / B))) / pi;
	else
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -3.3e+37], 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, 6.2e+165], N[(N[(-180.0 * N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -3.3000000000000001e37

   1. Initial program 71.1%

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

   2. Taylor expanded in A around 0 69.5%

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

      1. unpow2 69.5%

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

      2. unpow2 69.5%

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

      3. hypot-def 92.0%

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

   4. Simplified 92.0%

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

   if -3.3000000000000001e37 < C < 6.2000000000000003e165

   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. Taylor expanded in C around 0 52.9%

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

      1. associate-*r/ 52.9%

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

      2. mul-1-neg 52.9%

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

      3. +-commutative 52.9%

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

      4. unpow2 52.9%

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

      5. unpow2 52.9%

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

      6. hypot-def 72.6%

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

   4. Simplified 72.6%

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

      1. expm1-log1p-u 37.1%

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

      2. expm1-udef 37.1%

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

      3. distribute-frac-neg 37.1%

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

      4. atan-neg 37.1%

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

   6. Applied egg-rr 37.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(180 \cdot \frac{-\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 37.1%

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

      2. expm1-log1p 72.6%

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

      3. associate-*r/ 72.6%

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

      4. distribute-rgt-neg-out 72.6%

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

      5. distribute-lft-neg-in 72.6%

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

      6. metadata-eval 72.6%

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

      7. hypot-def 52.9%

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

      8. unpow2 52.9%

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

      9. unpow2 52.9%

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

      10. +-commutative 52.9%

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

      11. unpow2 52.9%

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

      12. unpow2 52.9%

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

      13. hypot-def 72.6%

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

   8. Simplified 72.6%

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

   if 6.2000000000000003e165 < C

   1. Initial program 3.8%

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

   2. Taylor expanded in C around inf 56.1%

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

      1. associate-*r/ 56.1%

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

      2. distribute-rgt1-in 56.1%

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

      3. metadata-eval 56.1%

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

      4. mul0-lft 56.1%

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

      5. metadata-eval 56.1%

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

   4. Simplified 56.1%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -3.3 \cdot 10^{+37}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.2 \cdot 10^{+165}:\\ \;\;\;\;\frac{-180 \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 47.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -1.65 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.85 \cdot 10^{-257}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -6.6 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{-237}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{-161}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{-116}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan -1.0) PI)))
        (t_1 (* 180.0 (/ (atan (* B (/ 0.5 A))) PI))))
   (if (<= A -1.65e-60)
     t_1
     (if (<= A -1.85e-257)
       t_0
       (if (<= A -6.6e-305)
         t_1
         (if (<= A 1.1e-237)
           t_0
           (if (<= A 8.5e-161)
             (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
             (if (<= A 1.45e-116)
               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) / ((double) M_PI));
	double t_1 = 180.0 * (atan((B * (0.5 / A))) / ((double) M_PI));
	double tmp;
	if (A <= -1.65e-60) {
		tmp = t_1;
	} else if (A <= -1.85e-257) {
		tmp = t_0;
	} else if (A <= -6.6e-305) {
		tmp = t_1;
	} else if (A <= 1.1e-237) {
		tmp = t_0;
	} else if (A <= 8.5e-161) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (A <= 1.45e-116) {
		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) / Math.PI);
	double t_1 = 180.0 * (Math.atan((B * (0.5 / A))) / Math.PI);
	double tmp;
	if (A <= -1.65e-60) {
		tmp = t_1;
	} else if (A <= -1.85e-257) {
		tmp = t_0;
	} else if (A <= -6.6e-305) {
		tmp = t_1;
	} else if (A <= 1.1e-237) {
		tmp = t_0;
	} else if (A <= 8.5e-161) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (A <= 1.45e-116) {
		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) / math.pi)
	t_1 = 180.0 * (math.atan((B * (0.5 / A))) / math.pi)
	tmp = 0
	if A <= -1.65e-60:
		tmp = t_1
	elif A <= -1.85e-257:
		tmp = t_0
	elif A <= -6.6e-305:
		tmp = t_1
	elif A <= 1.1e-237:
		tmp = t_0
	elif A <= 8.5e-161:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif A <= 1.45e-116:
		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(-1.0) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / A))) / pi))
	tmp = 0.0
	if (A <= -1.65e-60)
		tmp = t_1;
	elseif (A <= -1.85e-257)
		tmp = t_0;
	elseif (A <= -6.6e-305)
		tmp = t_1;
	elseif (A <= 1.1e-237)
		tmp = t_0;
	elseif (A <= 8.5e-161)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (A <= 1.45e-116)
		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) / pi);
	t_1 = 180.0 * (atan((B * (0.5 / A))) / pi);
	tmp = 0.0;
	if (A <= -1.65e-60)
		tmp = t_1;
	elseif (A <= -1.85e-257)
		tmp = t_0;
	elseif (A <= -6.6e-305)
		tmp = t_1;
	elseif (A <= 1.1e-237)
		tmp = t_0;
	elseif (A <= 8.5e-161)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (A <= 1.45e-116)
		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[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.65e-60], t$95$1, If[LessEqual[A, -1.85e-257], t$95$0, If[LessEqual[A, -6.6e-305], t$95$1, If[LessEqual[A, 1.1e-237], t$95$0, If[LessEqual[A, 8.5e-161], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.45e-116], 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 < -1.6499999999999999e-60 or -1.84999999999999992e-257 < A < -6.59999999999999965e-305

   1. Initial program 31.5%

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

   2. Taylor expanded in A around -inf 55.7%

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

      1. associate-*r/ 55.7%

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

   4. Simplified 55.7%

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

      1. expm1-log1p-u 45.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\right)\right)} \]

      2. expm1-udef 24.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\right)} - 1} \]

      3. associate-/l* 24.6%

         \[\leadsto e^{\mathsf{log1p}\left(180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0.5}{\frac{A}{B}}\right)}}{\pi}\right)} - 1 \]

   6. Applied egg-rr 24.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 45.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\right)\right)} \]

      2. expm1-log1p 55.6%

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

      3. associate-/r/ 55.7%

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

   8. Simplified 55.7%

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

   if -1.6499999999999999e-60 < A < -1.84999999999999992e-257 or -6.59999999999999965e-305 < A < 1.09999999999999999e-237 or 8.50000000000000054e-161 < A < 1.4499999999999999e-116

   1. Initial program 58.9%

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

   2. Taylor expanded in B around inf 43.3%

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

   if 1.09999999999999999e-237 < A < 8.50000000000000054e-161

   1. Initial program 90.8%

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

   2. Taylor expanded in C around -inf 51.7%

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

   if 1.4499999999999999e-116 < A

   1. Initial program 67.8%

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

   2. Taylor expanded in A around inf 57.1%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.65 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.85 \cdot 10^{-257}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq -6.6 \cdot 10^{-305}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.1 \cdot 10^{-237}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{-161}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.45 \cdot 10^{-116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \]

Alternative 5: 47.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -9.5 \cdot 10^{-49}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8.6 \cdot 10^{-262}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 11.2 \lor \neg \left(B \leq 6.2 \cdot 10^{+21}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- A) B)) PI)))
        (t_1 (* 180.0 (/ (atan (/ C B)) PI))))
   (if (<= B -9.5e-49)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 8.6e-262)
       t_0
       (if (<= B 2.3e-110)
         t_1
         (if (<= B 1.25e-60)
           t_0
           (if (or (<= B 11.2) (not (<= B 6.2e+21)))
             (* 180.0 (/ (atan -1.0) PI))
             t_1)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-A / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double tmp;
	if (B <= -9.5e-49) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 8.6e-262) {
		tmp = t_0;
	} else if (B <= 2.3e-110) {
		tmp = t_1;
	} else if (B <= 1.25e-60) {
		tmp = t_0;
	} else if ((B <= 11.2) || !(B <= 6.2e+21)) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((-A / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double tmp;
	if (B <= -9.5e-49) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 8.6e-262) {
		tmp = t_0;
	} else if (B <= 2.3e-110) {
		tmp = t_1;
	} else if (B <= 1.25e-60) {
		tmp = t_0;
	} else if ((B <= 11.2) || !(B <= 6.2e+21)) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-A / B)) / math.pi)
	t_1 = 180.0 * (math.atan((C / B)) / math.pi)
	tmp = 0
	if B <= -9.5e-49:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 8.6e-262:
		tmp = t_0
	elif B <= 2.3e-110:
		tmp = t_1
	elif B <= 1.25e-60:
		tmp = t_0
	elif (B <= 11.2) or not (B <= 6.2e+21):
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = t_1
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	tmp = 0.0
	if (B <= -9.5e-49)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 8.6e-262)
		tmp = t_0;
	elseif (B <= 2.3e-110)
		tmp = t_1;
	elseif (B <= 1.25e-60)
		tmp = t_0;
	elseif ((B <= 11.2) || !(B <= 6.2e+21))
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((-A / B)) / pi);
	t_1 = 180.0 * (atan((C / B)) / pi);
	tmp = 0.0;
	if (B <= -9.5e-49)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 8.6e-262)
		tmp = t_0;
	elseif (B <= 2.3e-110)
		tmp = t_1;
	elseif (B <= 1.25e-60)
		tmp = t_0;
	elseif ((B <= 11.2) || ~((B <= 6.2e+21)))
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -9.5e-49], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.6e-262], t$95$0, If[LessEqual[B, 2.3e-110], t$95$1, If[LessEqual[B, 1.25e-60], t$95$0, If[Or[LessEqual[B, 11.2], N[Not[LessEqual[B, 6.2e+21]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -9.50000000000000006e-49

   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 64.8%

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

   if -9.50000000000000006e-49 < B < 8.6000000000000002e-262 or 2.3000000000000001e-110 < B < 1.25e-60

   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 64.9%

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

   4. Taylor expanded in B around inf 49.3%

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

      1. +-commutative 49.3%

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

   6. Simplified 49.3%

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

   7. Taylor expanded in A around inf 37.2%

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

      1. associate-*r/ 37.2%

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

      2. mul-1-neg 37.2%

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

   9. Simplified 37.2%

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

   if 8.6000000000000002e-262 < B < 2.3000000000000001e-110 or 11.199999999999999 < B < 6.2e21

   1. Initial program 61.7%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in B around inf 58.7%

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

      1. +-commutative 58.7%

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

   6. Simplified 58.7%

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

   7. Taylor expanded in C around inf 53.8%

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

   if 1.25e-60 < B < 11.199999999999999 or 6.2e21 < B

   1. Initial program 50.4%

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

   2. Taylor expanded in B around inf 58.0%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9.5 \cdot 10^{-49}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8.6 \cdot 10^{-262}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-110}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 11.2 \lor \neg \left(B \leq 6.2 \cdot 10^{+21}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \end{array} \]

Alternative 6: 47.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.8 \cdot 10^{-48}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-261}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-111}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 4000 \lor \neg \left(B \leq 1.4 \cdot 10^{+21}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ C B)) PI))))
   (if (<= B -2.8e-48)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 4e-261)
       (* 180.0 (/ (atan (/ (- A) B)) PI))
       (if (<= B 2.15e-111)
         t_0
         (if (<= B 5.5e-60)
           (* 180.0 (/ (atan (* (/ A B) -2.0)) PI))
           (if (or (<= B 4000.0) (not (<= B 1.4e+21)))
             (* 180.0 (/ (atan -1.0) PI))
             t_0)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double tmp;
	if (B <= -2.8e-48) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4e-261) {
		tmp = 180.0 * (atan((-A / B)) / ((double) M_PI));
	} else if (B <= 2.15e-111) {
		tmp = t_0;
	} else if (B <= 5.5e-60) {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	} else if ((B <= 4000.0) || !(B <= 1.4e+21)) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double tmp;
	if (B <= -2.8e-48) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4e-261) {
		tmp = 180.0 * (Math.atan((-A / B)) / Math.PI);
	} else if (B <= 2.15e-111) {
		tmp = t_0;
	} else if (B <= 5.5e-60) {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	} else if ((B <= 4000.0) || !(B <= 1.4e+21)) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((C / B)) / math.pi)
	tmp = 0
	if B <= -2.8e-48:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4e-261:
		tmp = 180.0 * (math.atan((-A / B)) / math.pi)
	elif B <= 2.15e-111:
		tmp = t_0
	elif B <= 5.5e-60:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	elif (B <= 4000.0) or not (B <= 1.4e+21):
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	tmp = 0.0
	if (B <= -2.8e-48)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4e-261)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi));
	elseif (B <= 2.15e-111)
		tmp = t_0;
	elseif (B <= 5.5e-60)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	elseif ((B <= 4000.0) || !(B <= 1.4e+21))
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((C / B)) / pi);
	tmp = 0.0;
	if (B <= -2.8e-48)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4e-261)
		tmp = 180.0 * (atan((-A / B)) / pi);
	elseif (B <= 2.15e-111)
		tmp = t_0;
	elseif (B <= 5.5e-60)
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	elseif ((B <= 4000.0) || ~((B <= 1.4e+21)))
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.8e-48], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4e-261], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.15e-111], t$95$0, If[LessEqual[B, 5.5e-60], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 4000.0], N[Not[LessEqual[B, 1.4e+21]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.80000000000000005e-48

   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 64.8%

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

   if -2.80000000000000005e-48 < B < 3.99999999999999994e-261

   1. Initial program 49.5%

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

   3. Simplified 65.1%

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

   4. Taylor expanded in B around inf 45.2%

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

      1. +-commutative 45.2%

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

   6. Simplified 45.2%

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

   7. Taylor expanded in A around inf 36.4%

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

      1. associate-*r/ 36.4%

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

      2. mul-1-neg 36.4%

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

   9. Simplified 36.4%

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

   if 3.99999999999999994e-261 < B < 2.1499999999999999e-111 or 4e3 < B < 1.4e21

   1. Initial program 61.7%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in B around inf 58.7%

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

      1. +-commutative 58.7%

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

   6. Simplified 58.7%

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

   7. Taylor expanded in C around inf 53.8%

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

   if 2.1499999999999999e-111 < B < 5.4999999999999997e-60

   1. Initial program 64.1%

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

   2. Taylor expanded in A around inf 40.0%

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

   if 5.4999999999999997e-60 < B < 4e3 or 1.4e21 < B

   1. Initial program 50.4%

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

   2. Taylor expanded in B around inf 58.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.8 \cdot 10^{-48}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-261}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-111}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \mathbf{elif}\;B \leq 4000 \lor \neg \left(B \leq 1.4 \cdot 10^{+21}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 52.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.6 \cdot 10^{-56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.8 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-110}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.6e-56)
   (* 180.0 (/ (atan (/ (+ B C) B)) PI))
   (if (<= B -1.8e-173)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (if (<= B 4.6e-262)
       (* 180.0 (/ (atan (/ (- A) B)) PI))
       (if (<= B 1.85e-110)
         (* 180.0 (/ (atan (/ C B)) PI))
         (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.6e-56) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else if (B <= -1.8e-173) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 4.6e-262) {
		tmp = 180.0 * (atan((-A / B)) / ((double) M_PI));
	} else if (B <= 1.85e-110) {
		tmp = 180.0 * (atan((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 (B <= -3.6e-56) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else if (B <= -1.8e-173) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 4.6e-262) {
		tmp = 180.0 * (Math.atan((-A / B)) / Math.PI);
	} else if (B <= 1.85e-110) {
		tmp = 180.0 * (Math.atan((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 B <= -3.6e-56:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	elif B <= -1.8e-173:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 4.6e-262:
		tmp = 180.0 * (math.atan((-A / B)) / math.pi)
	elif B <= 1.85e-110:
		tmp = 180.0 * (math.atan((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 (B <= -3.6e-56)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	elseif (B <= -1.8e-173)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 4.6e-262)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi));
	elseif (B <= 1.85e-110)
		tmp = Float64(180.0 * Float64(atan(Float64(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 (B <= -3.6e-56)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	elseif (B <= -1.8e-173)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 4.6e-262)
		tmp = 180.0 * (atan((-A / B)) / pi);
	elseif (B <= 1.85e-110)
		tmp = 180.0 * (atan((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[B, -3.6e-56], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.8e-173], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.6e-262], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.85e-110], N[(180.0 * N[(N[ArcTan[N[(C / 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 5 regimes

2. if B < -3.59999999999999978e-56

   1. Initial program 53.5%

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

   3. Simplified 80.3%

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

   4. Taylor expanded in B around -inf 78.5%

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

      1. neg-mul-1 78.5%

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

      2. unsub-neg 78.5%

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

   6. Simplified 78.5%

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

   7. Taylor expanded in A around 0 70.9%

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

   if -3.59999999999999978e-56 < B < -1.79999999999999986e-173

   1. Initial program 25.5%

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

   2. Taylor expanded in C around inf 39.1%

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

      1. associate-*r/ 39.1%

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

      2. distribute-rgt1-in 39.1%

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

      3. metadata-eval 39.1%

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

      4. mul0-lft 39.1%

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

      5. metadata-eval 39.1%

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

   4. Simplified 39.1%

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

   if -1.79999999999999986e-173 < B < 4.6000000000000002e-262

   1. Initial program 63.2%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in B around inf 56.1%

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

      1. +-commutative 56.1%

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

   6. Simplified 56.1%

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

   7. Taylor expanded in A around inf 46.8%

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

      1. associate-*r/ 46.8%

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

      2. mul-1-neg 46.8%

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

   9. Simplified 46.8%

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

   if 4.6000000000000002e-262 < B < 1.85000000000000008e-110

   1. Initial program 58.6%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in B around inf 55.3%

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

      1. +-commutative 55.3%

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

   6. Simplified 55.3%

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

   7. Taylor expanded in C around inf 50.1%

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

   if 1.85000000000000008e-110 < B

   1. Initial program 54.4%

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

   2. Taylor expanded in C around 0 45.7%

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

      1. associate-*r/ 45.7%

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

      2. mul-1-neg 45.7%

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

      3. +-commutative 45.7%

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

      4. unpow2 45.7%

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

      5. unpow2 45.7%

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

      6. hypot-def 66.5%

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

   4. Simplified 66.5%

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

   5. Taylor expanded in A around 0 64.0%

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

      1. sub-neg 64.0%

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

      2. mul-1-neg 64.0%

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

      3. distribute-neg-in 64.0%

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

      4. +-commutative 64.0%

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

      5. distribute-neg-in 64.0%

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

      6. metadata-eval 64.0%

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

      7. unsub-neg 64.0%

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

   7. Simplified 64.0%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.6 \cdot 10^{-56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.8 \cdot 10^{-173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.85 \cdot 10^{-110}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 52.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -1.6 \cdot 10^{-60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.05 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{-305}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* B (/ 0.5 A))) PI))))
   (if (<= A -1.6e-60)
     t_0
     (if (<= A -2.05e-256)
       (* 180.0 (/ (atan -1.0) PI))
       (if (<= A -5.5e-305) 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((B * (0.5 / A))) / ((double) M_PI));
	double tmp;
	if (A <= -1.6e-60) {
		tmp = t_0;
	} else if (A <= -2.05e-256) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= -5.5e-305) {
		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((B * (0.5 / A))) / Math.PI);
	double tmp;
	if (A <= -1.6e-60) {
		tmp = t_0;
	} else if (A <= -2.05e-256) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= -5.5e-305) {
		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((B * (0.5 / A))) / math.pi)
	tmp = 0
	if A <= -1.6e-60:
		tmp = t_0
	elif A <= -2.05e-256:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= -5.5e-305:
		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(B * Float64(0.5 / A))) / pi))
	tmp = 0.0
	if (A <= -1.6e-60)
		tmp = t_0;
	elseif (A <= -2.05e-256)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= -5.5e-305)
		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((B * (0.5 / A))) / pi);
	tmp = 0.0;
	if (A <= -1.6e-60)
		tmp = t_0;
	elseif (A <= -2.05e-256)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= -5.5e-305)
		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[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.6e-60], t$95$0, If[LessEqual[A, -2.05e-256], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -5.5e-305], 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 A < -1.6000000000000001e-60 or -2.05e-256 < A < -5.5e-305

   1. Initial program 31.5%

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

   2. Taylor expanded in A around -inf 55.7%

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

      1. associate-*r/ 55.7%

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

   4. Simplified 55.7%

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

      1. expm1-log1p-u 45.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\right)\right)} \]

      2. expm1-udef 24.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\right)} - 1} \]

      3. associate-/l* 24.6%

         \[\leadsto e^{\mathsf{log1p}\left(180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0.5}{\frac{A}{B}}\right)}}{\pi}\right)} - 1 \]

   6. Applied egg-rr 24.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 45.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\right)\right)} \]

      2. expm1-log1p 55.6%

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

      3. associate-/r/ 55.7%

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

   8. Simplified 55.7%

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

   if -1.6000000000000001e-60 < A < -2.05e-256

   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 38.0%

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

   if -5.5e-305 < A

   1. Initial program 70.6%

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

   2. Taylor expanded in C around 0 67.2%

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

      1. associate-*r/ 67.2%

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

      2. mul-1-neg 67.2%

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

      3. +-commutative 67.2%

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

      4. unpow2 67.2%

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

      5. unpow2 67.2%

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

      6. hypot-def 78.4%

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

   4. Simplified 78.4%

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

   5. Taylor expanded in A around 0 62.2%

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

      1. sub-neg 62.2%

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

      2. mul-1-neg 62.2%

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

      3. distribute-neg-in 62.2%

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

      4. +-commutative 62.2%

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

      5. distribute-neg-in 62.2%

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

      6. metadata-eval 62.2%

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

      7. unsub-neg 62.2%

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

   7. Simplified 62.2%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.6 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.05 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq -5.5 \cdot 10^{-305}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9: 52.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.65 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3 \cdot 10^{-257}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq -1.35 \cdot 10^{-304}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.65e-60)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A -3e-257)
     (* 180.0 (/ (atan -1.0) PI))
     (if (<= A -1.35e-304)
       (* 180.0 (/ (atan (* B (/ 0.5 A))) PI))
       (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.65e-60) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= -3e-257) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= -1.35e-304) {
		tmp = 180.0 * (atan((B * (0.5 / A))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.65e-60) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= -3e-257) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= -1.35e-304) {
		tmp = 180.0 * (Math.atan((B * (0.5 / A))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.65e-60:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= -3e-257:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= -1.35e-304:
		tmp = 180.0 * (math.atan((B * (0.5 / A))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.65e-60)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= -3e-257)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= -1.35e-304)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / A))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.65e-60)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= -3e-257)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= -1.35e-304)
		tmp = 180.0 * (atan((B * (0.5 / A))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.65e-60], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -3e-257], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.35e-304], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $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 4 regimes

2. if A < -1.6499999999999999e-60

   1. Initial program 28.0%

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

   2. Taylor expanded in A around -inf 55.2%

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

      1. associate-*r/ 55.2%

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

   4. Simplified 55.2%

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

   if -1.6499999999999999e-60 < A < -2.9999999999999999e-257

   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 38.0%

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

   if -2.9999999999999999e-257 < A < -1.35000000000000005e-304

   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. Taylor expanded in A around -inf 59.6%

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

      1. associate-*r/ 59.6%

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

   4. Simplified 59.6%

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

      1. expm1-log1p-u 11.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\right)\right)} \]

      2. expm1-udef 11.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\right)} - 1} \]

      3. associate-/l* 11.8%

         \[\leadsto e^{\mathsf{log1p}\left(180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0.5}{\frac{A}{B}}\right)}}{\pi}\right)} - 1 \]

   6. Applied egg-rr 11.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 11.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\right)\right)} \]

      2. expm1-log1p 59.6%

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

      3. associate-/r/ 59.6%

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

   8. Simplified 59.6%

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

   if -1.35000000000000005e-304 < A

   1. Initial program 70.6%

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

   2. Taylor expanded in C around 0 67.2%

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

      1. associate-*r/ 67.2%

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

      2. mul-1-neg 67.2%

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

      3. +-commutative 67.2%

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

      4. unpow2 67.2%

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

      5. unpow2 67.2%

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

      6. hypot-def 78.4%

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

   4. Simplified 78.4%

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

   5. Taylor expanded in A around 0 62.2%

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

      1. sub-neg 62.2%

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

      2. mul-1-neg 62.2%

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

      3. distribute-neg-in 62.2%

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

      4. +-commutative 62.2%

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

      5. distribute-neg-in 62.2%

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

      6. metadata-eval 62.2%

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

      7. unsub-neg 62.2%

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

   7. Simplified 62.2%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.65 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3 \cdot 10^{-257}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq -1.35 \cdot 10^{-304}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10: 45.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.7 \cdot 10^{-56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-228}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{+21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.7e-56)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -3.5e-228)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (if (<= B 1.95e+21)
       (* 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 <= -3.7e-56) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -3.5e-228) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else if (B <= 1.95e+21) {
		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 <= -3.7e-56) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -3.5e-228) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else if (B <= 1.95e+21) {
		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 <= -3.7e-56:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -3.5e-228:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	elif B <= 1.95e+21:
		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 <= -3.7e-56)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -3.5e-228)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	elseif (B <= 1.95e+21)
		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 <= -3.7e-56)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -3.5e-228)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	elseif (B <= 1.95e+21)
		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, -3.7e-56], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.5e-228], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.95e+21], 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 4 regimes

2. if B < -3.7000000000000002e-56

   1. Initial program 53.5%

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

   2. Taylor expanded in B around -inf 63.5%

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

   if -3.7000000000000002e-56 < B < -3.49999999999999975e-228

   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. Taylor expanded in C around inf 36.1%

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

      1. associate-*r/ 36.1%

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

      2. distribute-rgt1-in 36.1%

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

      3. metadata-eval 36.1%

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

      4. mul0-lft 36.1%

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

      5. metadata-eval 36.1%

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

   4. Simplified 36.1%

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

   if -3.49999999999999975e-228 < B < 1.95e21

   1. Initial program 61.1%

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

   3. Simplified 68.9%

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

   4. Taylor expanded in B around inf 57.0%

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

      1. +-commutative 57.0%

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

   6. Simplified 57.0%

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

   7. Taylor expanded in C around inf 39.1%

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

   if 1.95e21 < B

   1. Initial program 50.9%

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

   2. Taylor expanded in B around inf 60.5%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.7 \cdot 10^{-56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-228}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.95 \cdot 10^{+21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11: 63.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.6 \cdot 10^{-47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.6e-47)
   (* 180.0 (/ (atan (/ (+ B C) B)) PI))
   (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.6e-47) {
		tmp = 180.0 * (atan(((B + C) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.6e-47) {
		tmp = 180.0 * (Math.atan(((B + C) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5.6e-47:
		tmp = 180.0 * (math.atan(((B + C) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5.6e-47)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B + C) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5.6e-47)
		tmp = 180.0 * (atan(((B + C) / B)) / pi);
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5.6e-47], N[(180.0 * N[(N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -5.59999999999999986e-47

   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. Step-by-step derivation

   3. Simplified 79.8%

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

   4. Taylor expanded in B around -inf 77.9%

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

      1. neg-mul-1 77.9%

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

      2. unsub-neg 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in A around 0 71.2%

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

   if -5.59999999999999986e-47 < B

   1. Initial program 53.7%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in B around inf 62.0%

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

      1. +-commutative 62.0%

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

   6. Simplified 62.0%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.6 \cdot 10^{-47}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B + C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 12: 65.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-51)
   (* 180.0 (/ (atan (/ (- C (- A B)) B)) PI))
   (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-51) {
		tmp = 180.0 * (atan(((C - (A - B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-51) {
		tmp = 180.0 * (Math.atan(((C - (A - B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5e-51:
		tmp = 180.0 * (math.atan(((C - (A - B)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5e-51)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A - B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5e-51)
		tmp = 180.0 * (atan(((C - (A - B)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5e-51], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A - B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -5.00000000000000004e-51

   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. Step-by-step derivation

   3. Simplified 79.8%

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

   4. Taylor expanded in B around -inf 77.9%

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

      1. neg-mul-1 77.9%

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

      2. unsub-neg 77.9%

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

   6. Simplified 77.9%

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

   if -5.00000000000000004e-51 < B

   1. Initial program 53.7%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in B around inf 62.0%

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

      1. +-commutative 62.0%

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

   6. Simplified 62.0%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A - B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 13: 44.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.6 \cdot 10^{-56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.6e-56)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.45e-132)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.6e-56) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.45e-132) {
		tmp = 180.0 * (atan((0.0 / 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 <= -3.6e-56) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.45e-132) {
		tmp = 180.0 * (Math.atan((0.0 / 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 <= -3.6e-56:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.45e-132:
		tmp = 180.0 * (math.atan((0.0 / 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 <= -3.6e-56)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.45e-132)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / 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 <= -3.6e-56)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.45e-132)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.6e-56], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.45e-132], N[(180.0 * N[(N[ArcTan[N[(0.0 / 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 < -3.59999999999999978e-56

   1. Initial program 53.5%

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

   2. Taylor expanded in B around -inf 63.5%

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

   if -3.59999999999999978e-56 < B < 1.44999999999999992e-132

   1. Initial program 50.4%

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

   2. Taylor expanded in C around inf 32.3%

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

      1. associate-*r/ 32.3%

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

      2. distribute-rgt1-in 32.3%

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

      3. metadata-eval 32.3%

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

      4. mul0-lft 32.3%

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

      5. metadata-eval 32.3%

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

   4. Simplified 32.3%

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

   if 1.44999999999999992e-132 < B

   1. Initial program 55.7%

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

   2. Taylor expanded in B around inf 49.9%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.6 \cdot 10^{-56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-132}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 14: 39.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.2 \cdot 10^{-299}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.2e-299)
   (* 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 <= -6.2e-299) {
		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 <= -6.2e-299) {
		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 <= -6.2e-299:
		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 <= -6.2e-299)
		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 <= -6.2e-299)
		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, -6.2e-299], 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 < -6.1999999999999999e-299

   1. Initial program 51.2%

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

   2. Taylor expanded in B around -inf 44.7%

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

   if -6.1999999999999999e-299 < B

   1. Initial program 55.0%

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

   2. Taylor expanded in B around inf 37.6%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.2 \cdot 10^{-299}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 15: 20.5% accurate, 2.5× 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 53.3%

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

2. Taylor expanded in B around inf 21.8%

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

3. Final simplification 21.8%

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

Reproduce

herbie shell --seed 2023337 
(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)))