ABCF->ab-angle angle

Percentage Accurate: 53.3% → 80.8%

Time: 22.1s

Alternatives: 14

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: 53.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{+182}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.5e+182)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e+182) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e+182) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.5e+182:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.5e+182)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.5e+182)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	else
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.5e+182], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -8.5e182

   1. Initial program 11.8%

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

   2. Taylor expanded in A around -inf 86.6%

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

      1. associate-*r/ 86.6%

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

   4. Simplified 86.6%

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

   if -8.5e182 < A

   1. Initial program 64.4%

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

      1. associate-*l/ 64.4%

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

      2. *-lft-identity 64.4%

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

      3. +-commutative 64.4%

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

      4. unpow2 64.4%

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

      5. unpow2 64.4%

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

      6. hypot-def 83.8%

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

   3. Simplified 83.8%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{+182}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 2: 80.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(B \cdot \left(\frac{1}{A} + \frac{1}{A} \cdot \frac{C}{A}\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.2e+15)
   (* 180.0 (/ (atan (* 0.5 (* B (+ (/ 1.0 A) (* (/ 1.0 A) (/ C A)))))) PI))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.2e+15) {
		tmp = 180.0 * (atan((0.5 * (B * ((1.0 / A) + ((1.0 / A) * (C / A)))))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.2e+15) {
		tmp = 180.0 * (Math.atan((0.5 * (B * ((1.0 / A) + ((1.0 / A) * (C / A)))))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.2e+15:
		tmp = 180.0 * (math.atan((0.5 * (B * ((1.0 / A) + ((1.0 / A) * (C / A)))))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.2e+15)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B * Float64(Float64(1.0 / A) + Float64(Float64(1.0 / A) * Float64(C / A)))))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.2e+15)
		tmp = 180.0 * (atan((0.5 * (B * ((1.0 / A) + ((1.0 / A) * (C / A)))))) / pi);
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.2e+15], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B * N[(N[(1.0 / A), $MachinePrecision] + N[(N[(1.0 / A), $MachinePrecision] * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -5.2e15

   1. Initial program 26.1%

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

   2. Taylor expanded in A around -inf 65.6%

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

      1. distribute-lft-out 65.6%

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

      2. associate-/l* 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in B around 0 70.9%

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

      1. *-un-lft-identity 70.9%

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

      2. unpow2 70.9%

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

      3. times-frac 70.7%

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

   7. Applied egg-rr 70.7%

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

   if -5.2e15 < A

   1. Initial program 68.6%

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

   3. Simplified 86.7%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(B \cdot \left(\frac{1}{A} + \frac{1}{A} \cdot \frac{C}{A}\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 3: 77.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(B \cdot \left(\frac{1}{A} + \frac{1}{A} \cdot \frac{C}{A}\right)\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.1 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.8e+19)
   (* 180.0 (/ (atan (* 0.5 (* B (+ (/ 1.0 A) (* (/ 1.0 A) (/ C A)))))) PI))
   (if (<= A 3.1e+25)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (/ (- (- A) (hypot B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+19) {
		tmp = 180.0 * (atan((0.5 * (B * ((1.0 / A) + ((1.0 / A) * (C / A)))))) / ((double) M_PI));
	} else if (A <= 3.1e+25) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+19) {
		tmp = 180.0 * (Math.atan((0.5 * (B * ((1.0 / A) + ((1.0 / A) * (C / A)))))) / Math.PI);
	} else if (A <= 3.1e+25) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(B, A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.8e+19:
		tmp = 180.0 * (math.atan((0.5 * (B * ((1.0 / A) + ((1.0 / A) * (C / A)))))) / math.pi)
	elif A <= 3.1e+25:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((-A - math.hypot(B, A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.8e+19)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B * Float64(Float64(1.0 / A) + Float64(Float64(1.0 / A) * Float64(C / A)))))) / pi));
	elseif (A <= 3.1e+25)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(B, A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.8e+19)
		tmp = 180.0 * (atan((0.5 * (B * ((1.0 / A) + ((1.0 / A) * (C / A)))))) / pi);
	elseif (A <= 3.1e+25)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.8e+19], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B * N[(N[(1.0 / A), $MachinePrecision] + N[(N[(1.0 / A), $MachinePrecision] * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.1e+25], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.8e19

   1. Initial program 26.1%

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

   2. Taylor expanded in A around -inf 65.6%

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

      1. distribute-lft-out 65.6%

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

      2. associate-/l* 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in B around 0 70.9%

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

      1. *-un-lft-identity 70.9%

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

      2. unpow2 70.9%

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

      3. times-frac 70.7%

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

   7. Applied egg-rr 70.7%

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

   if -1.8e19 < A < 3.0999999999999998e25

   1. Initial program 61.3%

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

   2. Taylor expanded in A around 0 57.9%

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

      1. unpow2 57.9%

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

      2. unpow2 57.9%

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

      3. hypot-def 78.0%

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

   4. Simplified 78.0%

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

   if 3.0999999999999998e25 < A

   1. Initial program 83.6%

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

   2. Taylor expanded in C around 0 82.4%

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

      1. associate-*r/ 82.4%

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

      2. mul-1-neg 82.4%

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

      3. +-commutative 82.4%

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

      4. unpow2 82.4%

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

      5. unpow2 82.4%

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

      6. hypot-def 92.9%

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

   4. Simplified 92.9%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(B \cdot \left(\frac{1}{A} + \frac{1}{A} \cdot \frac{C}{A}\right)\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.1 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 74.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(B \cdot \left(\frac{1}{A} + \frac{1}{A} \cdot \frac{C}{A}\right)\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{+147}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.5e+19)
   (* 180.0 (/ (atan (* 0.5 (* B (+ (/ 1.0 A) (* (/ 1.0 A) (/ C A)))))) PI))
   (if (<= A 2.4e+147)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.5e+19) {
		tmp = 180.0 * (atan((0.5 * (B * ((1.0 / A) + ((1.0 / A) * (C / A)))))) / ((double) M_PI));
	} else if (A <= 2.4e+147) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.5e+19) {
		tmp = 180.0 * (Math.atan((0.5 * (B * ((1.0 / A) + ((1.0 / A) * (C / A)))))) / Math.PI);
	} else if (A <= 2.4e+147) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.5e+19:
		tmp = 180.0 * (math.atan((0.5 * (B * ((1.0 / A) + ((1.0 / A) * (C / A)))))) / math.pi)
	elif A <= 2.4e+147:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.5e+19)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B * Float64(Float64(1.0 / A) + Float64(Float64(1.0 / A) * Float64(C / A)))))) / pi));
	elseif (A <= 2.4e+147)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.5e+19)
		tmp = 180.0 * (atan((0.5 * (B * ((1.0 / A) + ((1.0 / A) * (C / A)))))) / pi);
	elseif (A <= 2.4e+147)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.5e+19], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B * N[(N[(1.0 / A), $MachinePrecision] + N[(N[(1.0 / A), $MachinePrecision] * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.4e+147], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.5e19

   1. Initial program 26.1%

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

   2. Taylor expanded in A around -inf 65.6%

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

      1. distribute-lft-out 65.6%

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

      2. associate-/l* 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in B around 0 70.9%

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

      1. *-un-lft-identity 70.9%

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

      2. unpow2 70.9%

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

      3. times-frac 70.7%

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

   7. Applied egg-rr 70.7%

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

   if -1.5e19 < A < 2.40000000000000002e147

   1. Initial program 62.2%

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

   2. Taylor expanded in A around 0 56.5%

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

      1. unpow2 56.5%

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

      2. unpow2 56.5%

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

      3. hypot-def 77.9%

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

   4. Simplified 77.9%

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

   if 2.40000000000000002e147 < A

   1. Initial program 93.1%

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

   2. Taylor expanded in B around -inf 92.2%

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

      1. associate--l+ 92.2%

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

      2. div-sub 94.6%

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

   4. Simplified 94.6%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(B \cdot \left(\frac{1}{A} + \frac{1}{A} \cdot \frac{C}{A}\right)\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{+147}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 47.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -2.4 \cdot 10^{-90}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -8 \cdot 10^{-235}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 3.8 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 1.15 \cdot 10^{-139}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;C \leq 4.4 \cdot 10^{-7}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan -1.0) PI)))
        (t_1 (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))))
   (if (<= C -2.4e-90)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= C -8e-235)
       t_0
       (if (<= C 3.8e-264)
         t_1
         (if (<= C 1.15e-139)
           t_0
           (if (<= C 8.2e-85)
             t_1
             (if (<= C 4.4e-7)
               t_0
               (* 180.0 (/ (atan (/ (* B -0.5) C)) 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((-2.0 * (A / B))) / ((double) M_PI));
	double tmp;
	if (C <= -2.4e-90) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= -8e-235) {
		tmp = t_0;
	} else if (C <= 3.8e-264) {
		tmp = t_1;
	} else if (C <= 1.15e-139) {
		tmp = t_0;
	} else if (C <= 8.2e-85) {
		tmp = t_1;
	} else if (C <= 4.4e-7) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(-1.0) / Math.PI);
	double t_1 = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	double tmp;
	if (C <= -2.4e-90) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= -8e-235) {
		tmp = t_0;
	} else if (C <= 3.8e-264) {
		tmp = t_1;
	} else if (C <= 1.15e-139) {
		tmp = t_0;
	} else if (C <= 8.2e-85) {
		tmp = t_1;
	} else if (C <= 4.4e-7) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / 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((-2.0 * (A / B))) / math.pi)
	tmp = 0
	if C <= -2.4e-90:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= -8e-235:
		tmp = t_0
	elif C <= 3.8e-264:
		tmp = t_1
	elif C <= 1.15e-139:
		tmp = t_0
	elif C <= 8.2e-85:
		tmp = t_1
	elif C <= 4.4e-7:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / 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(-2.0 * Float64(A / B))) / pi))
	tmp = 0.0
	if (C <= -2.4e-90)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= -8e-235)
		tmp = t_0;
	elseif (C <= 3.8e-264)
		tmp = t_1;
	elseif (C <= 1.15e-139)
		tmp = t_0;
	elseif (C <= 8.2e-85)
		tmp = t_1;
	elseif (C <= 4.4e-7)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / 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((-2.0 * (A / B))) / pi);
	tmp = 0.0;
	if (C <= -2.4e-90)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= -8e-235)
		tmp = t_0;
	elseif (C <= 3.8e-264)
		tmp = t_1;
	elseif (C <= 1.15e-139)
		tmp = t_0;
	elseif (C <= 8.2e-85)
		tmp = t_1;
	elseif (C <= 4.4e-7)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -2.4e-90], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -8e-235], t$95$0, If[LessEqual[C, 3.8e-264], t$95$1, If[LessEqual[C, 1.15e-139], t$95$0, If[LessEqual[C, 8.2e-85], t$95$1, If[LessEqual[C, 4.4e-7], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -2.4000000000000002e-90

   1. Initial program 78.2%

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

   2. Taylor expanded in C around -inf 68.2%

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

   if -2.4000000000000002e-90 < C < -7.9999999999999997e-235 or 3.80000000000000013e-264 < C < 1.15000000000000006e-139 or 8.19999999999999987e-85 < C < 4.4000000000000002e-7

   1. Initial program 57.8%

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

   2. Taylor expanded in B around inf 44.0%

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

   if -7.9999999999999997e-235 < C < 3.80000000000000013e-264 or 1.15000000000000006e-139 < C < 8.19999999999999987e-85

   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 45.3%

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

   if 4.4000000000000002e-7 < C

   1. Initial program 22.8%

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

   2. Taylor expanded in A around 0 17.1%

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

      1. associate--l+ 17.0%

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

      2. fma-def 17.0%

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

   4. Simplified 31.5%

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

   5. Taylor expanded in C around 0 35.2%

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

      1. mul-1-neg 35.2%

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

      2. unsub-neg 35.2%

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

   7. Simplified 35.2%

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

   8. Taylor expanded in A around 0 19.0%

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

      1. associate-*l/ 19.0%

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

      2. *-lft-identity 19.0%

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

      3. unpow2 19.0%

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

      4. unpow2 19.0%

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

      5. hypot-def 32.8%

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

      6. div-sub 48.7%

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

      7. hypot-def 22.8%

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

      8. unpow2 22.8%

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

      9. unpow2 22.8%

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

      10. +-commutative 22.8%

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

      11. unpow2 22.8%

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

      12. unpow2 22.8%

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

      13. hypot-def 48.7%

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

   10. Simplified 48.7%

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

   11. Taylor expanded in C around inf 64.4%

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

       1. associate-*r/ 64.4%

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

   13. Simplified 64.4%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.4 \cdot 10^{-90}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -8 \cdot 10^{-235}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 3.8 \cdot 10^{-264}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.15 \cdot 10^{-139}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.4 \cdot 10^{-7}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \]

Alternative 6: 46.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{if}\;A \leq -2.2 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.9 \cdot 10^{-232}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2.02 \cdot 10^{-277}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.1 \cdot 10^{-109}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.85 \cdot 10^{+27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan -1.0) PI))))
   (if (<= A -2.2e-101)
     (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
     (if (<= A -5.9e-232)
       t_0
       (if (<= A 2.02e-277)
         (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
         (if (<= A 7.1e-109)
           t_0
           (if (<= A 1.85e+27)
             (* 180.0 (/ (atan 1.0) PI))
             (* 180.0 (/ (atan (* -2.0 (/ A B))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(-1.0) / ((double) M_PI));
	double tmp;
	if (A <= -2.2e-101) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= -5.9e-232) {
		tmp = t_0;
	} else if (A <= 2.02e-277) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (A <= 7.1e-109) {
		tmp = t_0;
	} else if (A <= 1.85e+27) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(-1.0) / Math.PI);
	double tmp;
	if (A <= -2.2e-101) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= -5.9e-232) {
		tmp = t_0;
	} else if (A <= 2.02e-277) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (A <= 7.1e-109) {
		tmp = t_0;
	} else if (A <= 1.85e+27) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(-1.0) / math.pi)
	tmp = 0
	if A <= -2.2e-101:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= -5.9e-232:
		tmp = t_0
	elif A <= 2.02e-277:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif A <= 7.1e-109:
		tmp = t_0
	elif A <= 1.85e+27:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(-1.0) / pi))
	tmp = 0.0
	if (A <= -2.2e-101)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= -5.9e-232)
		tmp = t_0;
	elseif (A <= 2.02e-277)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (A <= 7.1e-109)
		tmp = t_0;
	elseif (A <= 1.85e+27)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(-1.0) / pi);
	tmp = 0.0;
	if (A <= -2.2e-101)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= -5.9e-232)
		tmp = t_0;
	elseif (A <= 2.02e-277)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (A <= 7.1e-109)
		tmp = t_0;
	elseif (A <= 1.85e+27)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -2.2e-101], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -5.9e-232], t$95$0, If[LessEqual[A, 2.02e-277], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 7.1e-109], t$95$0, If[LessEqual[A, 1.85e+27], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -2.1999999999999999e-101

   1. Initial program 32.5%

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

   2. Taylor expanded in A around -inf 61.5%

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

      1. associate-*r/ 61.5%

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

   4. Simplified 61.5%

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

   if -2.1999999999999999e-101 < A < -5.90000000000000017e-232 or 2.02e-277 < A < 7.0999999999999999e-109

   1. Initial program 65.5%

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

   2. Taylor expanded in B around inf 44.1%

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

   if -5.90000000000000017e-232 < A < 2.02e-277

   1. Initial program 69.0%

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

   2. Taylor expanded in C around -inf 38.9%

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

   if 7.0999999999999999e-109 < A < 1.85000000000000001e27

   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 42.0%

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

   if 1.85000000000000001e27 < A

   1. Initial program 84.7%

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

   2. Taylor expanded in A around inf 79.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-2 \cdot \frac{A}{B}\right)}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.2 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -5.9 \cdot 10^{-232}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 2.02 \cdot 10^{-277}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.1 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.85 \cdot 10^{+27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 57.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{-103}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{-231} \lor \neg \left(A \leq 3.3 \cdot 10^{-274}\right) \land A \leq 4.4 \cdot 10^{-231}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9e-103)
   (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
   (if (or (<= A -2.3e-231) (and (not (<= A 3.3e-274)) (<= A 4.4e-231)))
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9e-103) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if ((A <= -2.3e-231) || (!(A <= 3.3e-274) && (A <= 4.4e-231))) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -9e-103) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if ((A <= -2.3e-231) || (!(A <= 3.3e-274) && (A <= 4.4e-231))) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -9e-103:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif (A <= -2.3e-231) or (not (A <= 3.3e-274) and (A <= 4.4e-231)):
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -9e-103)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif ((A <= -2.3e-231) || (!(A <= 3.3e-274) && (A <= 4.4e-231)))
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -9e-103)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif ((A <= -2.3e-231) || (~((A <= 3.3e-274)) && (A <= 4.4e-231)))
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -9e-103], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[A, -2.3e-231], And[N[Not[LessEqual[A, 3.3e-274]], $MachinePrecision], LessEqual[A, 4.4e-231]]], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -9e-103

   1. Initial program 32.5%

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

   2. Taylor expanded in A around -inf 61.5%

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

      1. associate-*r/ 61.5%

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

   4. Simplified 61.5%

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

   if -9e-103 < A < -2.3e-231 or 3.2999999999999998e-274 < A < 4.40000000000000018e-231

   1. Initial program 60.1%

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

   2. Taylor expanded in B around inf 52.7%

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

   if -2.3e-231 < A < 3.2999999999999998e-274 or 4.40000000000000018e-231 < A

   1. Initial program 76.0%

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

   2. Taylor expanded in B around -inf 73.8%

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

      1. associate--l+ 73.8%

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

      2. div-sub 74.6%

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

   4. Simplified 74.6%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{-103}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{-231} \lor \neg \left(A \leq 3.3 \cdot 10^{-274}\right) \land A \leq 4.4 \cdot 10^{-231}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 46.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -3.35 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.05 \cdot 10^{-196}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-155}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{-115}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))))
   (if (<= B -3.35e+19)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -2.05e-196)
       t_0
       (if (<= B 4.2e-155)
         (* 180.0 (/ (atan (/ (- A) B)) PI))
         (if (<= B 3.4e-115) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	double tmp;
	if (B <= -3.35e+19) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2.05e-196) {
		tmp = t_0;
	} else if (B <= 4.2e-155) {
		tmp = 180.0 * (atan((-A / B)) / ((double) M_PI));
	} else if (B <= 3.4e-115) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	double tmp;
	if (B <= -3.35e+19) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2.05e-196) {
		tmp = t_0;
	} else if (B <= 4.2e-155) {
		tmp = 180.0 * (Math.atan((-A / B)) / Math.PI);
	} else if (B <= 3.4e-115) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	tmp = 0
	if B <= -3.35e+19:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2.05e-196:
		tmp = t_0
	elif B <= 4.2e-155:
		tmp = 180.0 * (math.atan((-A / B)) / math.pi)
	elif B <= 3.4e-115:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi))
	tmp = 0.0
	if (B <= -3.35e+19)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2.05e-196)
		tmp = t_0;
	elseif (B <= 4.2e-155)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi));
	elseif (B <= 3.4e-115)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((2.0 * (C / B))) / pi);
	tmp = 0.0;
	if (B <= -3.35e+19)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2.05e-196)
		tmp = t_0;
	elseif (B <= 4.2e-155)
		tmp = 180.0 * (atan((-A / B)) / pi);
	elseif (B <= 3.4e-115)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3.35e+19], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.05e-196], t$95$0, If[LessEqual[B, 4.2e-155], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.4e-115], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -3.35e19

   1. Initial program 51.6%

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

   2. Taylor expanded in B around -inf 64.3%

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

   if -3.35e19 < B < -2.05000000000000011e-196 or 4.2000000000000003e-155 < B < 3.3999999999999998e-115

   1. Initial program 68.3%

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

   2. Taylor expanded in C around -inf 45.5%

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

   if -2.05000000000000011e-196 < B < 4.2000000000000003e-155

   1. Initial program 56.2%

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

   2. Taylor expanded in A around 0 41.4%

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

      1. associate--l+ 41.4%

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

      2. fma-def 41.4%

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

   4. Simplified 38.1%

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

   5. Taylor expanded in C around 0 34.5%

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

      1. mul-1-neg 34.5%

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

      2. unsub-neg 34.5%

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

   7. Simplified 34.5%

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

   8. Taylor expanded in A around inf 32.9%

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

      1. associate-*l/ 32.9%

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

      2. associate-*r* 32.9%

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

      3. associate-*r/ 32.9%

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

      4. neg-mul-1 32.9%

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

   10. Simplified 32.9%

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

   11. Taylor expanded in B around inf 41.4%

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

       1. mul-1-neg 41.4%

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

       2. distribute-neg-frac 41.4%

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

   13. Simplified 41.4%

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

   if 3.3999999999999998e-115 < B

   1. Initial program 58.7%

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

   2. Taylor expanded in B around inf 58.5%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.35 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.05 \cdot 10^{-196}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-155}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.4 \cdot 10^{-115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 9: 66.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.1 \cdot 10^{-299}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-307}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.1e-299)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= B 5e-307)
     (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
     (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.1e-299) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= 5e-307) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.1e-299) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= 5e-307) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + B)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.1e-299:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= 5e-307:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (A + B)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.1e-299)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= 5e-307)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + B)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.1e-299)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= 5e-307)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	else
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.1e-299], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5e-307], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.1000000000000001e-299

   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 B around -inf 69.9%

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

      1. associate--l+ 69.9%

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

      2. div-sub 71.6%

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

   4. Simplified 71.6%

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

   if -2.1000000000000001e-299 < B < 5.00000000000000014e-307

   1. Initial program 34.3%

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

   2. Taylor expanded in A around -inf 85.1%

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

      1. associate-*r/ 85.1%

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

   4. Simplified 85.1%

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

   if 5.00000000000000014e-307 < B

   1. Initial program 59.5%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in B around inf 70.3%

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

      1. +-commutative 70.3%

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

   6. Simplified 70.3%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.1 \cdot 10^{-299}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-307}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10: 45.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7 \cdot 10^{-162}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-121}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7e-162)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.9e-121)
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7e-162) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.9e-121) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -7e-162) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.9e-121) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7e-162:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.9e-121:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -7e-162)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.9e-121)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / 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 <= -7e-162)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.9e-121)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7e-162], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.9e-121], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $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 < -6.9999999999999998e-162

   1. Initial program 57.2%

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

   2. Taylor expanded in B around -inf 49.8%

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

   if -6.9999999999999998e-162 < B < 1.9e-121

   1. Initial program 59.6%

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

   2. Taylor expanded in A around inf 38.4%

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

   if 1.9e-121 < B

   1. Initial program 59.3%

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

   2. Taylor expanded in B around inf 56.7%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7 \cdot 10^{-162}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-121}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11: 45.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7.5 \cdot 10^{-162}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7.5e-162)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.4e-120)
     (* 180.0 (/ (atan (/ (- A) B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.5e-162) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.4e-120) {
		tmp = 180.0 * (atan((-A / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.5e-162) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.4e-120) {
		tmp = 180.0 * (Math.atan((-A / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7.5e-162:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.4e-120:
		tmp = 180.0 * (math.atan((-A / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -7.5e-162)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.4e-120)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / 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 <= -7.5e-162)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.4e-120)
		tmp = 180.0 * (atan((-A / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7.5e-162], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.4e-120], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -7.49999999999999972e-162

   1. Initial program 57.2%

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

   2. Taylor expanded in B around -inf 49.8%

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

   if -7.49999999999999972e-162 < B < 4.40000000000000025e-120

   1. Initial program 59.6%

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

   2. Taylor expanded in A around 0 47.3%

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

      1. associate--l+ 47.3%

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

      2. fma-def 47.3%

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

   4. Simplified 44.5%

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

   5. Taylor expanded in C around 0 37.3%

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

      1. mul-1-neg 37.3%

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

      2. unsub-neg 37.3%

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

   7. Simplified 37.3%

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

   8. Taylor expanded in A around inf 35.9%

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

      1. associate-*l/ 35.9%

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

      2. associate-*r* 35.9%

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

      3. associate-*r/ 35.9%

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

      4. neg-mul-1 35.9%

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

   10. Simplified 35.9%

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

   11. Taylor expanded in B around inf 38.4%

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

       1. mul-1-neg 38.4%

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

       2. distribute-neg-frac 38.4%

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

   13. Simplified 38.4%

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

   if 4.40000000000000025e-120 < B

   1. Initial program 59.3%

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

   2. Taylor expanded in B around inf 56.7%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.5 \cdot 10^{-162}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12: 45.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.8 \cdot 10^{-160}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-142}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.8e-160)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.6e-142)
     (* 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 <= -4.8e-160) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.6e-142) {
		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 <= -4.8e-160) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.6e-142) {
		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 <= -4.8e-160:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.6e-142:
		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 <= -4.8e-160)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.6e-142)
		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 <= -4.8e-160)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.6e-142)
		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, -4.8e-160], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.6e-142], 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 < -4.79999999999999982e-160

   1. Initial program 57.8%

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

   2. Taylor expanded in B around -inf 50.4%

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

   if -4.79999999999999982e-160 < B < 1.5999999999999999e-142

   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 C around inf 31.0%

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

      1. associate-*r/ 31.0%

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

      2. distribute-rgt1-in 31.0%

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

      3. metadata-eval 31.0%

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

      4. mul0-lft 31.0%

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

      5. metadata-eval 31.0%

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

   4. Simplified 31.0%

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

   if 1.5999999999999999e-142 < B

   1. Initial program 60.5%

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

   2. Taylor expanded in B around inf 55.5%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.8 \cdot 10^{-160}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-142}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 13: 39.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4 \cdot 10^{-303}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4e-303) (* 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 <= -4e-303) {
		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 <= -4e-303) {
		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 <= -4e-303:
		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 <= -4e-303)
		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 <= -4e-303)
		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, -4e-303], 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 < -3.99999999999999972e-303

   1. Initial program 58.8%

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

   2. Taylor expanded in B around -inf 39.7%

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

   if -3.99999999999999972e-303 < B

   1. Initial program 58.5%

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

   2. Taylor expanded in B around inf 43.9%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4 \cdot 10^{-303}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 14: 21.1% 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 58.7%

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

2. Taylor expanded in B around inf 24.0%

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

3. Final simplification 24.0%

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

Reproduce

herbie shell --seed 2023311 
(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)))