ABCF->ab-angle angle

Percentage Accurate: 54.7% → 83.0%

Time: 28.3s

Alternatives: 18

Speedup: 3.6×

• could not determine a ground truth

  1. A = -5.251677446117434e-32
  2. B = 2.112597581775749e-141
  3. C = -2.28626281603048e-57

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.7% 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: 83.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 6.5 \cdot 10^{+159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C \cdot 2}{B}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 6.5e+159)
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))
   (* 180.0 (/ (atan (/ -1.0 (/ (* C 2.0) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 6.5e+159) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 / ((C * 2.0) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 6.5e+159) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 / ((C * 2.0) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 6.5e+159:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 / ((C * 2.0) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 6.5e+159)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(Float64(C * 2.0) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 6.5e+159)
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	else
		tmp = 180.0 * (atan((-1.0 / ((C * 2.0) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 6.5e+159], 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], N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 6.5000000000000001e159

   1. Initial program 60.6%

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

   3. Simplified 84.0%

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

   if 6.5000000000000001e159 < C

   1. Initial program 8.7%

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

      1. associate--l- 8.7%

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

      2. +-commutative 8.7%

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

      3. unpow2 8.7%

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

      4. unpow2 8.7%

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

      5. hypot-undefine 47.3%

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

      6. associate-/r/ 47.3%

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

      7. frac-2neg 47.3%

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

      8. metadata-eval 47.3%

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

      9. associate--r+ 54.3%

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

      10. hypot-undefine 8.7%

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

      11. unpow2 8.7%

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

      12. unpow2 8.7%

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

      13. +-commutative 8.7%

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

      14. unpow2 8.7%

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

      15. unpow2 8.7%

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

      16. hypot-define 54.3%

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

   4. Applied egg-rr 54.3%

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

   6. Simplified 19.6%

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

   7. Taylor expanded in C around inf 31.4%

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

   8. Taylor expanded in B around inf 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-*l/ 88.9%

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

   10. Simplified 88.9%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 6.5 \cdot 10^{+159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C \cdot 2}{B}}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -1 \cdot 10^{+155}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{-245}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C \cdot 2}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.05 \cdot 10^{+114}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{B}{A + B}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))))
   (if (<= A -1e+155)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (if (<= A -2.4e-245)
       t_0
       (if (<= A -9.5e-269)
         (* 180.0 (/ (atan (/ -1.0 (/ (* C 2.0) B))) PI))
         (if (<= A 2.05e+114)
           t_0
           (* 180.0 (/ (atan (/ -1.0 (/ 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 tmp;
	if (A <= -1e+155) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= -2.4e-245) {
		tmp = t_0;
	} else if (A <= -9.5e-269) {
		tmp = 180.0 * (atan((-1.0 / ((C * 2.0) / B))) / ((double) M_PI));
	} else if (A <= 2.05e+114) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-1.0 / (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 tmp;
	if (A <= -1e+155) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= -2.4e-245) {
		tmp = t_0;
	} else if (A <= -9.5e-269) {
		tmp = 180.0 * (Math.atan((-1.0 / ((C * 2.0) / B))) / Math.PI);
	} else if (A <= 2.05e+114) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-1.0 / (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)
	tmp = 0
	if A <= -1e+155:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= -2.4e-245:
		tmp = t_0
	elif A <= -9.5e-269:
		tmp = 180.0 * (math.atan((-1.0 / ((C * 2.0) / B))) / math.pi)
	elif A <= 2.05e+114:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-1.0 / (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))
	tmp = 0.0
	if (A <= -1e+155)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= -2.4e-245)
		tmp = t_0;
	elseif (A <= -9.5e-269)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(Float64(C * 2.0) / B))) / pi));
	elseif (A <= 2.05e+114)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(B / Float64(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);
	tmp = 0.0;
	if (A <= -1e+155)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= -2.4e-245)
		tmp = t_0;
	elseif (A <= -9.5e-269)
		tmp = 180.0 * (atan((-1.0 / ((C * 2.0) / B))) / pi);
	elseif (A <= 2.05e+114)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-1.0 / (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]}, If[LessEqual[A, -1e+155], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.4e-245], t$95$0, If[LessEqual[A, -9.5e-269], N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.05e+114], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(B / N[(A + B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.00000000000000001e155

   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. Add Preprocessing

   3. Taylor expanded in A around -inf 73.9%

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

   if -1.00000000000000001e155 < A < -2.4e-245 or -9.5000000000000006e-269 < A < 2.05e114

   1. Initial program 55.9%

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

   3. Taylor expanded in A around 0 51.5%

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

      1. unpow2 51.5%

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

      2. unpow2 51.5%

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

      3. hypot-define 78.8%

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

   5. Simplified 78.8%

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

   if -2.4e-245 < A < -9.5000000000000006e-269

   1. Initial program 25.8%

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

      1. associate--l- 25.8%

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

      2. +-commutative 25.8%

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

      3. unpow2 25.8%

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

      4. unpow2 25.8%

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

      5. hypot-undefine 26.2%

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

      6. associate-/r/ 26.2%

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

      7. frac-2neg 26.2%

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

      8. metadata-eval 26.2%

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

      9. associate--r+ 26.2%

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

      10. hypot-undefine 25.8%

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

      11. unpow2 25.8%

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

      12. unpow2 25.8%

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

      13. +-commutative 25.8%

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

      14. unpow2 25.8%

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

      15. unpow2 25.8%

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

      16. hypot-define 26.2%

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

   4. Applied egg-rr 26.2%

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

   6. Simplified 24.9%

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

   7. Taylor expanded in C around inf 38.0%

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

   8. Taylor expanded in B around inf 79.7%

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

      1. *-commutative 79.7%

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

      2. associate-*l/ 79.7%

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

   10. Simplified 79.7%

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

   if 2.05e114 < A

   1. Initial program 89.8%

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

      1. associate--l- 89.8%

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

      2. +-commutative 89.8%

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

      3. unpow2 89.8%

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

      4. unpow2 89.8%

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

      5. hypot-undefine 98.0%

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

      6. associate-/r/ 98.0%

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

      7. frac-2neg 98.0%

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

      8. metadata-eval 98.0%

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

      9. associate--r+ 98.0%

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

      10. hypot-undefine 89.8%

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

      11. unpow2 89.8%

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

      12. unpow2 89.8%

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

      13. +-commutative 89.8%

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

      14. unpow2 89.8%

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

      15. unpow2 89.8%

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

      16. hypot-define 98.0%

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

   4. Applied egg-rr 98.0%

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

   6. Simplified 96.1%

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

   7. Taylor expanded in B around inf 92.7%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1 \cdot 10^{+155}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{-245}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C \cdot 2}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.05 \cdot 10^{+114}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{B}{A + B}}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.2 \cdot 10^{+154}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{-245}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C \cdot 2}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.2e+154)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A -2.4e-245)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (if (<= A -9.5e-269)
       (* 180.0 (/ (atan (/ -1.0 (/ (* C 2.0) B))) 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 <= -4.2e+154) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= -2.4e-245) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else if (A <= -9.5e-269) {
		tmp = 180.0 * (atan((-1.0 / ((C * 2.0) / B))) / ((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 <= -4.2e+154) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= -2.4e-245) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else if (A <= -9.5e-269) {
		tmp = 180.0 * (Math.atan((-1.0 / ((C * 2.0) / B))) / 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 <= -4.2e+154:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= -2.4e-245:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	elif A <= -9.5e-269:
		tmp = 180.0 * (math.atan((-1.0 / ((C * 2.0) / B))) / 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 <= -4.2e+154)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= -2.4e-245)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	elseif (A <= -9.5e-269)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(Float64(C * 2.0) / B))) / 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 <= -4.2e+154)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= -2.4e-245)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	elseif (A <= -9.5e-269)
		tmp = 180.0 * (atan((-1.0 / ((C * 2.0) / B))) / 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, -4.2e+154], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.4e-245], 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[A, -9.5e-269], N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(N[(C * 2.0), $MachinePrecision] / B), $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 4 regimes

2. if A < -4.19999999999999989e154

   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. Add Preprocessing

   3. Taylor expanded in A around -inf 73.9%

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

   if -4.19999999999999989e154 < A < -2.4e-245

   1. Initial program 51.7%

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

   3. Taylor expanded in A around 0 49.3%

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

      1. unpow2 49.3%

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

      2. unpow2 49.3%

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

      3. hypot-define 74.7%

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

   5. Simplified 74.7%

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

   if -2.4e-245 < A < -9.5000000000000006e-269

   1. Initial program 25.8%

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

      1. associate--l- 25.8%

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

      2. +-commutative 25.8%

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

      3. unpow2 25.8%

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

      4. unpow2 25.8%

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

      5. hypot-undefine 26.2%

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

      6. associate-/r/ 26.2%

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

      7. frac-2neg 26.2%

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

      8. metadata-eval 26.2%

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

      9. associate--r+ 26.2%

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

      10. hypot-undefine 25.8%

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

      11. unpow2 25.8%

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

      12. unpow2 25.8%

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

      13. +-commutative 25.8%

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

      14. unpow2 25.8%

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

      15. unpow2 25.8%

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

      16. hypot-define 26.2%

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

   4. Applied egg-rr 26.2%

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

   6. Simplified 24.9%

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

   7. Taylor expanded in C around inf 38.0%

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

   8. Taylor expanded in B around inf 79.7%

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

      1. *-commutative 79.7%

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

      2. associate-*l/ 79.7%

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

   10. Simplified 79.7%

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

   if -9.5000000000000006e-269 < A

   1. Initial program 69.8%

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

   3. Simplified 91.1%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.2 \cdot 10^{+154}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{-245}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C \cdot 2}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.02 \cdot 10^{-55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.05 \cdot 10^{+159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C \cdot 2}{B}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.02e-55)
   (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
   (if (<= C 2.05e+159)
     (* 180.0 (/ (atan (/ (+ A (hypot B A)) (- B))) PI))
     (* 180.0 (/ (atan (/ -1.0 (/ (* C 2.0) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.02e-55) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else if (C <= 2.05e+159) {
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 / ((C * 2.0) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.02e-55) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else if (C <= 2.05e+159) {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(B, A)) / -B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 / ((C * 2.0) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.02e-55:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	elif C <= 2.05e+159:
		tmp = 180.0 * (math.atan(((A + math.hypot(B, A)) / -B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 / ((C * 2.0) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.02e-55)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	elseif (C <= 2.05e+159)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / Float64(-B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(Float64(C * 2.0) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.02e-55)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	elseif (C <= 2.05e+159)
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / pi);
	else
		tmp = 180.0 * (atan((-1.0 / ((C * 2.0) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.02e-55], 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, 2.05e+159], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.02e-55

   1. Initial program 77.4%

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

   3. Taylor expanded in A around 0 75.6%

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

      1. unpow2 75.6%

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

      2. unpow2 75.6%

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

      3. hypot-define 85.7%

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

   5. Simplified 85.7%

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

   if -1.02e-55 < C < 2.05000000000000007e159

   1. Initial program 52.9%

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

   3. Taylor expanded in C around 0 50.3%

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

      1. associate-*r/ 50.3%

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

      2. mul-1-neg 50.3%

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

      3. +-commutative 50.3%

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

      4. unpow2 50.3%

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

      5. unpow2 50.3%

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

      6. hypot-define 78.2%

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

   5. Simplified 78.2%

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

   if 2.05000000000000007e159 < C

   1. Initial program 8.7%

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

      1. associate--l- 8.7%

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

      2. +-commutative 8.7%

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

      3. unpow2 8.7%

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

      4. unpow2 8.7%

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

      5. hypot-undefine 47.3%

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

      6. associate-/r/ 47.3%

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

      7. frac-2neg 47.3%

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

      8. metadata-eval 47.3%

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

      9. associate--r+ 54.3%

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

      10. hypot-undefine 8.7%

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

      11. unpow2 8.7%

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

      12. unpow2 8.7%

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

      13. +-commutative 8.7%

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

      14. unpow2 8.7%

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

      15. unpow2 8.7%

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

      16. hypot-define 54.3%

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

   4. Applied egg-rr 54.3%

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

   6. Simplified 19.6%

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

   7. Taylor expanded in C around inf 31.4%

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

   8. Taylor expanded in B around inf 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-*l/ 88.9%

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

   10. Simplified 88.9%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.02 \cdot 10^{-55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.05 \cdot 10^{+159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C \cdot 2}{B}}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := A + \mathsf{hypot}\left(B, A\right)\\ \mathbf{if}\;C \leq -7 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - t\_0}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.7 \cdot 10^{+159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{t\_0}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C \cdot 2}{B}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (+ A (hypot B A))))
   (if (<= C -7e-78)
     (* 180.0 (/ (atan (/ (- C t_0) B)) PI))
     (if (<= C 6.7e+159)
       (* 180.0 (/ (atan (/ t_0 (- B))) PI))
       (* 180.0 (/ (atan (/ -1.0 (/ (* C 2.0) B))) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = A + hypot(B, A);
	double tmp;
	if (C <= -7e-78) {
		tmp = 180.0 * (atan(((C - t_0) / B)) / ((double) M_PI));
	} else if (C <= 6.7e+159) {
		tmp = 180.0 * (atan((t_0 / -B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 / ((C * 2.0) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = A + Math.hypot(B, A);
	double tmp;
	if (C <= -7e-78) {
		tmp = 180.0 * (Math.atan(((C - t_0) / B)) / Math.PI);
	} else if (C <= 6.7e+159) {
		tmp = 180.0 * (Math.atan((t_0 / -B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 / ((C * 2.0) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = A + math.hypot(B, A)
	tmp = 0
	if C <= -7e-78:
		tmp = 180.0 * (math.atan(((C - t_0) / B)) / math.pi)
	elif C <= 6.7e+159:
		tmp = 180.0 * (math.atan((t_0 / -B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 / ((C * 2.0) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(A + hypot(B, A))
	tmp = 0.0
	if (C <= -7e-78)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - t_0) / B)) / pi));
	elseif (C <= 6.7e+159)
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 / Float64(-B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(Float64(C * 2.0) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = A + hypot(B, A);
	tmp = 0.0;
	if (C <= -7e-78)
		tmp = 180.0 * (atan(((C - t_0) / B)) / pi);
	elseif (C <= 6.7e+159)
		tmp = 180.0 * (atan((t_0 / -B)) / pi);
	else
		tmp = 180.0 * (atan((-1.0 / ((C * 2.0) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -7e-78], N[(180.0 * N[(N[ArcTan[N[(N[(C - t$95$0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.7e+159], N[(180.0 * N[(N[ArcTan[N[(t$95$0 / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if C < -6.9999999999999999e-78

   1. Initial program 74.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in C around 0 73.0%

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

      1. +-commutative 73.0%

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

      2. unpow2 73.0%

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

      3. unpow2 73.0%

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

      4. hypot-define 84.7%

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

   7. Simplified 84.7%

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

   if -6.9999999999999999e-78 < C < 6.70000000000000018e159

   1. Initial program 53.0%

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

   3. Taylor expanded in C around 0 50.9%

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

      1. associate-*r/ 50.9%

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

      2. mul-1-neg 50.9%

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

      3. +-commutative 50.9%

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

      4. unpow2 50.9%

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

      5. unpow2 50.9%

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

      6. hypot-define 79.0%

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

   5. Simplified 79.0%

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

   if 6.70000000000000018e159 < C

   1. Initial program 8.7%

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

      1. associate--l- 8.7%

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

      2. +-commutative 8.7%

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

      3. unpow2 8.7%

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

      4. unpow2 8.7%

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

      5. hypot-undefine 47.3%

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

      6. associate-/r/ 47.3%

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

      7. frac-2neg 47.3%

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

      8. metadata-eval 47.3%

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

      9. associate--r+ 54.3%

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

      10. hypot-undefine 8.7%

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

      11. unpow2 8.7%

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

      12. unpow2 8.7%

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

      13. +-commutative 8.7%

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

      14. unpow2 8.7%

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

      15. unpow2 8.7%

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

      16. hypot-define 54.3%

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

   4. Applied egg-rr 54.3%

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

   6. Simplified 19.6%

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

   7. Taylor expanded in C around inf 31.4%

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

   8. Taylor expanded in B around inf 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-*l/ 88.9%

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

   10. Simplified 88.9%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -7 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.7 \cdot 10^{+159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C \cdot 2}{B}}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C \cdot 2}{B}}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -9 \cdot 10^{+149}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;A \leq -3.1 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{-43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{-245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{-269}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq 4.8 \cdot 10^{-287}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq 10^{-158}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{B}{A + B}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ -1.0 (/ (* C 2.0) B))) PI)))
        (t_1 (* 180.0 (/ (atan (/ (+ C B) B)) PI)))
        (t_2 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= A -9e+149)
     t_2
     (if (<= A -3.1e+41)
       t_1
       (if (<= A -2.9e-43)
         t_2
         (if (<= A -2.4e-245)
           t_1
           (if (<= A -9.5e-269)
             t_0
             (if (<= A 1.8e-304)
               t_1
               (if (<= A 4.8e-287)
                 t_0
                 (if (<= A 1e-158)
                   (* 180.0 (/ (atan (/ (- C B) B)) PI))
                   (if (<= A 1e-48)
                     t_1
                     (* 180.0 (/ (atan (/ -1.0 (/ B (+ A B)))) PI)))))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((-1.0 / ((C * 2.0) / B))) / ((double) M_PI));
	double t_1 = 180.0 * (atan(((C + B) / B)) / ((double) M_PI));
	double t_2 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (A <= -9e+149) {
		tmp = t_2;
	} else if (A <= -3.1e+41) {
		tmp = t_1;
	} else if (A <= -2.9e-43) {
		tmp = t_2;
	} else if (A <= -2.4e-245) {
		tmp = t_1;
	} else if (A <= -9.5e-269) {
		tmp = t_0;
	} else if (A <= 1.8e-304) {
		tmp = t_1;
	} else if (A <= 4.8e-287) {
		tmp = t_0;
	} else if (A <= 1e-158) {
		tmp = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	} else if (A <= 1e-48) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (atan((-1.0 / (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((-1.0 / ((C * 2.0) / B))) / Math.PI);
	double t_1 = 180.0 * (Math.atan(((C + B) / B)) / Math.PI);
	double t_2 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (A <= -9e+149) {
		tmp = t_2;
	} else if (A <= -3.1e+41) {
		tmp = t_1;
	} else if (A <= -2.9e-43) {
		tmp = t_2;
	} else if (A <= -2.4e-245) {
		tmp = t_1;
	} else if (A <= -9.5e-269) {
		tmp = t_0;
	} else if (A <= 1.8e-304) {
		tmp = t_1;
	} else if (A <= 4.8e-287) {
		tmp = t_0;
	} else if (A <= 1e-158) {
		tmp = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	} else if (A <= 1e-48) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (Math.atan((-1.0 / (B / (A + B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((-1.0 / ((C * 2.0) / B))) / math.pi)
	t_1 = 180.0 * (math.atan(((C + B) / B)) / math.pi)
	t_2 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	tmp = 0
	if A <= -9e+149:
		tmp = t_2
	elif A <= -3.1e+41:
		tmp = t_1
	elif A <= -2.9e-43:
		tmp = t_2
	elif A <= -2.4e-245:
		tmp = t_1
	elif A <= -9.5e-269:
		tmp = t_0
	elif A <= 1.8e-304:
		tmp = t_1
	elif A <= 4.8e-287:
		tmp = t_0
	elif A <= 1e-158:
		tmp = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	elif A <= 1e-48:
		tmp = t_1
	else:
		tmp = 180.0 * (math.atan((-1.0 / (B / (A + B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(Float64(C * 2.0) / B))) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(C + B) / B)) / pi))
	t_2 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (A <= -9e+149)
		tmp = t_2;
	elseif (A <= -3.1e+41)
		tmp = t_1;
	elseif (A <= -2.9e-43)
		tmp = t_2;
	elseif (A <= -2.4e-245)
		tmp = t_1;
	elseif (A <= -9.5e-269)
		tmp = t_0;
	elseif (A <= 1.8e-304)
		tmp = t_1;
	elseif (A <= 4.8e-287)
		tmp = t_0;
	elseif (A <= 1e-158)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi));
	elseif (A <= 1e-48)
		tmp = t_1;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(B / Float64(A + B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((-1.0 / ((C * 2.0) / B))) / pi);
	t_1 = 180.0 * (atan(((C + B) / B)) / pi);
	t_2 = 180.0 * (atan((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (A <= -9e+149)
		tmp = t_2;
	elseif (A <= -3.1e+41)
		tmp = t_1;
	elseif (A <= -2.9e-43)
		tmp = t_2;
	elseif (A <= -2.4e-245)
		tmp = t_1;
	elseif (A <= -9.5e-269)
		tmp = t_0;
	elseif (A <= 1.8e-304)
		tmp = t_1;
	elseif (A <= 4.8e-287)
		tmp = t_0;
	elseif (A <= 1e-158)
		tmp = 180.0 * (atan(((C - B) / B)) / pi);
	elseif (A <= 1e-48)
		tmp = t_1;
	else
		tmp = 180.0 * (atan((-1.0 / (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[(-1.0 / N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(C + B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -9e+149], t$95$2, If[LessEqual[A, -3.1e+41], t$95$1, If[LessEqual[A, -2.9e-43], t$95$2, If[LessEqual[A, -2.4e-245], t$95$1, If[LessEqual[A, -9.5e-269], t$95$0, If[LessEqual[A, 1.8e-304], t$95$1, If[LessEqual[A, 4.8e-287], t$95$0, If[LessEqual[A, 1e-158], N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1e-48], t$95$1, N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(B / N[(A + B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -8.99999999999999965e149 or -3.1e41 < A < -2.9000000000000001e-43

   1. Initial program 16.5%

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

   3. Taylor expanded in A around -inf 66.0%

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

   if -8.99999999999999965e149 < A < -3.1e41 or -2.9000000000000001e-43 < A < -2.4e-245 or -9.5000000000000006e-269 < A < 1.8000000000000001e-304 or 1.00000000000000006e-158 < A < 9.9999999999999997e-49

   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. Step-by-step derivation

   3. Simplified 81.7%

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

   5. Taylor expanded in C around 0 53.3%

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

      1. +-commutative 53.3%

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

      2. unpow2 53.3%

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

      3. unpow2 53.3%

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

      4. hypot-define 76.4%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in B around -inf 70.4%

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

      1. mul-1-neg 70.4%

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

   10. Simplified 70.4%

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

   if -2.4e-245 < A < -9.5000000000000006e-269 or 1.8000000000000001e-304 < A < 4.79999999999999999e-287

   1. Initial program 19.4%

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

      1. associate--l- 19.4%

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

      2. +-commutative 19.4%

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

      3. unpow2 19.4%

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

      4. unpow2 19.4%

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

      5. hypot-undefine 25.2%

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

      6. associate-/r/ 25.2%

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

      7. frac-2neg 25.2%

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

      8. metadata-eval 25.2%

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

      9. associate--r+ 25.2%

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

      10. hypot-undefine 19.4%

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

      11. unpow2 19.4%

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

      12. unpow2 19.4%

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

      13. +-commutative 19.4%

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

      14. unpow2 19.4%

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

      15. unpow2 19.4%

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

      16. hypot-define 25.2%

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

   4. Applied egg-rr 25.2%

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

   6. Simplified 24.7%

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

   7. Taylor expanded in C around inf 39.7%

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

   8. Taylor expanded in B around inf 79.6%

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

      1. *-commutative 79.6%

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

      2. associate-*l/ 79.6%

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

   10. Simplified 79.6%

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

   if 4.79999999999999999e-287 < A < 1.00000000000000006e-158

   1. Initial program 64.0%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in C around 0 63.9%

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

      1. +-commutative 63.9%

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

      2. unpow2 63.9%

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

      3. unpow2 63.9%

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

      4. hypot-define 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in A around 0 52.4%

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

   if 9.9999999999999997e-49 < A

   1. Initial program 81.7%

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

      1. associate--l- 81.7%

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

      2. +-commutative 81.7%

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

      3. unpow2 81.7%

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

      4. unpow2 81.7%

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

      5. hypot-undefine 97.5%

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

      6. associate-/r/ 97.5%

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

      7. frac-2neg 97.5%

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

      8. metadata-eval 97.5%

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

      9. associate--r+ 97.5%

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

      10. hypot-undefine 81.7%

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

      11. unpow2 81.7%

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

      12. unpow2 81.7%

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

      13. +-commutative 81.7%

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

      14. unpow2 81.7%

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

      15. unpow2 81.7%

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

      16. hypot-define 97.5%

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

   4. Applied egg-rr 97.5%

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

   6. Simplified 95.1%

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

   7. Taylor expanded in B around inf 82.4%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{+149}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -3.1 \cdot 10^{+41}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.9 \cdot 10^{-43}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{-245}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{-269}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C \cdot 2}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-304}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.8 \cdot 10^{-287}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C \cdot 2}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{-158}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{-48}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{B}{A + B}}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -9 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{+136}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -2.5 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -9.2 \cdot 10^{-248}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;A \leq -1.55 \cdot 10^{-305}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq 1.38 \cdot 10^{-155}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-102}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{+89}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan 1.0) PI)))
        (t_1 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI)))
        (t_2 (* 180.0 (/ (atan (/ (- C B) B)) PI))))
   (if (<= A -9e+149)
     t_1
     (if (<= A -2.8e+136)
       t_0
       (if (<= A -2.5e-131)
         t_1
         (if (<= A -9.2e-248)
           t_2
           (if (<= A -1.55e-305)
             t_0
             (if (<= A 1.38e-155)
               t_2
               (if (<= A 3.8e-102)
                 t_0
                 (if (<= A 7.5e+89)
                   t_2
                   (* 180.0 (/ (atan (/ (* A -2.0) B)) 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((0.5 * (B / A))) / ((double) M_PI));
	double t_2 = 180.0 * (atan(((C - B) / B)) / ((double) M_PI));
	double tmp;
	if (A <= -9e+149) {
		tmp = t_1;
	} else if (A <= -2.8e+136) {
		tmp = t_0;
	} else if (A <= -2.5e-131) {
		tmp = t_1;
	} else if (A <= -9.2e-248) {
		tmp = t_2;
	} else if (A <= -1.55e-305) {
		tmp = t_0;
	} else if (A <= 1.38e-155) {
		tmp = t_2;
	} else if (A <= 3.8e-102) {
		tmp = t_0;
	} else if (A <= 7.5e+89) {
		tmp = t_2;
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(1.0) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double t_2 = 180.0 * (Math.atan(((C - B) / B)) / Math.PI);
	double tmp;
	if (A <= -9e+149) {
		tmp = t_1;
	} else if (A <= -2.8e+136) {
		tmp = t_0;
	} else if (A <= -2.5e-131) {
		tmp = t_1;
	} else if (A <= -9.2e-248) {
		tmp = t_2;
	} else if (A <= -1.55e-305) {
		tmp = t_0;
	} else if (A <= 1.38e-155) {
		tmp = t_2;
	} else if (A <= 3.8e-102) {
		tmp = t_0;
	} else if (A <= 7.5e+89) {
		tmp = t_2;
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / 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((0.5 * (B / A))) / math.pi)
	t_2 = 180.0 * (math.atan(((C - B) / B)) / math.pi)
	tmp = 0
	if A <= -9e+149:
		tmp = t_1
	elif A <= -2.8e+136:
		tmp = t_0
	elif A <= -2.5e-131:
		tmp = t_1
	elif A <= -9.2e-248:
		tmp = t_2
	elif A <= -1.55e-305:
		tmp = t_0
	elif A <= 1.38e-155:
		tmp = t_2
	elif A <= 3.8e-102:
		tmp = t_0
	elif A <= 7.5e+89:
		tmp = t_2
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / 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(0.5 * Float64(B / A))) / pi))
	t_2 = Float64(180.0 * Float64(atan(Float64(Float64(C - B) / B)) / pi))
	tmp = 0.0
	if (A <= -9e+149)
		tmp = t_1;
	elseif (A <= -2.8e+136)
		tmp = t_0;
	elseif (A <= -2.5e-131)
		tmp = t_1;
	elseif (A <= -9.2e-248)
		tmp = t_2;
	elseif (A <= -1.55e-305)
		tmp = t_0;
	elseif (A <= 1.38e-155)
		tmp = t_2;
	elseif (A <= 3.8e-102)
		tmp = t_0;
	elseif (A <= 7.5e+89)
		tmp = t_2;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / 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((0.5 * (B / A))) / pi);
	t_2 = 180.0 * (atan(((C - B) / B)) / pi);
	tmp = 0.0;
	if (A <= -9e+149)
		tmp = t_1;
	elseif (A <= -2.8e+136)
		tmp = t_0;
	elseif (A <= -2.5e-131)
		tmp = t_1;
	elseif (A <= -9.2e-248)
		tmp = t_2;
	elseif (A <= -1.55e-305)
		tmp = t_0;
	elseif (A <= 1.38e-155)
		tmp = t_2;
	elseif (A <= 3.8e-102)
		tmp = t_0;
	elseif (A <= 7.5e+89)
		tmp = t_2;
	else
		tmp = 180.0 * (atan(((A * -2.0) / 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]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -9e+149], t$95$1, If[LessEqual[A, -2.8e+136], t$95$0, If[LessEqual[A, -2.5e-131], t$95$1, If[LessEqual[A, -9.2e-248], t$95$2, If[LessEqual[A, -1.55e-305], t$95$0, If[LessEqual[A, 1.38e-155], t$95$2, If[LessEqual[A, 3.8e-102], t$95$0, If[LessEqual[A, 7.5e+89], t$95$2, N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -8.99999999999999965e149 or -2.8000000000000002e136 < A < -2.5000000000000002e-131

   1. Initial program 27.6%

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

   3. Taylor expanded in A around -inf 58.1%

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

   if -8.99999999999999965e149 < A < -2.8000000000000002e136 or -9.2000000000000001e-248 < A < -1.5499999999999999e-305 or 1.38000000000000007e-155 < A < 3.80000000000000026e-102

   1. Initial program 38.2%

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

   3. Taylor expanded in B around -inf 67.1%

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

   if -2.5000000000000002e-131 < A < -9.2000000000000001e-248 or -1.5499999999999999e-305 < A < 1.38000000000000007e-155 or 3.80000000000000026e-102 < A < 7.49999999999999947e89

   1. Initial program 65.2%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in C around 0 63.9%

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

      1. +-commutative 63.9%

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

      2. unpow2 63.9%

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

      3. unpow2 63.9%

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

      4. hypot-define 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in A around 0 57.2%

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

   if 7.49999999999999947e89 < A

   1. Initial program 89.2%

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

   3. Taylor expanded in A around inf 88.1%

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

      1. associate-*r/ 88.1%

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

      2. *-commutative 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{+149}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{+136}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq -2.5 \cdot 10^{-131}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -9.2 \cdot 10^{-248}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.55 \cdot 10^{-305}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.38 \cdot 10^{-155}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{+89}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 45.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -9 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{+136}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -8.6 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -1.2 \cdot 10^{-222}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.9 \cdot 10^{-247}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 3.6 \cdot 10^{+18}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan 1.0) PI)))
        (t_1 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= A -9e+149)
     t_1
     (if (<= A -2.8e+136)
       t_0
       (if (<= A -8.6e-133)
         t_1
         (if (<= A -1.2e-222)
           (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
           (if (<= A -1.9e-247)
             (* 180.0 (/ (atan -1.0) PI))
             (if (<= A 3.6e+18)
               t_0
               (* 180.0 (/ (atan (/ (* A -2.0) B)) 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((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (A <= -9e+149) {
		tmp = t_1;
	} else if (A <= -2.8e+136) {
		tmp = t_0;
	} else if (A <= -8.6e-133) {
		tmp = t_1;
	} else if (A <= -1.2e-222) {
		tmp = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	} else if (A <= -1.9e-247) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (A <= 3.6e+18) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(1.0) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (A <= -9e+149) {
		tmp = t_1;
	} else if (A <= -2.8e+136) {
		tmp = t_0;
	} else if (A <= -8.6e-133) {
		tmp = t_1;
	} else if (A <= -1.2e-222) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else if (A <= -1.9e-247) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (A <= 3.6e+18) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / 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((0.5 * (B / A))) / math.pi)
	tmp = 0
	if A <= -9e+149:
		tmp = t_1
	elif A <= -2.8e+136:
		tmp = t_0
	elif A <= -8.6e-133:
		tmp = t_1
	elif A <= -1.2e-222:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	elif A <= -1.9e-247:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif A <= 3.6e+18:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / 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(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (A <= -9e+149)
		tmp = t_1;
	elseif (A <= -2.8e+136)
		tmp = t_0;
	elseif (A <= -8.6e-133)
		tmp = t_1;
	elseif (A <= -1.2e-222)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	elseif (A <= -1.9e-247)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (A <= 3.6e+18)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / 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((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (A <= -9e+149)
		tmp = t_1;
	elseif (A <= -2.8e+136)
		tmp = t_0;
	elseif (A <= -8.6e-133)
		tmp = t_1;
	elseif (A <= -1.2e-222)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	elseif (A <= -1.9e-247)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (A <= 3.6e+18)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((A * -2.0) / 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]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -9e+149], t$95$1, If[LessEqual[A, -2.8e+136], t$95$0, If[LessEqual[A, -8.6e-133], t$95$1, If[LessEqual[A, -1.2e-222], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.9e-247], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.6e+18], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -8.99999999999999965e149 or -2.8000000000000002e136 < A < -8.60000000000000032e-133

   1. Initial program 27.6%

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

   3. Taylor expanded in A around -inf 58.1%

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

   if -8.99999999999999965e149 < A < -2.8000000000000002e136 or -1.89999999999999994e-247 < A < 3.6e18

   1. Initial program 51.8%

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

   3. Taylor expanded in B around -inf 42.0%

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

   if -8.60000000000000032e-133 < A < -1.19999999999999997e-222

   1. Initial program 83.9%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in C around -inf 62.2%

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

   if -1.19999999999999997e-222 < A < -1.89999999999999994e-247

   1. Initial program 68.9%

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

   3. Taylor expanded in B around inf 67.9%

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

   if 3.6e18 < A

   1. Initial program 85.6%

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

   3. Taylor expanded in A around inf 82.6%

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

      1. associate-*r/ 82.6%

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

      2. *-commutative 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{+149}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{+136}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq -8.6 \cdot 10^{-133}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.2 \cdot 10^{-222}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.9 \cdot 10^{-247}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 3.6 \cdot 10^{+18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -7 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.8 \cdot 10^{-203}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 6.9 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-218}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 4.1 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI)))
        (t_1 (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))))
   (if (<= B -7e-60)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -7.8e-203)
       t_0
       (if (<= B 6.9e-274)
         t_1
         (if (<= B 8.2e-218)
           t_0
           (if (<= B 4.1e+15) t_1 (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double t_1 = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	double tmp;
	if (B <= -7e-60) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -7.8e-203) {
		tmp = t_0;
	} else if (B <= 6.9e-274) {
		tmp = t_1;
	} else if (B <= 8.2e-218) {
		tmp = t_0;
	} else if (B <= 4.1e+15) {
		tmp = t_1;
	} 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((0.5 * (B / A))) / Math.PI);
	double t_1 = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	double tmp;
	if (B <= -7e-60) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -7.8e-203) {
		tmp = t_0;
	} else if (B <= 6.9e-274) {
		tmp = t_1;
	} else if (B <= 8.2e-218) {
		tmp = t_0;
	} else if (B <= 4.1e+15) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	t_1 = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	tmp = 0
	if B <= -7e-60:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -7.8e-203:
		tmp = t_0
	elif B <= 6.9e-274:
		tmp = t_1
	elif B <= 8.2e-218:
		tmp = t_0
	elif B <= 4.1e+15:
		tmp = t_1
	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(0.5 * Float64(B / A))) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi))
	tmp = 0.0
	if (B <= -7e-60)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -7.8e-203)
		tmp = t_0;
	elseif (B <= 6.9e-274)
		tmp = t_1;
	elseif (B <= 8.2e-218)
		tmp = t_0;
	elseif (B <= 4.1e+15)
		tmp = t_1;
	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((0.5 * (B / A))) / pi);
	t_1 = 180.0 * (atan(((C * 2.0) / B)) / pi);
	tmp = 0.0;
	if (B <= -7e-60)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -7.8e-203)
		tmp = t_0;
	elseif (B <= 6.9e-274)
		tmp = t_1;
	elseif (B <= 8.2e-218)
		tmp = t_0;
	elseif (B <= 4.1e+15)
		tmp = t_1;
	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[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -7e-60], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7.8e-203], t$95$0, If[LessEqual[B, 6.9e-274], t$95$1, If[LessEqual[B, 8.2e-218], t$95$0, If[LessEqual[B, 4.1e+15], t$95$1, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -6.99999999999999952e-60

   1. Initial program 49.3%

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

   3. Taylor expanded in B around -inf 61.7%

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

   if -6.99999999999999952e-60 < B < -7.7999999999999998e-203 or 6.89999999999999963e-274 < B < 8.1999999999999995e-218

   1. Initial program 47.0%

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

   3. Taylor expanded in A around -inf 41.4%

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

   if -7.7999999999999998e-203 < B < 6.89999999999999963e-274 or 8.1999999999999995e-218 < B < 4.1e15

   1. Initial program 66.2%

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

   3. Simplified 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. Add Preprocessing

   5. Taylor expanded in C around -inf 40.9%

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

   if 4.1e15 < B

   1. Initial program 54.6%

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

   3. Taylor expanded in B around inf 62.0%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.8 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.9 \cdot 10^{-274}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-218}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.1 \cdot 10^{+15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.1 \cdot 10^{-59}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-193}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-218}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI)))
        (t_1 (* 180.0 (/ (atan (/ C B)) PI))))
   (if (<= B -1.1e-59)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -2e-193)
       t_0
       (if (<= B 2.7e-274)
         t_1
         (if (<= B 4e-218)
           t_0
           (if (<= B 5.4e+22) t_1 (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double t_1 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double tmp;
	if (B <= -1.1e-59) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2e-193) {
		tmp = t_0;
	} else if (B <= 2.7e-274) {
		tmp = t_1;
	} else if (B <= 4e-218) {
		tmp = t_0;
	} else if (B <= 5.4e+22) {
		tmp = t_1;
	} 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((0.5 * (B / A))) / Math.PI);
	double t_1 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double tmp;
	if (B <= -1.1e-59) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2e-193) {
		tmp = t_0;
	} else if (B <= 2.7e-274) {
		tmp = t_1;
	} else if (B <= 4e-218) {
		tmp = t_0;
	} else if (B <= 5.4e+22) {
		tmp = t_1;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	t_1 = 180.0 * (math.atan((C / B)) / math.pi)
	tmp = 0
	if B <= -1.1e-59:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2e-193:
		tmp = t_0
	elif B <= 2.7e-274:
		tmp = t_1
	elif B <= 4e-218:
		tmp = t_0
	elif B <= 5.4e+22:
		tmp = t_1
	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(0.5 * Float64(B / A))) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	tmp = 0.0
	if (B <= -1.1e-59)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2e-193)
		tmp = t_0;
	elseif (B <= 2.7e-274)
		tmp = t_1;
	elseif (B <= 4e-218)
		tmp = t_0;
	elseif (B <= 5.4e+22)
		tmp = t_1;
	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((0.5 * (B / A))) / pi);
	t_1 = 180.0 * (atan((C / B)) / pi);
	tmp = 0.0;
	if (B <= -1.1e-59)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2e-193)
		tmp = t_0;
	elseif (B <= 2.7e-274)
		tmp = t_1;
	elseif (B <= 4e-218)
		tmp = t_0;
	elseif (B <= 5.4e+22)
		tmp = t_1;
	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[(0.5 * N[(B / A), $MachinePrecision]), $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, -1.1e-59], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2e-193], t$95$0, If[LessEqual[B, 2.7e-274], t$95$1, If[LessEqual[B, 4e-218], t$95$0, If[LessEqual[B, 5.4e+22], t$95$1, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.0999999999999999e-59

   1. Initial program 49.3%

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

   3. Taylor expanded in B around -inf 61.7%

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

   if -1.0999999999999999e-59 < B < -2.0000000000000001e-193 or 2.7e-274 < B < 4.0000000000000001e-218

   1. Initial program 47.0%

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

   3. Taylor expanded in A around -inf 41.4%

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

   if -2.0000000000000001e-193 < B < 2.7e-274 or 4.0000000000000001e-218 < B < 5.4000000000000004e22

   1. Initial program 66.2%

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

   3. Simplified 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. Add Preprocessing

   5. Taylor expanded in C around 0 60.9%

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

      1. +-commutative 60.9%

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

      2. unpow2 60.9%

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

      3. unpow2 60.9%

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

      4. hypot-define 60.9%

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

   7. Simplified 60.9%

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

   8. Taylor expanded in C around inf 40.8%

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

   if 5.4000000000000004e22 < B

   1. Initial program 54.6%

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

   3. Taylor expanded in B around inf 62.0%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.1 \cdot 10^{-59}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2 \cdot 10^{-193}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{-274}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4 \cdot 10^{-218}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{+22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -9 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{+41}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq 8.8 \cdot 10^{-49}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{B}{A + B}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (+ C B) B)) PI)))
        (t_1 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= A -9e+149)
     t_1
     (if (<= A -9.5e+41)
       t_0
       (if (<= A -7.5e-43)
         t_1
         (if (<= A 8.8e-49)
           t_0
           (* 180.0 (/ (atan (/ -1.0 (/ B (+ A B)))) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C + B) / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (A <= -9e+149) {
		tmp = t_1;
	} else if (A <= -9.5e+41) {
		tmp = t_0;
	} else if (A <= -7.5e-43) {
		tmp = t_1;
	} else if (A <= 8.8e-49) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-1.0 / (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 + B) / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (A <= -9e+149) {
		tmp = t_1;
	} else if (A <= -9.5e+41) {
		tmp = t_0;
	} else if (A <= -7.5e-43) {
		tmp = t_1;
	} else if (A <= 8.8e-49) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-1.0 / (B / (A + B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C + B) / B)) / math.pi)
	t_1 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	tmp = 0
	if A <= -9e+149:
		tmp = t_1
	elif A <= -9.5e+41:
		tmp = t_0
	elif A <= -7.5e-43:
		tmp = t_1
	elif A <= 8.8e-49:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-1.0 / (B / (A + B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C + B) / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (A <= -9e+149)
		tmp = t_1;
	elseif (A <= -9.5e+41)
		tmp = t_0;
	elseif (A <= -7.5e-43)
		tmp = t_1;
	elseif (A <= 8.8e-49)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(B / Float64(A + B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C + B) / B)) / pi);
	t_1 = 180.0 * (atan((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (A <= -9e+149)
		tmp = t_1;
	elseif (A <= -9.5e+41)
		tmp = t_0;
	elseif (A <= -7.5e-43)
		tmp = t_1;
	elseif (A <= 8.8e-49)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-1.0 / (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 + B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -9e+149], t$95$1, If[LessEqual[A, -9.5e+41], t$95$0, If[LessEqual[A, -7.5e-43], t$95$1, If[LessEqual[A, 8.8e-49], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(B / N[(A + B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.99999999999999965e149 or -9.4999999999999996e41 < A < -7.50000000000000068e-43

   1. Initial program 16.5%

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

   3. Taylor expanded in A around -inf 66.0%

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

   if -8.99999999999999965e149 < A < -9.4999999999999996e41 or -7.50000000000000068e-43 < A < 8.79999999999999959e-49

   1. Initial program 55.8%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in C around 0 51.8%

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

      1. +-commutative 51.8%

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

      2. unpow2 51.8%

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

      3. unpow2 51.8%

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

      4. hypot-define 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in B around -inf 58.1%

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

      1. mul-1-neg 58.1%

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

   10. Simplified 58.1%

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

   if 8.79999999999999959e-49 < A

   1. Initial program 81.7%

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

      1. associate--l- 81.7%

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

      2. +-commutative 81.7%

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

      3. unpow2 81.7%

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

      4. unpow2 81.7%

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

      5. hypot-undefine 97.5%

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

      6. associate-/r/ 97.5%

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

      7. frac-2neg 97.5%

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

      8. metadata-eval 97.5%

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

      9. associate--r+ 97.5%

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

      10. hypot-undefine 81.7%

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

      11. unpow2 81.7%

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

      12. unpow2 81.7%

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

      13. +-commutative 81.7%

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

      14. unpow2 81.7%

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

      15. unpow2 81.7%

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

      16. hypot-define 97.5%

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

   4. Applied egg-rr 97.5%

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

   6. Simplified 95.1%

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

   7. Taylor expanded in B around inf 82.4%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{+149}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -9.5 \cdot 10^{+41}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{-43}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 8.8 \cdot 10^{-49}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{B}{A + B}}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{if}\;A \leq -9 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq -9 \cdot 10^{+41}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;A \leq 2.05 \cdot 10^{+114}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ (+ C B) B)) PI)))
        (t_1 (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))))
   (if (<= A -9e+149)
     t_1
     (if (<= A -9e+41)
       t_0
       (if (<= A -7.5e-43)
         t_1
         (if (<= A 2.05e+114)
           t_0
           (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((C + B) / B)) / ((double) M_PI));
	double t_1 = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	double tmp;
	if (A <= -9e+149) {
		tmp = t_1;
	} else if (A <= -9e+41) {
		tmp = t_0;
	} else if (A <= -7.5e-43) {
		tmp = t_1;
	} else if (A <= 2.05e+114) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((C + B) / B)) / Math.PI);
	double t_1 = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	double tmp;
	if (A <= -9e+149) {
		tmp = t_1;
	} else if (A <= -9e+41) {
		tmp = t_0;
	} else if (A <= -7.5e-43) {
		tmp = t_1;
	} else if (A <= 2.05e+114) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((C + B) / B)) / math.pi)
	t_1 = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	tmp = 0
	if A <= -9e+149:
		tmp = t_1
	elif A <= -9e+41:
		tmp = t_0
	elif A <= -7.5e-43:
		tmp = t_1
	elif A <= 2.05e+114:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(C + B) / B)) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi))
	tmp = 0.0
	if (A <= -9e+149)
		tmp = t_1;
	elseif (A <= -9e+41)
		tmp = t_0;
	elseif (A <= -7.5e-43)
		tmp = t_1;
	elseif (A <= 2.05e+114)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((C + B) / B)) / pi);
	t_1 = 180.0 * (atan((0.5 * (B / A))) / pi);
	tmp = 0.0;
	if (A <= -9e+149)
		tmp = t_1;
	elseif (A <= -9e+41)
		tmp = t_0;
	elseif (A <= -7.5e-43)
		tmp = t_1;
	elseif (A <= 2.05e+114)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(((A * -2.0) / 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 + B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -9e+149], t$95$1, If[LessEqual[A, -9e+41], t$95$0, If[LessEqual[A, -7.5e-43], t$95$1, If[LessEqual[A, 2.05e+114], t$95$0, N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.99999999999999965e149 or -9.0000000000000002e41 < A < -7.50000000000000068e-43

   1. Initial program 16.5%

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

   3. Taylor expanded in A around -inf 66.0%

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

   if -8.99999999999999965e149 < A < -9.0000000000000002e41 or -7.50000000000000068e-43 < A < 2.05e114

   1. Initial program 58.2%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in C around 0 54.8%

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

      1. +-commutative 54.8%

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

      2. unpow2 54.8%

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

      3. unpow2 54.8%

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

      4. hypot-define 76.4%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in B around -inf 57.4%

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

      1. mul-1-neg 57.4%

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

   10. Simplified 57.4%

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

   if 2.05e114 < A

   1. Initial program 89.8%

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

   3. Taylor expanded in A around inf 90.5%

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

      1. associate-*r/ 90.5%

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

      2. *-commutative 90.5%

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

   5. Simplified 90.5%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{+149}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -9 \cdot 10^{+41}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -7.5 \cdot 10^{-43}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.05 \cdot 10^{+114}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 46.3% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.7 \cdot 10^{-147}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-46}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.7e-147)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.4e-46)
     (* 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 <= -1.7e-147) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.4e-46) {
		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 <= -1.7e-147) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.4e-46) {
		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 <= -1.7e-147:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.4e-46:
		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 <= -1.7e-147)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.4e-46)
		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 <= -1.7e-147)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.4e-46)
		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, -1.7e-147], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.4e-46], 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 < -1.69999999999999998e-147

   1. Initial program 50.7%

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

   3. Taylor expanded in B around -inf 53.8%

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

   if -1.69999999999999998e-147 < B < 1.3999999999999999e-46

   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. Add Preprocessing

   3. Taylor expanded in C around inf 31.6%

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

      1. associate-*r/ 31.6%

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

      2. mul-1-neg 31.6%

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

      3. distribute-rgt1-in 31.6%

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

      4. metadata-eval 31.6%

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

      5. mul0-lft 31.6%

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

      6. metadata-eval 31.6%

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

   5. Simplified 31.6%

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

   if 1.3999999999999999e-46 < B

   1. Initial program 58.4%

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

   3. Taylor expanded in B around inf 56.1%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.7 \cdot 10^{-147}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-46}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.6% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.75 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{+15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.75e-20)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2e+15)
     (* 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 <= -1.75e-20) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2e+15) {
		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 <= -1.75e-20) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2e+15) {
		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 <= -1.75e-20:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2e+15:
		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 <= -1.75e-20)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2e+15)
		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 <= -1.75e-20)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2e+15)
		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, -1.75e-20], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2e+15], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.75000000000000002e-20

   1. Initial program 46.0%

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

   3. Taylor expanded in B around -inf 67.7%

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

   if -1.75000000000000002e-20 < B < 2e15

   1. Initial program 59.7%

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

   3. Simplified 65.8%

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

   5. Taylor expanded in C around 0 56.1%

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

      1. +-commutative 56.1%

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

      2. unpow2 56.1%

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

      3. unpow2 56.1%

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

      4. hypot-define 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in C around inf 33.6%

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

   if 2e15 < B

   1. Initial program 54.6%

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

   3. Taylor expanded in B around inf 62.0%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.75 \cdot 10^{-20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2 \cdot 10^{+15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 0.014:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{B}{A + B}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 0.014)
   (* 180.0 (/ (atan (/ (- (+ C B) A) B)) PI))
   (* 180.0 (/ (atan (/ -1.0 (/ B (+ A B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 0.014) {
		tmp = 180.0 * (atan((((C + B) - A) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 / (B / (A + B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 0.014) {
		tmp = 180.0 * (Math.atan((((C + B) - A) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 / (B / (A + B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 0.014:
		tmp = 180.0 * (math.atan((((C + B) - A) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 / (B / (A + B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 0.014)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C + B) - A) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(B / Float64(A + B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 0.014)
		tmp = 180.0 * (atan((((C + B) - A) / B)) / pi);
	else
		tmp = 180.0 * (atan((-1.0 / (B / (A + B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 0.014], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C + B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(B / N[(A + B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 0.0140000000000000003

   1. Initial program 55.1%

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

   3. Simplified 71.7%

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

   5. Taylor expanded in B around -inf 63.7%

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

   if 0.0140000000000000003 < B

   1. Initial program 54.5%

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

      1. associate--l- 54.5%

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

      2. +-commutative 54.5%

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

      3. unpow2 54.5%

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

      4. unpow2 54.5%

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

      5. hypot-undefine 83.8%

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

      6. associate-/r/ 83.8%

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

      7. frac-2neg 83.8%

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

      8. metadata-eval 83.8%

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

      9. associate--r+ 83.8%

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

      10. hypot-undefine 54.5%

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

      11. unpow2 54.5%

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

      12. unpow2 54.5%

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

      13. +-commutative 54.5%

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

      14. unpow2 54.5%

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

      15. unpow2 54.5%

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

      16. hypot-define 83.8%

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

   4. Applied egg-rr 83.8%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in B around inf 75.7%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 0.014:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{B}{A + B}}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 66.4% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 10^{-198}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - B\right) - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1e-198)
   (* 180.0 (/ (atan (/ (- (+ C B) A) B)) PI))
   (* 180.0 (/ (atan (/ (- (- C B) A) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1e-198) {
		tmp = 180.0 * (atan((((C + B) - A) / 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 <= 1e-198) {
		tmp = 180.0 * (Math.atan((((C + B) - A) / 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 <= 1e-198:
		tmp = 180.0 * (math.atan((((C + B) - A) / 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 <= 1e-198)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C + B) - A) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - B) - A) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 1e-198)
		tmp = 180.0 * (atan((((C + B) - A) / 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, 1e-198], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C + B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 9.9999999999999991e-199

   1. Initial program 52.6%

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

   3. Simplified 70.7%

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

   5. Taylor expanded in B around -inf 64.1%

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

   if 9.9999999999999991e-199 < B

   1. Initial program 59.8%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in B around inf 75.6%

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

      1. neg-mul-1 75.6%

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

      2. unsub-neg 75.6%

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

   7. Simplified 75.6%

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

4. Final simplification 67.8%

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

Alternative 17: 40.3% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7.5 \cdot 10^{-308}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7.5e-308)
   (* 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 <= -7.5e-308) {
		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 <= -7.5e-308) {
		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 <= -7.5e-308:
		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 <= -7.5e-308)
		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 <= -7.5e-308)
		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, -7.5e-308], 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 < -7.4999999999999998e-308

   1. Initial program 52.6%

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

   3. Taylor expanded in B around -inf 44.6%

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

   if -7.4999999999999998e-308 < B

   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. Add Preprocessing

   3. Taylor expanded in B around inf 34.0%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.5 \cdot 10^{-308}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 21.6% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 54.9%

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

3. Taylor expanded in B around inf 16.4%

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

4. Final simplification 16.4%

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

Reproduce

herbie shell --seed 2024046 
(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)))