ABCF->ab-angle angle

Percentage Accurate: 53.7% → 87.9%

Time: 22.0s

Alternatives: 16

Speedup: 2.4×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.6 \cdot 10^{+79}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)\\ \mathbf{elif}\;A \leq 1.65 \cdot 10^{-69}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-B}{C + \mathsf{hypot}\left(B, C\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.6e+79)
   (* (/ 180.0 PI) (atan (* 0.5 (+ (/ B A) (* (/ B A) (/ C A))))))
   (if (<= A 1.65e-69)
     (/ (* 180.0 (atan (/ (- B) (+ C (hypot B C))))) 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 <= -4.6e+79) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * ((B / A) + ((B / A) * (C / A)))));
	} else if (A <= 1.65e-69) {
		tmp = (180.0 * atan((-B / (C + hypot(B, C))))) / ((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 <= -4.6e+79) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * ((B / A) + ((B / A) * (C / A)))));
	} else if (A <= 1.65e-69) {
		tmp = (180.0 * Math.atan((-B / (C + Math.hypot(B, C))))) / 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 <= -4.6e+79:
		tmp = (180.0 / math.pi) * math.atan((0.5 * ((B / A) + ((B / A) * (C / A)))))
	elif A <= 1.65e-69:
		tmp = (180.0 * math.atan((-B / (C + math.hypot(B, C))))) / 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 <= -4.6e+79)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(Float64(B / A) + Float64(Float64(B / A) * Float64(C / A))))));
	elseif (A <= 1.65e-69)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-B) / Float64(C + hypot(B, C))))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.6e+79)
		tmp = (180.0 / pi) * atan((0.5 * ((B / A) + ((B / A) * (C / A)))));
	elseif (A <= 1.65e-69)
		tmp = (180.0 * atan((-B / (C + hypot(B, C))))) / 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, -4.6e+79], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(N[(B / A), $MachinePrecision] * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.65e-69], N[(N[(180.0 * N[ArcTan[N[((-B) / N[(C + N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -4.6000000000000001e79

   1. Initial program 16.7%

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

      1. associate-*r/ 16.7%

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

      2. associate-*l/ 16.7%

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

      3. associate-*l/ 16.7%

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

      4. *-lft-identity 16.7%

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

      5. sub-neg 16.7%

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

      6. associate-+l- 12.4%

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

      7. sub-neg 12.4%

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

      8. remove-double-neg 12.4%

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

      9. +-commutative 12.4%

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

      10. unpow2 12.4%

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

      11. unpow2 12.4%

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

      12. hypot-def 22.8%

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

   3. Simplified 22.8%

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

      1. add-sqr-sqrt 22.7%

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

      2. pow2 22.7%

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

   5. Applied egg-rr 22.7%

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

      1. unpow2 22.7%

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

      2. add-sqr-sqrt 22.8%

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

      3. add-log-exp 30.2%

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

   7. Applied egg-rr 30.2%

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

   8. Taylor expanded in A around -inf 81.4%

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

      1. distribute-lft-out 81.4%

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

      2. *-commutative 81.4%

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

      3. unpow2 81.4%

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

      4. times-frac 85.0%

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

   10. Simplified 85.0%

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

   if -4.6000000000000001e79 < A < 1.65e-69

   1. Initial program 56.0%

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

      1. associate-*r/ 56.0%

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

      2. unpow2 56.0%

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

   3. Simplified 56.0%

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

      1. associate--l- 55.9%

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

      2. +-commutative 55.9%

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

      3. unpow2 55.9%

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

      4. hypot-udef 73.3%

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

      5. flip-- 29.5%

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

      6. frac-times 26.0%

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

      7. *-un-lft-identity 26.0%

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

      8. pow2 26.0%

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

   5. Applied egg-rr 26.0%

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

      1. associate-+r+ 26.0%

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

   7. Simplified 26.0%

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

   8. Taylor expanded in A around 0 52.6%

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

      1. associate-*r/ 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unpow2 52.6%

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

      4. unpow2 52.6%

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

      5. hypot-def 89.7%

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

   10. Simplified 89.7%

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

   if 1.65e-69 < A

   1. Initial program 77.3%

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

      1. associate-*l/ 77.3%

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

      2. *-lft-identity 77.3%

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

      3. +-commutative 77.3%

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

      4. unpow2 77.3%

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

      5. unpow2 77.3%

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

      6. hypot-def 95.2%

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

   3. Simplified 95.2%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.6 \cdot 10^{+79}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)\\ \mathbf{elif}\;A \leq 1.65 \cdot 10^{-69}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-B}{C + \mathsf{hypot}\left(B, C\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 2: 84.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.8 \cdot 10^{+79}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-B}{C + \mathsf{hypot}\left(B, C\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.8e+79)
   (* (/ 180.0 PI) (atan (* 0.5 (+ (/ B A) (* (/ B A) (/ C A))))))
   (if (<= A 3.8e+93)
     (/ (* 180.0 (atan (/ (- B) (+ C (hypot B C))))) PI)
     (* (/ 180.0 PI) (atan (/ (- C (+ A B)) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.8e+79) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * ((B / A) + ((B / A) * (C / A)))));
	} else if (A <= 3.8e+93) {
		tmp = (180.0 * atan((-B / (C + hypot(B, C))))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + B)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.8e+79) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * ((B / A) + ((B / A) * (C / A)))));
	} else if (A <= 3.8e+93) {
		tmp = (180.0 * Math.atan((-B / (C + Math.hypot(B, C))))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + B)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.8e+79:
		tmp = (180.0 / math.pi) * math.atan((0.5 * ((B / A) + ((B / A) * (C / A)))))
	elif A <= 3.8e+93:
		tmp = (180.0 * math.atan((-B / (C + math.hypot(B, C))))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + B)) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.8e+79)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(Float64(B / A) + Float64(Float64(B / A) * Float64(C / A))))));
	elseif (A <= 3.8e+93)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-B) / Float64(C + hypot(B, C))))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + B)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.8e+79)
		tmp = (180.0 / pi) * atan((0.5 * ((B / A) + ((B / A) * (C / A)))));
	elseif (A <= 3.8e+93)
		tmp = (180.0 * atan((-B / (C + hypot(B, C))))) / pi;
	else
		tmp = (180.0 / pi) * atan(((C - (A + B)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.8e+79], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(N[(B / A), $MachinePrecision] * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.8e+93], N[(N[(180.0 * N[ArcTan[N[((-B) / N[(C + N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.8000000000000001e79

   1. Initial program 16.7%

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

      1. associate-*r/ 16.7%

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

      2. associate-*l/ 16.7%

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

      3. associate-*l/ 16.7%

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

      4. *-lft-identity 16.7%

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

      5. sub-neg 16.7%

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

      6. associate-+l- 12.4%

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

      7. sub-neg 12.4%

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

      8. remove-double-neg 12.4%

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

      9. +-commutative 12.4%

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

      10. unpow2 12.4%

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

      11. unpow2 12.4%

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

      12. hypot-def 22.8%

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

   3. Simplified 22.8%

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

      1. add-sqr-sqrt 22.7%

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

      2. pow2 22.7%

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

   5. Applied egg-rr 22.7%

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

      1. unpow2 22.7%

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

      2. add-sqr-sqrt 22.8%

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

      3. add-log-exp 30.2%

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

   7. Applied egg-rr 30.2%

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

   8. Taylor expanded in A around -inf 81.4%

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

      1. distribute-lft-out 81.4%

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

      2. *-commutative 81.4%

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

      3. unpow2 81.4%

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

      4. times-frac 85.0%

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

   10. Simplified 85.0%

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

   if -2.8000000000000001e79 < A < 3.7999999999999998e93

   1. Initial program 57.5%

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

      1. associate-*r/ 57.4%

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

      2. unpow2 57.4%

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

   3. Simplified 57.4%

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

      1. associate--l- 57.4%

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

      2. +-commutative 57.4%

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

      3. unpow2 57.4%

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

      4. hypot-udef 76.2%

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

      5. flip-- 31.8%

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

      6. frac-times 28.2%

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

      7. *-un-lft-identity 28.2%

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

      8. pow2 28.2%

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

   5. Applied egg-rr 28.2%

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

      1. associate-+r+ 28.2%

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

   7. Simplified 28.2%

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

   8. Taylor expanded in A around 0 49.4%

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

      1. associate-*r/ 49.4%

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

      2. mul-1-neg 49.4%

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

      3. unpow2 49.4%

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

      4. unpow2 49.4%

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

      5. hypot-def 88.0%

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

   10. Simplified 88.0%

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

   if 3.7999999999999998e93 < A

   1. Initial program 86.4%

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

      1. associate-*r/ 86.5%

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

      2. associate-*l/ 86.5%

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

      3. associate-*l/ 86.5%

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

      4. *-lft-identity 86.5%

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

      5. sub-neg 86.5%

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

      6. associate-+l- 86.5%

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

      7. sub-neg 86.5%

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

      8. remove-double-neg 86.5%

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

      9. +-commutative 86.5%

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

      10. unpow2 86.5%

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

      11. unpow2 86.5%

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

      12. hypot-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in B around inf 89.3%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.8 \cdot 10^{+79}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{+93}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-B}{C + \mathsf{hypot}\left(B, C\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \end{array} \]

Alternative 3: 74.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.25 \cdot 10^{+58}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)\\ \mathbf{elif}\;A \leq 2.35 \cdot 10^{-101}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.25e+58)
   (* (/ 180.0 PI) (atan (* 0.5 (+ (/ B A) (* (/ B A) (/ C A))))))
   (if (<= A 2.35e-101)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (* (/ 180.0 PI) (atan (/ (- C (+ A B)) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.25e+58) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * ((B / A) + ((B / A) * (C / A)))));
	} else if (A <= 2.35e-101) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + B)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.25e+58) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * ((B / A) + ((B / A) * (C / A)))));
	} else if (A <= 2.35e-101) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + B)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.25e+58:
		tmp = (180.0 / math.pi) * math.atan((0.5 * ((B / A) + ((B / A) * (C / A)))))
	elif A <= 2.35e-101:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + B)) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.25e+58)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(Float64(B / A) + Float64(Float64(B / A) * Float64(C / A))))));
	elseif (A <= 2.35e-101)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + B)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.25e+58)
		tmp = (180.0 / pi) * atan((0.5 * ((B / A) + ((B / A) * (C / A)))));
	elseif (A <= 2.35e-101)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = (180.0 / pi) * atan(((C - (A + B)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.25e+58], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(N[(B / A), $MachinePrecision] * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.35e-101], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.24999999999999996e58

   1. Initial program 15.8%

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

      1. associate-*r/ 15.8%

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

      2. associate-*l/ 15.8%

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

      3. associate-*l/ 15.8%

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

      4. *-lft-identity 15.8%

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

      5. sub-neg 15.8%

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

      6. associate-+l- 11.9%

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

      7. sub-neg 11.9%

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

      8. remove-double-neg 11.9%

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

      9. +-commutative 11.9%

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

      10. unpow2 11.9%

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

      11. unpow2 11.9%

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

      12. hypot-def 24.4%

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

   3. Simplified 24.4%

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

      1. add-sqr-sqrt 24.2%

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

      2. pow2 24.2%

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

   5. Applied egg-rr 24.2%

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

      1. unpow2 24.2%

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

      2. add-sqr-sqrt 24.4%

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

      3. add-log-exp 30.9%

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

   7. Applied egg-rr 30.9%

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

   8. Taylor expanded in A around -inf 77.1%

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

      1. distribute-lft-out 77.1%

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

      2. *-commutative 77.1%

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

      3. unpow2 77.1%

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

      4. times-frac 80.3%

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

   10. Simplified 80.3%

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

   if -1.24999999999999996e58 < A < 2.35e-101

   1. Initial program 58.9%

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

      1. associate-*r/ 58.9%

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

      2. associate-*l/ 58.9%

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

      3. associate-*l/ 58.9%

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

      4. *-lft-identity 58.9%

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

      5. sub-neg 58.9%

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

      6. associate-+l- 58.8%

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

      7. sub-neg 58.8%

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

      8. remove-double-neg 58.8%

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

      9. +-commutative 58.8%

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

      10. unpow2 58.8%

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

      11. unpow2 58.8%

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

      12. hypot-def 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in A around 0 58.0%

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

      1. unpow2 58.0%

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

      2. unpow2 58.0%

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

      3. hypot-def 75.4%

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

   6. Simplified 75.4%

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

   if 2.35e-101 < A

   1. Initial program 76.0%

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

      1. associate-*r/ 76.0%

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

      2. associate-*l/ 76.0%

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

      3. associate-*l/ 76.0%

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

      4. *-lft-identity 76.0%

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

      5. sub-neg 76.0%

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

      6. associate-+l- 76.0%

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

      7. sub-neg 76.0%

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

      8. remove-double-neg 76.0%

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

      9. +-commutative 76.0%

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

      10. unpow2 76.0%

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

      11. unpow2 76.0%

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

      12. hypot-def 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in B around inf 83.6%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.25 \cdot 10^{+58}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)\\ \mathbf{elif}\;A \leq 2.35 \cdot 10^{-101}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \end{array} \]

Alternative 4: 47.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;A \leq -1.65 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -4.1 \cdot 10^{-23}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.1 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -4.6 \cdot 10^{-205}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -3.7 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -2.6 \cdot 10^{-226}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -3.3 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-247}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 9.8 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

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 1.0) PI))))
   (if (<= A -1.65e+35)
     t_1
     (if (<= A -4.1e-23)
       (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
       (if (<= A -4.1e-125)
         t_1
         (if (<= A -4.6e-205)
           t_0
           (if (<= A -3.7e-222)
             t_1
             (if (<= A -2.6e-226)
               t_0
               (if (<= A -3.3e-254)
                 t_2
                 (if (<= A 4.5e-247)
                   t_0
                   (if (<= A 9.8e-169)
                     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(1.0) / ((double) M_PI));
	double tmp;
	if (A <= -1.65e+35) {
		tmp = t_1;
	} else if (A <= -4.1e-23) {
		tmp = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	} else if (A <= -4.1e-125) {
		tmp = t_1;
	} else if (A <= -4.6e-205) {
		tmp = t_0;
	} else if (A <= -3.7e-222) {
		tmp = t_1;
	} else if (A <= -2.6e-226) {
		tmp = t_0;
	} else if (A <= -3.3e-254) {
		tmp = t_2;
	} else if (A <= 4.5e-247) {
		tmp = t_0;
	} else if (A <= 9.8e-169) {
		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(1.0) / Math.PI);
	double tmp;
	if (A <= -1.65e+35) {
		tmp = t_1;
	} else if (A <= -4.1e-23) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else if (A <= -4.1e-125) {
		tmp = t_1;
	} else if (A <= -4.6e-205) {
		tmp = t_0;
	} else if (A <= -3.7e-222) {
		tmp = t_1;
	} else if (A <= -2.6e-226) {
		tmp = t_0;
	} else if (A <= -3.3e-254) {
		tmp = t_2;
	} else if (A <= 4.5e-247) {
		tmp = t_0;
	} else if (A <= 9.8e-169) {
		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(1.0) / math.pi)
	tmp = 0
	if A <= -1.65e+35:
		tmp = t_1
	elif A <= -4.1e-23:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	elif A <= -4.1e-125:
		tmp = t_1
	elif A <= -4.6e-205:
		tmp = t_0
	elif A <= -3.7e-222:
		tmp = t_1
	elif A <= -2.6e-226:
		tmp = t_0
	elif A <= -3.3e-254:
		tmp = t_2
	elif A <= 4.5e-247:
		tmp = t_0
	elif A <= 9.8e-169:
		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(1.0) / pi))
	tmp = 0.0
	if (A <= -1.65e+35)
		tmp = t_1;
	elseif (A <= -4.1e-23)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	elseif (A <= -4.1e-125)
		tmp = t_1;
	elseif (A <= -4.6e-205)
		tmp = t_0;
	elseif (A <= -3.7e-222)
		tmp = t_1;
	elseif (A <= -2.6e-226)
		tmp = t_0;
	elseif (A <= -3.3e-254)
		tmp = t_2;
	elseif (A <= 4.5e-247)
		tmp = t_0;
	elseif (A <= 9.8e-169)
		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(1.0) / pi);
	tmp = 0.0;
	if (A <= -1.65e+35)
		tmp = t_1;
	elseif (A <= -4.1e-23)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	elseif (A <= -4.1e-125)
		tmp = t_1;
	elseif (A <= -4.6e-205)
		tmp = t_0;
	elseif (A <= -3.7e-222)
		tmp = t_1;
	elseif (A <= -2.6e-226)
		tmp = t_0;
	elseif (A <= -3.3e-254)
		tmp = t_2;
	elseif (A <= 4.5e-247)
		tmp = t_0;
	elseif (A <= 9.8e-169)
		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[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.65e+35], t$95$1, If[LessEqual[A, -4.1e-23], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -4.1e-125], t$95$1, If[LessEqual[A, -4.6e-205], t$95$0, If[LessEqual[A, -3.7e-222], t$95$1, If[LessEqual[A, -2.6e-226], t$95$0, If[LessEqual[A, -3.3e-254], t$95$2, If[LessEqual[A, 4.5e-247], t$95$0, If[LessEqual[A, 9.8e-169], 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 5 regimes

2. if A < -1.6500000000000001e35 or -4.10000000000000029e-23 < A < -4.0999999999999997e-125 or -4.5999999999999998e-205 < A < -3.6999999999999999e-222

   1. Initial program 25.5%

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

      1. associate-*l/ 25.5%

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

      2. *-lft-identity 25.5%

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

      3. +-commutative 25.5%

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

      4. unpow2 25.5%

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

      5. unpow2 25.5%

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

      6. hypot-def 52.7%

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

   3. Simplified 52.7%

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

   4. Taylor expanded in A around -inf 61.9%

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

   if -1.6500000000000001e35 < A < -4.10000000000000029e-23

   1. Initial program 70.1%

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

      1. associate-*l/ 70.1%

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

      2. *-lft-identity 70.1%

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

      3. +-commutative 70.1%

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

      4. unpow2 70.1%

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

      5. unpow2 70.1%

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

      6. hypot-def 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in C around -inf 54.6%

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

   if -4.0999999999999997e-125 < A < -4.5999999999999998e-205 or -3.6999999999999999e-222 < A < -2.5999999999999998e-226 or -3.30000000000000016e-254 < A < 4.5000000000000002e-247

   1. Initial program 62.0%

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

      1. associate-*l/ 62.0%

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

      2. *-lft-identity 62.0%

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

      3. +-commutative 62.0%

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

      4. unpow2 62.0%

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

      5. unpow2 62.0%

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

      6. hypot-def 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in B around inf 42.2%

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

   if -2.5999999999999998e-226 < A < -3.30000000000000016e-254 or 4.5000000000000002e-247 < A < 9.7999999999999999e-169

   1. Initial program 60.2%

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

      1. associate-*l/ 60.2%

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

      2. *-lft-identity 60.2%

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

      3. +-commutative 60.2%

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

      4. unpow2 60.2%

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

      5. unpow2 60.2%

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

      6. hypot-def 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in B around -inf 55.8%

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

   if 9.7999999999999999e-169 < A

   1. Initial program 75.3%

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

      1. associate-*l/ 75.3%

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

      2. *-lft-identity 75.3%

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

      3. +-commutative 75.3%

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

      4. unpow2 75.3%

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

      5. unpow2 75.3%

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

      6. hypot-def 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in A around inf 65.7%

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

      1. *-commutative 65.7%

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

   6. Simplified 65.7%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.65 \cdot 10^{+35}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.1 \cdot 10^{-23}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.1 \cdot 10^{-125}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -4.6 \cdot 10^{-205}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq -3.7 \cdot 10^{-222}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.6 \cdot 10^{-226}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq -3.3 \cdot 10^{-254}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-247}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 9.8 \cdot 10^{-169}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 47.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ t_1 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ t_2 := 180 \cdot \frac{t_1}{\pi}\\ t_3 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;A \leq -2.7 \cdot 10^{+35}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_1\\ \mathbf{elif}\;A \leq -3.1 \cdot 10^{-24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.8 \cdot 10^{-125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{-205}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.2 \cdot 10^{-222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq -2.35 \cdot 10^{-226}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -8 \cdot 10^{-252}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;A \leq 1.7 \cdot 10^{-251}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 3.45 \cdot 10^{-168}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan -1.0) PI)))
        (t_1 (atan (* 0.5 (/ B A))))
        (t_2 (* 180.0 (/ t_1 PI)))
        (t_3 (* 180.0 (/ (atan 1.0) PI))))
   (if (<= A -2.7e+35)
     (* (/ 180.0 PI) t_1)
     (if (<= A -3.1e-24)
       (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
       (if (<= A -1.8e-125)
         t_2
         (if (<= A -2.4e-205)
           t_0
           (if (<= A -2.2e-222)
             t_2
             (if (<= A -2.35e-226)
               t_0
               (if (<= A -8e-252)
                 t_3
                 (if (<= A 1.7e-251)
                   t_0
                   (if (<= A 3.45e-168)
                     t_3
                     (* 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 = atan((0.5 * (B / A)));
	double t_2 = 180.0 * (t_1 / ((double) M_PI));
	double t_3 = 180.0 * (atan(1.0) / ((double) M_PI));
	double tmp;
	if (A <= -2.7e+35) {
		tmp = (180.0 / ((double) M_PI)) * t_1;
	} else if (A <= -3.1e-24) {
		tmp = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	} else if (A <= -1.8e-125) {
		tmp = t_2;
	} else if (A <= -2.4e-205) {
		tmp = t_0;
	} else if (A <= -2.2e-222) {
		tmp = t_2;
	} else if (A <= -2.35e-226) {
		tmp = t_0;
	} else if (A <= -8e-252) {
		tmp = t_3;
	} else if (A <= 1.7e-251) {
		tmp = t_0;
	} else if (A <= 3.45e-168) {
		tmp = t_3;
	} 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 = Math.atan((0.5 * (B / A)));
	double t_2 = 180.0 * (t_1 / Math.PI);
	double t_3 = 180.0 * (Math.atan(1.0) / Math.PI);
	double tmp;
	if (A <= -2.7e+35) {
		tmp = (180.0 / Math.PI) * t_1;
	} else if (A <= -3.1e-24) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else if (A <= -1.8e-125) {
		tmp = t_2;
	} else if (A <= -2.4e-205) {
		tmp = t_0;
	} else if (A <= -2.2e-222) {
		tmp = t_2;
	} else if (A <= -2.35e-226) {
		tmp = t_0;
	} else if (A <= -8e-252) {
		tmp = t_3;
	} else if (A <= 1.7e-251) {
		tmp = t_0;
	} else if (A <= 3.45e-168) {
		tmp = t_3;
	} 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 = math.atan((0.5 * (B / A)))
	t_2 = 180.0 * (t_1 / math.pi)
	t_3 = 180.0 * (math.atan(1.0) / math.pi)
	tmp = 0
	if A <= -2.7e+35:
		tmp = (180.0 / math.pi) * t_1
	elif A <= -3.1e-24:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	elif A <= -1.8e-125:
		tmp = t_2
	elif A <= -2.4e-205:
		tmp = t_0
	elif A <= -2.2e-222:
		tmp = t_2
	elif A <= -2.35e-226:
		tmp = t_0
	elif A <= -8e-252:
		tmp = t_3
	elif A <= 1.7e-251:
		tmp = t_0
	elif A <= 3.45e-168:
		tmp = t_3
	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 = atan(Float64(0.5 * Float64(B / A)))
	t_2 = Float64(180.0 * Float64(t_1 / pi))
	t_3 = Float64(180.0 * Float64(atan(1.0) / pi))
	tmp = 0.0
	if (A <= -2.7e+35)
		tmp = Float64(Float64(180.0 / pi) * t_1);
	elseif (A <= -3.1e-24)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	elseif (A <= -1.8e-125)
		tmp = t_2;
	elseif (A <= -2.4e-205)
		tmp = t_0;
	elseif (A <= -2.2e-222)
		tmp = t_2;
	elseif (A <= -2.35e-226)
		tmp = t_0;
	elseif (A <= -8e-252)
		tmp = t_3;
	elseif (A <= 1.7e-251)
		tmp = t_0;
	elseif (A <= 3.45e-168)
		tmp = t_3;
	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 = atan((0.5 * (B / A)));
	t_2 = 180.0 * (t_1 / pi);
	t_3 = 180.0 * (atan(1.0) / pi);
	tmp = 0.0;
	if (A <= -2.7e+35)
		tmp = (180.0 / pi) * t_1;
	elseif (A <= -3.1e-24)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	elseif (A <= -1.8e-125)
		tmp = t_2;
	elseif (A <= -2.4e-205)
		tmp = t_0;
	elseif (A <= -2.2e-222)
		tmp = t_2;
	elseif (A <= -2.35e-226)
		tmp = t_0;
	elseif (A <= -8e-252)
		tmp = t_3;
	elseif (A <= 1.7e-251)
		tmp = t_0;
	elseif (A <= 3.45e-168)
		tmp = t_3;
	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[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(t$95$1 / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -2.7e+35], N[(N[(180.0 / Pi), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[A, -3.1e-24], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.8e-125], t$95$2, If[LessEqual[A, -2.4e-205], t$95$0, If[LessEqual[A, -2.2e-222], t$95$2, If[LessEqual[A, -2.35e-226], t$95$0, If[LessEqual[A, -8e-252], t$95$3, If[LessEqual[A, 1.7e-251], t$95$0, If[LessEqual[A, 3.45e-168], t$95$3, N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if A < -2.70000000000000003e35

   1. Initial program 15.8%

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

      1. associate-*r/ 15.8%

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

      2. associate-*l/ 15.8%

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

      3. associate-*l/ 15.8%

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

      4. *-lft-identity 15.8%

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

      5. sub-neg 15.8%

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

      6. associate-+l- 11.9%

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

      7. sub-neg 11.9%

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

      8. remove-double-neg 11.9%

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

      9. +-commutative 11.9%

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

      10. unpow2 11.9%

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

      11. unpow2 11.9%

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

      12. hypot-def 24.4%

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

   3. Simplified 24.4%

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

   4. Taylor expanded in A around -inf 46.9%

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

      1. unpow2 46.9%

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

   6. Simplified 46.9%

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

   7. Taylor expanded in C around 0 77.2%

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

   if -2.70000000000000003e35 < A < -3.1e-24

   1. Initial program 70.1%

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

      1. associate-*l/ 70.1%

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

      2. *-lft-identity 70.1%

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

      3. +-commutative 70.1%

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

      4. unpow2 70.1%

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

      5. unpow2 70.1%

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

      6. hypot-def 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in C around -inf 54.6%

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

   if -3.1e-24 < A < -1.8000000000000001e-125 or -2.4000000000000002e-205 < A < -2.2e-222

   1. Initial program 42.9%

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

      1. associate-*l/ 42.9%

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

      2. *-lft-identity 42.9%

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

      3. +-commutative 42.9%

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

      4. unpow2 42.9%

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

      5. unpow2 42.9%

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

      6. hypot-def 57.3%

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

   3. Simplified 57.3%

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

   4. Taylor expanded in A around -inf 35.1%

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

   if -1.8000000000000001e-125 < A < -2.4000000000000002e-205 or -2.2e-222 < A < -2.34999999999999999e-226 or -7.99999999999999954e-252 < A < 1.70000000000000008e-251

   1. Initial program 62.0%

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

      1. associate-*l/ 62.0%

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

      2. *-lft-identity 62.0%

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

      3. +-commutative 62.0%

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

      4. unpow2 62.0%

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

      5. unpow2 62.0%

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

      6. hypot-def 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in B around inf 42.2%

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

   if -2.34999999999999999e-226 < A < -7.99999999999999954e-252 or 1.70000000000000008e-251 < A < 3.45e-168

   1. Initial program 60.2%

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

      1. associate-*l/ 60.2%

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

      2. *-lft-identity 60.2%

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

      3. +-commutative 60.2%

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

      4. unpow2 60.2%

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

      5. unpow2 60.2%

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

      6. hypot-def 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in B around -inf 55.8%

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

   if 3.45e-168 < A

   1. Initial program 75.3%

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

      1. associate-*l/ 75.3%

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

      2. *-lft-identity 75.3%

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

      3. +-commutative 75.3%

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

      4. unpow2 75.3%

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

      5. unpow2 75.3%

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

      6. hypot-def 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in A around inf 65.7%

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

      1. *-commutative 65.7%

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

   6. Simplified 65.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{A \cdot -2}}{B}\right)}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.7 \cdot 10^{+35}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq -3.1 \cdot 10^{-24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.8 \cdot 10^{-125}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{-205}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq -2.2 \cdot 10^{-222}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.35 \cdot 10^{-226}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq -8 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.7 \cdot 10^{-251}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 3.45 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 6: 47.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ t_2 := \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{if}\;A \leq -1 \cdot 10^{+36}:\\ \;\;\;\;\frac{180}{\pi} \cdot t_2\\ \mathbf{elif}\;A \leq -1.05 \cdot 10^{-23}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-124}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -4.1 \cdot 10^{-221}:\\ \;\;\;\;180 \cdot \frac{t_2}{\pi}\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -7.6 \cdot 10^{-256}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 2.35 \cdot 10^{-163}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan 1.0) PI)))
        (t_1 (* 180.0 (/ (atan -1.0) PI)))
        (t_2 (atan (* 0.5 (/ B A)))))
   (if (<= A -1e+36)
     (* (/ 180.0 PI) t_2)
     (if (<= A -1.05e-23)
       (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
       (if (<= A -8.5e-124)
         (* 180.0 (/ (atan (/ 0.5 (/ A B))) PI))
         (if (<= A -2e-205)
           t_1
           (if (<= A -4.1e-221)
             (* 180.0 (/ t_2 PI))
             (if (<= A -2e-226)
               t_1
               (if (<= A -7.6e-256)
                 t_0
                 (if (<= A 1.35e-248)
                   t_1
                   (if (<= A 2.35e-163)
                     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(-1.0) / ((double) M_PI));
	double t_2 = atan((0.5 * (B / A)));
	double tmp;
	if (A <= -1e+36) {
		tmp = (180.0 / ((double) M_PI)) * t_2;
	} else if (A <= -1.05e-23) {
		tmp = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	} else if (A <= -8.5e-124) {
		tmp = 180.0 * (atan((0.5 / (A / B))) / ((double) M_PI));
	} else if (A <= -2e-205) {
		tmp = t_1;
	} else if (A <= -4.1e-221) {
		tmp = 180.0 * (t_2 / ((double) M_PI));
	} else if (A <= -2e-226) {
		tmp = t_1;
	} else if (A <= -7.6e-256) {
		tmp = t_0;
	} else if (A <= 1.35e-248) {
		tmp = t_1;
	} else if (A <= 2.35e-163) {
		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(-1.0) / Math.PI);
	double t_2 = Math.atan((0.5 * (B / A)));
	double tmp;
	if (A <= -1e+36) {
		tmp = (180.0 / Math.PI) * t_2;
	} else if (A <= -1.05e-23) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else if (A <= -8.5e-124) {
		tmp = 180.0 * (Math.atan((0.5 / (A / B))) / Math.PI);
	} else if (A <= -2e-205) {
		tmp = t_1;
	} else if (A <= -4.1e-221) {
		tmp = 180.0 * (t_2 / Math.PI);
	} else if (A <= -2e-226) {
		tmp = t_1;
	} else if (A <= -7.6e-256) {
		tmp = t_0;
	} else if (A <= 1.35e-248) {
		tmp = t_1;
	} else if (A <= 2.35e-163) {
		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(-1.0) / math.pi)
	t_2 = math.atan((0.5 * (B / A)))
	tmp = 0
	if A <= -1e+36:
		tmp = (180.0 / math.pi) * t_2
	elif A <= -1.05e-23:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	elif A <= -8.5e-124:
		tmp = 180.0 * (math.atan((0.5 / (A / B))) / math.pi)
	elif A <= -2e-205:
		tmp = t_1
	elif A <= -4.1e-221:
		tmp = 180.0 * (t_2 / math.pi)
	elif A <= -2e-226:
		tmp = t_1
	elif A <= -7.6e-256:
		tmp = t_0
	elif A <= 1.35e-248:
		tmp = t_1
	elif A <= 2.35e-163:
		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(-1.0) / pi))
	t_2 = atan(Float64(0.5 * Float64(B / A)))
	tmp = 0.0
	if (A <= -1e+36)
		tmp = Float64(Float64(180.0 / pi) * t_2);
	elseif (A <= -1.05e-23)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	elseif (A <= -8.5e-124)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 / Float64(A / B))) / pi));
	elseif (A <= -2e-205)
		tmp = t_1;
	elseif (A <= -4.1e-221)
		tmp = Float64(180.0 * Float64(t_2 / pi));
	elseif (A <= -2e-226)
		tmp = t_1;
	elseif (A <= -7.6e-256)
		tmp = t_0;
	elseif (A <= 1.35e-248)
		tmp = t_1;
	elseif (A <= 2.35e-163)
		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(-1.0) / pi);
	t_2 = atan((0.5 * (B / A)));
	tmp = 0.0;
	if (A <= -1e+36)
		tmp = (180.0 / pi) * t_2;
	elseif (A <= -1.05e-23)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	elseif (A <= -8.5e-124)
		tmp = 180.0 * (atan((0.5 / (A / B))) / pi);
	elseif (A <= -2e-205)
		tmp = t_1;
	elseif (A <= -4.1e-221)
		tmp = 180.0 * (t_2 / pi);
	elseif (A <= -2e-226)
		tmp = t_1;
	elseif (A <= -7.6e-256)
		tmp = t_0;
	elseif (A <= 1.35e-248)
		tmp = t_1;
	elseif (A <= 2.35e-163)
		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[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[A, -1e+36], N[(N[(180.0 / Pi), $MachinePrecision] * t$95$2), $MachinePrecision], If[LessEqual[A, -1.05e-23], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -8.5e-124], N[(180.0 * N[(N[ArcTan[N[(0.5 / N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2e-205], t$95$1, If[LessEqual[A, -4.1e-221], N[(180.0 * N[(t$95$2 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2e-226], t$95$1, If[LessEqual[A, -7.6e-256], t$95$0, If[LessEqual[A, 1.35e-248], t$95$1, If[LessEqual[A, 2.35e-163], 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 7 regimes

2. if A < -1.00000000000000004e36

   1. Initial program 15.8%

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

      1. associate-*r/ 15.8%

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

      2. associate-*l/ 15.8%

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

      3. associate-*l/ 15.8%

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

      4. *-lft-identity 15.8%

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

      5. sub-neg 15.8%

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

      6. associate-+l- 11.9%

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

      7. sub-neg 11.9%

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

      8. remove-double-neg 11.9%

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

      9. +-commutative 11.9%

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

      10. unpow2 11.9%

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

      11. unpow2 11.9%

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

      12. hypot-def 24.4%

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

   3. Simplified 24.4%

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

   4. Taylor expanded in A around -inf 46.9%

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

      1. unpow2 46.9%

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

   6. Simplified 46.9%

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

   7. Taylor expanded in C around 0 77.2%

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

   if -1.00000000000000004e36 < A < -1.05e-23

   1. Initial program 70.1%

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

      1. associate-*l/ 70.1%

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

      2. *-lft-identity 70.1%

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

      3. +-commutative 70.1%

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

      4. unpow2 70.1%

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

      5. unpow2 70.1%

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

      6. hypot-def 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in C around -inf 54.6%

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

   if -1.05e-23 < A < -8.5000000000000002e-124

   1. Initial program 40.7%

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

      1. associate-*l/ 40.7%

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

      2. *-lft-identity 40.7%

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

      3. +-commutative 40.7%

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

      4. unpow2 40.7%

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

      5. unpow2 40.7%

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

      6. hypot-def 54.3%

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

   3. Simplified 54.3%

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

   4. Taylor expanded in A around -inf 10.4%

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

      1. distribute-lft-out 10.4%

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

      2. associate-/l* 10.1%

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

      3. unpow2 10.1%

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

      4. unpow2 10.1%

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

      5. unpow2 10.1%

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

   6. Simplified 10.1%

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

      1. add-cube-cbrt 10.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{C}{\frac{A \cdot A}{B \cdot B}} + \frac{B \cdot B}{A}} \cdot \sqrt[3]{\frac{C}{\frac{A \cdot A}{B \cdot B}} + \frac{B \cdot B}{A}}\right) \cdot \sqrt[3]{\frac{C}{\frac{A \cdot A}{B \cdot B}} + \frac{B \cdot B}{A}}\right)}}{B}\right)}{\pi} \]

      2. pow3 10.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot \color{blue}{{\left(\sqrt[3]{\frac{C}{\frac{A \cdot A}{B \cdot B}} + \frac{B \cdot B}{A}}\right)}^{3}}}{B}\right)}{\pi} \]

      3. times-frac 14.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot {\left(\sqrt[3]{\frac{C}{\color{blue}{\frac{A}{B} \cdot \frac{A}{B}}} + \frac{B \cdot B}{A}}\right)}^{3}}{B}\right)}{\pi} \]

      4. pow2 14.1%

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

      5. associate-/l* 18.0%

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

   8. Applied egg-rr 18.0%

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

   9. Taylor expanded in C around 0 2.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot {\color{blue}{\left({\left(\frac{{B}^{2}}{A}\right)}^{0.3333333333333333}\right)}}^{3}}{B}\right)}{\pi} \]
   10. Step-by-step derivation

       1. unpow1/3 12.4%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot {\color{blue}{\left(\sqrt[3]{\frac{{B}^{2}}{A}}\right)}}^{3}}{B}\right)}{\pi} \]

       2. unpow2 12.4%

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

   11. Simplified 12.4%

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

       1. expm1-log1p-u 8.8%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{0.5 \cdot {\left(\sqrt[3]{\frac{B \cdot B}{A}}\right)}^{3}}{B}\right)\right)\right)}}{\pi} \]

       2. expm1-udef 12.4%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{0.5 \cdot {\left(\sqrt[3]{\frac{B \cdot B}{A}}\right)}^{3}}{B}\right)} - 1\right)}}{\pi} \]

       3. rem-cube-cbrt 12.4%

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

       4. associate-/l* 12.4%

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

       5. associate-/l* 12.4%

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

   13. Applied egg-rr 12.4%

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

       1. expm1-def 12.6%

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

       2. expm1-log1p 16.2%

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

       3. associate-/r/ 31.6%

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

       4. *-inverses 31.6%

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

   15. Simplified 31.6%

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

   if -8.5000000000000002e-124 < A < -2e-205 or -4.09999999999999981e-221 < A < -1.99999999999999984e-226 or -7.59999999999999953e-256 < A < 1.35e-248

   1. Initial program 62.0%

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

      1. associate-*l/ 62.0%

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

      2. *-lft-identity 62.0%

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

      3. +-commutative 62.0%

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

      4. unpow2 62.0%

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

      5. unpow2 62.0%

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

      6. hypot-def 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in B around inf 42.2%

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

   if -2e-205 < A < -4.09999999999999981e-221

   1. Initial program 57.0%

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

      1. associate-*l/ 57.0%

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

      2. *-lft-identity 57.0%

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

      3. +-commutative 57.0%

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

      4. unpow2 57.0%

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

      5. unpow2 57.0%

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

      6. hypot-def 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in A around -inf 57.0%

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

   if -1.99999999999999984e-226 < A < -7.59999999999999953e-256 or 1.35e-248 < A < 2.35e-163

   1. Initial program 60.2%

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

      1. associate-*l/ 60.2%

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

      2. *-lft-identity 60.2%

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

      3. +-commutative 60.2%

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

      4. unpow2 60.2%

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

      5. unpow2 60.2%

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

      6. hypot-def 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in B around -inf 55.8%

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

   if 2.35e-163 < A

   1. Initial program 75.3%

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

      1. associate-*l/ 75.3%

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

      2. *-lft-identity 75.3%

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

      3. +-commutative 75.3%

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

      4. unpow2 75.3%

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

      5. unpow2 75.3%

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

      6. hypot-def 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in A around inf 65.7%

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

      1. *-commutative 65.7%

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

   6. Simplified 65.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{A \cdot -2}}{B}\right)}{\pi} \]
3. Recombined 7 regimes into one program.

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1 \cdot 10^{+36}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq -1.05 \cdot 10^{-23}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-124}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-205}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq -4.1 \cdot 10^{-221}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-226}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq -7.6 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{-248}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 2.35 \cdot 10^{-163}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 53.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A \cdot 2}{B}\right)\\ \mathbf{if}\;B \leq -2 \cdot 10^{+101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-92}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq 6200000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (- C (* A 2.0)) B)))))
   (if (<= B -2e+101)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 4.5e-92)
       t_0
       (if (<= B 5.4e-9)
         (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
         (if (<= B 6200000.0) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((C - (A * 2.0)) / B));
	double tmp;
	if (B <= -2e+101) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.5e-92) {
		tmp = t_0;
	} else if (B <= 5.4e-9) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (B <= 6200000.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(((C - (A * 2.0)) / B));
	double tmp;
	if (B <= -2e+101) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.5e-92) {
		tmp = t_0;
	} else if (B <= 5.4e-9) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (B <= 6200000.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(((C - (A * 2.0)) / B))
	tmp = 0
	if B <= -2e+101:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.5e-92:
		tmp = t_0
	elif B <= 5.4e-9:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif B <= 6200000.0:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A * 2.0)) / B)))
	tmp = 0.0
	if (B <= -2e+101)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.5e-92)
		tmp = t_0;
	elseif (B <= 5.4e-9)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (B <= 6200000.0)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(((C - (A * 2.0)) / B));
	tmp = 0.0;
	if (B <= -2e+101)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.5e-92)
		tmp = t_0;
	elseif (B <= 5.4e-9)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (B <= 6200000.0)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A * 2.0), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2e+101], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.5e-92], t$95$0, If[LessEqual[B, 5.4e-9], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6200000.0], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2e101

   1. Initial program 42.8%

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

      1. associate-*l/ 42.8%

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

      2. *-lft-identity 42.8%

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

      3. +-commutative 42.8%

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

      4. unpow2 42.8%

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

      5. unpow2 42.8%

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

      6. hypot-def 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in B around -inf 65.2%

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

   if -2e101 < B < 4.5e-92 or 5.4000000000000004e-9 < B < 6.2e6

   1. Initial program 66.9%

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

      1. associate-*r/ 66.9%

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

      2. associate-*l/ 66.9%

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

      3. associate-*l/ 66.9%

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

      4. *-lft-identity 66.9%

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

      5. sub-neg 66.9%

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

      6. associate-+l- 65.4%

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

      7. sub-neg 65.4%

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

      8. remove-double-neg 65.4%

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

      9. +-commutative 65.4%

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

      10. unpow2 65.4%

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

      11. unpow2 65.4%

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

      12. hypot-def 69.5%

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

   3. Simplified 69.5%

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

   4. Taylor expanded in A around inf 58.9%

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

      1. *-commutative 58.9%

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

   6. Simplified 58.9%

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

   if 4.5e-92 < B < 5.4000000000000004e-9

   1. Initial program 33.0%

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

      1. associate-*r/ 33.0%

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

      2. associate-*l/ 33.0%

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

      3. associate-*l/ 33.0%

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

      4. *-lft-identity 33.0%

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

      5. sub-neg 33.0%

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

      6. associate-+l- 32.7%

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

      7. sub-neg 32.7%

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

      8. remove-double-neg 32.7%

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

      9. +-commutative 32.7%

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

      10. unpow2 32.7%

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

      11. unpow2 32.7%

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

      12. hypot-def 33.1%

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

   3. Simplified 33.1%

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

   4. Taylor expanded in A around -inf 11.6%

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

      1. unpow2 11.6%

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

   6. Simplified 11.6%

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

   7. Taylor expanded in C around 0 40.4%

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

   if 6.2e6 < B

   1. Initial program 47.4%

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

      1. associate-*l/ 47.4%

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

      2. *-lft-identity 47.4%

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

      3. +-commutative 47.4%

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

      4. unpow2 47.4%

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

      5. unpow2 47.4%

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

      6. hypot-def 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in B around inf 68.7%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{+101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A \cdot 2}{B}\right)\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq 6200000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A \cdot 2}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 8: 61.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.1 \cdot 10^{+31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq -1 \cdot 10^{-226} \lor \neg \left(A \leq -2.3 \cdot 10^{-250}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.1e+31)
   (* 180.0 (/ (atan (* 0.5 (+ (/ B A) (* (/ B A) (/ C A))))) PI))
   (if (or (<= A -1e-226) (not (<= A -2.3e-250)))
     (* (/ 180.0 PI) (atan (/ (- C (+ A B)) B)))
     (* 180.0 (/ (atan 1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.1e+31) {
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / ((double) M_PI));
	} else if ((A <= -1e-226) || !(A <= -2.3e-250)) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + B)) / B));
	} 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 (A <= -5.1e+31) {
		tmp = 180.0 * (Math.atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / Math.PI);
	} else if ((A <= -1e-226) || !(A <= -2.3e-250)) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + B)) / B));
	} else {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.1e+31:
		tmp = 180.0 * (math.atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / math.pi)
	elif (A <= -1e-226) or not (A <= -2.3e-250):
		tmp = (180.0 / math.pi) * math.atan(((C - (A + B)) / B))
	else:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.1e+31)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(Float64(B / A) + Float64(Float64(B / A) * Float64(C / A))))) / pi));
	elseif ((A <= -1e-226) || !(A <= -2.3e-250))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + B)) / B)));
	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 (A <= -5.1e+31)
		tmp = 180.0 * (atan((0.5 * ((B / A) + ((B / A) * (C / A))))) / pi);
	elseif ((A <= -1e-226) || ~((A <= -2.3e-250)))
		tmp = (180.0 / pi) * atan(((C - (A + B)) / B));
	else
		tmp = 180.0 * (atan(1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.1e+31], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(N[(B / A), $MachinePrecision] * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[A, -1e-226], N[Not[LessEqual[A, -2.3e-250]], $MachinePrecision]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.0999999999999997e31

   1. Initial program 17.2%

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

      1. associate-*l/ 17.2%

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

      2. *-lft-identity 17.2%

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

      3. +-commutative 17.2%

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

      4. unpow2 17.2%

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

      5. unpow2 17.2%

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

      6. hypot-def 51.1%

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

   3. Simplified 51.1%

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

   4. Taylor expanded in A around -inf 75.4%

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

      1. distribute-lft-out 75.4%

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

      2. *-commutative 75.4%

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

      3. unpow2 75.4%

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

      4. times-frac 78.5%

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

   6. Simplified 78.5%

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

   if -5.0999999999999997e31 < A < -9.99999999999999921e-227 or -2.2999999999999999e-250 < A

   1. Initial program 67.1%

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

      1. associate-*r/ 67.1%

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

      2. associate-*l/ 67.1%

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

      3. associate-*l/ 67.1%

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

      4. *-lft-identity 67.1%

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

      5. sub-neg 67.1%

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

      6. associate-+l- 67.1%

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

      7. sub-neg 67.1%

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

      8. remove-double-neg 67.1%

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

      9. +-commutative 67.1%

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

      10. unpow2 67.1%

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

      11. unpow2 67.1%

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

      12. hypot-def 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in B around inf 68.8%

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

   if -9.99999999999999921e-227 < A < -2.2999999999999999e-250

   1. Initial program 54.4%

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

      1. associate-*l/ 54.4%

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

      2. *-lft-identity 54.4%

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

      3. +-commutative 54.4%

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

      4. unpow2 54.4%

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

      5. unpow2 54.4%

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

      6. hypot-def 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in B around -inf 64.8%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.1 \cdot 10^{+31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)}{\pi}\\ \mathbf{elif}\;A \leq -1 \cdot 10^{-226} \lor \neg \left(A \leq -2.3 \cdot 10^{-250}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \end{array} \]

Alternative 9: 61.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.06 \cdot 10^{+32}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)\\ \mathbf{elif}\;A \leq -1.48 \cdot 10^{-226} \lor \neg \left(A \leq -2.2 \cdot 10^{-250}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.06e+32)
   (* (/ 180.0 PI) (atan (* 0.5 (+ (/ B A) (* (/ B A) (/ C A))))))
   (if (or (<= A -1.48e-226) (not (<= A -2.2e-250)))
     (* (/ 180.0 PI) (atan (/ (- C (+ A B)) B)))
     (* 180.0 (/ (atan 1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.06e+32) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * ((B / A) + ((B / A) * (C / A)))));
	} else if ((A <= -1.48e-226) || !(A <= -2.2e-250)) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + B)) / B));
	} 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 (A <= -1.06e+32) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * ((B / A) + ((B / A) * (C / A)))));
	} else if ((A <= -1.48e-226) || !(A <= -2.2e-250)) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + B)) / B));
	} else {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.06e+32:
		tmp = (180.0 / math.pi) * math.atan((0.5 * ((B / A) + ((B / A) * (C / A)))))
	elif (A <= -1.48e-226) or not (A <= -2.2e-250):
		tmp = (180.0 / math.pi) * math.atan(((C - (A + B)) / B))
	else:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.06e+32)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(Float64(B / A) + Float64(Float64(B / A) * Float64(C / A))))));
	elseif ((A <= -1.48e-226) || !(A <= -2.2e-250))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + B)) / B)));
	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 (A <= -1.06e+32)
		tmp = (180.0 / pi) * atan((0.5 * ((B / A) + ((B / A) * (C / A)))));
	elseif ((A <= -1.48e-226) || ~((A <= -2.2e-250)))
		tmp = (180.0 / pi) * atan(((C - (A + B)) / B));
	else
		tmp = 180.0 * (atan(1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.06e+32], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(N[(B / A), $MachinePrecision] + N[(N[(B / A), $MachinePrecision] * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[A, -1.48e-226], N[Not[LessEqual[A, -2.2e-250]], $MachinePrecision]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.0600000000000001e32

   1. Initial program 17.2%

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

      1. associate-*r/ 17.2%

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

      2. associate-*l/ 17.2%

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

      3. associate-*l/ 17.2%

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

      4. *-lft-identity 17.2%

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

      5. sub-neg 17.2%

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

      6. associate-+l- 13.5%

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

      7. sub-neg 13.5%

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

      8. remove-double-neg 13.5%

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

      9. +-commutative 13.5%

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

      10. unpow2 13.5%

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

      11. unpow2 13.5%

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

      12. hypot-def 26.8%

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

   3. Simplified 26.8%

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

      1. add-sqr-sqrt 26.6%

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

      2. pow2 26.6%

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

   5. Applied egg-rr 26.6%

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

      1. unpow2 26.6%

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

      2. add-sqr-sqrt 26.8%

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

      3. add-log-exp 33.0%

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

   7. Applied egg-rr 33.0%

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

   8. Taylor expanded in A around -inf 75.7%

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

      1. distribute-lft-out 75.7%

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

      2. *-commutative 75.7%

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

      3. unpow2 75.7%

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

      4. times-frac 78.7%

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

   10. Simplified 78.7%

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

   if -1.0600000000000001e32 < A < -1.47999999999999991e-226 or -2.2e-250 < A

   1. Initial program 67.1%

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

      1. associate-*r/ 67.1%

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

      2. associate-*l/ 67.1%

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

      3. associate-*l/ 67.1%

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

      4. *-lft-identity 67.1%

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

      5. sub-neg 67.1%

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

      6. associate-+l- 67.1%

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

      7. sub-neg 67.1%

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

      8. remove-double-neg 67.1%

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

      9. +-commutative 67.1%

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

      10. unpow2 67.1%

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

      11. unpow2 67.1%

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

      12. hypot-def 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in B around inf 68.8%

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

   if -1.47999999999999991e-226 < A < -2.2e-250

   1. Initial program 54.4%

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

      1. associate-*l/ 54.4%

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

      2. *-lft-identity 54.4%

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

      3. +-commutative 54.4%

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

      4. unpow2 54.4%

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

      5. unpow2 54.4%

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

      6. hypot-def 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in B around -inf 64.8%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.06 \cdot 10^{+32}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{A} \cdot \frac{C}{A}\right)\right)\\ \mathbf{elif}\;A \leq -1.48 \cdot 10^{-226} \lor \neg \left(A \leq -2.2 \cdot 10^{-250}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \end{array} \]

Alternative 10: 60.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.65 \cdot 10^{+35}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq -5.1 \cdot 10^{-226} \lor \neg \left(A \leq -2.3 \cdot 10^{-250}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.65e+35)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (if (or (<= A -5.1e-226) (not (<= A -2.3e-250)))
     (* (/ 180.0 PI) (atan (/ (- C (+ A B)) B)))
     (* 180.0 (/ (atan 1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.65e+35) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if ((A <= -5.1e-226) || !(A <= -2.3e-250)) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + B)) / B));
	} 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 (A <= -1.65e+35) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if ((A <= -5.1e-226) || !(A <= -2.3e-250)) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + B)) / B));
	} else {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.65e+35:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif (A <= -5.1e-226) or not (A <= -2.3e-250):
		tmp = (180.0 / math.pi) * math.atan(((C - (A + B)) / B))
	else:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.65e+35)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif ((A <= -5.1e-226) || !(A <= -2.3e-250))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + B)) / B)));
	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 (A <= -1.65e+35)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif ((A <= -5.1e-226) || ~((A <= -2.3e-250)))
		tmp = (180.0 / pi) * atan(((C - (A + B)) / B));
	else
		tmp = 180.0 * (atan(1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.65e+35], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[A, -5.1e-226], N[Not[LessEqual[A, -2.3e-250]], $MachinePrecision]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.6500000000000001e35

   1. Initial program 15.8%

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

      1. associate-*r/ 15.8%

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

      2. associate-*l/ 15.8%

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

      3. associate-*l/ 15.8%

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

      4. *-lft-identity 15.8%

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

      5. sub-neg 15.8%

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

      6. associate-+l- 11.9%

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

      7. sub-neg 11.9%

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

      8. remove-double-neg 11.9%

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

      9. +-commutative 11.9%

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

      10. unpow2 11.9%

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

      11. unpow2 11.9%

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

      12. hypot-def 24.4%

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

   3. Simplified 24.4%

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

   4. Taylor expanded in A around -inf 46.9%

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

      1. unpow2 46.9%

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

   6. Simplified 46.9%

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

   7. Taylor expanded in C around 0 77.2%

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

   if -1.6500000000000001e35 < A < -5.09999999999999973e-226 or -2.2999999999999999e-250 < A

   1. Initial program 66.7%

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

      1. associate-*r/ 66.7%

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

      2. associate-*l/ 66.7%

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

      3. associate-*l/ 66.7%

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

      4. *-lft-identity 66.7%

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

      5. sub-neg 66.7%

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

      6. associate-+l- 66.7%

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

      7. sub-neg 66.7%

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

      8. remove-double-neg 66.7%

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

      9. +-commutative 66.7%

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

      10. unpow2 66.7%

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

      11. unpow2 66.7%

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

      12. hypot-def 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in B around inf 68.3%

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

   if -5.09999999999999973e-226 < A < -2.2999999999999999e-250

   1. Initial program 54.4%

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

      1. associate-*l/ 54.4%

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

      2. *-lft-identity 54.4%

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

      3. +-commutative 54.4%

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

      4. unpow2 54.4%

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

      5. unpow2 54.4%

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

      6. hypot-def 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in B around -inf 64.8%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.65 \cdot 10^{+35}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq -5.1 \cdot 10^{-226} \lor \neg \left(A \leq -2.3 \cdot 10^{-250}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \end{array} \]

Alternative 11: 46.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{if}\;B \leq -2.5 \cdot 10^{+57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.02 \cdot 10^{-101}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-8}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3500:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ C B)))))
   (if (<= B -2.5e+57)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 1.02e-101)
       t_0
       (if (<= B 1.5e-8)
         (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
         (if (<= B 3500.0) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan((C / B));
	double tmp;
	if (B <= -2.5e+57) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.02e-101) {
		tmp = t_0;
	} else if (B <= 1.5e-8) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (B <= 3500.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan((C / B));
	double tmp;
	if (B <= -2.5e+57) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.02e-101) {
		tmp = t_0;
	} else if (B <= 1.5e-8) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (B <= 3500.0) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan((C / B))
	tmp = 0
	if B <= -2.5e+57:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.02e-101:
		tmp = t_0
	elif B <= 1.5e-8:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif B <= 3500.0:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(C / B)))
	tmp = 0.0
	if (B <= -2.5e+57)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.02e-101)
		tmp = t_0;
	elseif (B <= 1.5e-8)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (B <= 3500.0)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan((C / B));
	tmp = 0.0;
	if (B <= -2.5e+57)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.02e-101)
		tmp = t_0;
	elseif (B <= 1.5e-8)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (B <= 3500.0)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.5e+57], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.02e-101], t$95$0, If[LessEqual[B, 1.5e-8], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3500.0], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.49999999999999986e57

   1. Initial program 42.8%

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

      1. associate-*l/ 42.8%

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

      2. *-lft-identity 42.8%

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

      3. +-commutative 42.8%

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

      4. unpow2 42.8%

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

      5. unpow2 42.8%

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

      6. hypot-def 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in B around -inf 59.2%

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

   if -2.49999999999999986e57 < B < 1.02e-101 or 1.49999999999999987e-8 < B < 3500

   1. Initial program 68.6%

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

      1. associate-*r/ 68.6%

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

      2. associate-*l/ 68.6%

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

      3. associate-*l/ 68.6%

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

      4. *-lft-identity 68.6%

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

      5. sub-neg 68.6%

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

      6. associate-+l- 67.0%

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

      7. sub-neg 67.0%

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

      8. remove-double-neg 67.0%

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

      9. +-commutative 67.0%

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

      10. unpow2 67.0%

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

      11. unpow2 67.0%

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

      12. hypot-def 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in A around inf 60.2%

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

      1. *-commutative 60.2%

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

   6. Simplified 60.2%

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

   7. Taylor expanded in C around inf 39.7%

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

   if 1.02e-101 < B < 1.49999999999999987e-8

   1. Initial program 33.4%

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

      1. associate-*l/ 33.4%

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

      2. *-lft-identity 33.4%

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

      3. +-commutative 33.4%

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

      4. unpow2 33.4%

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

      5. unpow2 33.4%

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

      6. hypot-def 41.9%

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

   3. Simplified 41.9%

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

   4. Taylor expanded in A around -inf 36.1%

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

   if 3500 < B

   1. Initial program 47.4%

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

      1. associate-*l/ 47.4%

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

      2. *-lft-identity 47.4%

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

      3. +-commutative 47.4%

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

      4. unpow2 47.4%

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

      5. unpow2 47.4%

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

      6. hypot-def 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in B around inf 68.7%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.5 \cdot 10^{+57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.02 \cdot 10^{-101}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-8}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3500:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12: 46.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.75 \cdot 10^{+58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3 \cdot 10^{-10}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3400:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.75e+58)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.35e-101)
     (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
     (if (<= B 3e-10)
       (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
       (if (<= B 3400.0)
         (* (/ 180.0 PI) (atan (/ C B)))
         (* 180.0 (/ (atan -1.0) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.75e+58) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.35e-101) {
		tmp = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	} else if (B <= 3e-10) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (B <= 3400.0) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / B));
	} 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+58) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.35e-101) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else if (B <= 3e-10) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (B <= 3400.0) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.75e+58:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.35e-101:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	elif B <= 3e-10:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif B <= 3400.0:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	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+58)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.35e-101)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	elseif (B <= 3e-10)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (B <= 3400.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / B)));
	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+58)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.35e-101)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	elseif (B <= 3e-10)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (B <= 3400.0)
		tmp = (180.0 / pi) * atan((C / B));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.75e+58], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.35e-101], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3e-10], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3400.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.7499999999999999e58

   1. Initial program 42.8%

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

      1. associate-*l/ 42.8%

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

      2. *-lft-identity 42.8%

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

      3. +-commutative 42.8%

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

      4. unpow2 42.8%

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

      5. unpow2 42.8%

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

      6. hypot-def 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in B around -inf 59.2%

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

   if -1.7499999999999999e58 < B < 1.3500000000000001e-101

   1. Initial program 67.3%

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

      1. associate-*l/ 67.3%

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

      2. *-lft-identity 67.3%

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

      3. +-commutative 67.3%

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

      4. unpow2 67.3%

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

      5. unpow2 67.3%

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

      6. hypot-def 79.8%

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

   3. Simplified 79.8%

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

   4. Taylor expanded in C around -inf 38.3%

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

   if 1.3500000000000001e-101 < B < 3e-10

   1. Initial program 33.4%

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

      1. associate-*l/ 33.4%

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

      2. *-lft-identity 33.4%

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

      3. +-commutative 33.4%

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

      4. unpow2 33.4%

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

      5. unpow2 33.4%

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

      6. hypot-def 41.9%

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

   3. Simplified 41.9%

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

   4. Taylor expanded in A around -inf 36.1%

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

   if 3e-10 < B < 3400

   1. Initial program 88.0%

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

      1. associate-*r/ 88.0%

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

      2. associate-*l/ 88.0%

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

      3. associate-*l/ 88.0%

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

      4. *-lft-identity 88.0%

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

      5. sub-neg 88.0%

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

      6. associate-+l- 88.0%

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

      7. sub-neg 88.0%

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

      8. remove-double-neg 88.0%

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

      9. +-commutative 88.0%

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

      10. unpow2 88.0%

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

      11. unpow2 88.0%

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

      12. hypot-def 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in A around inf 75.6%

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

      1. *-commutative 75.6%

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

   6. Simplified 75.6%

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

   7. Taylor expanded in C around inf 63.3%

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

   if 3400 < B

   1. Initial program 47.4%

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

      1. associate-*l/ 47.4%

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

      2. *-lft-identity 47.4%

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

      3. +-commutative 47.4%

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

      4. unpow2 47.4%

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

      5. unpow2 47.4%

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

      6. hypot-def 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in B around inf 68.7%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.75 \cdot 10^{+58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3 \cdot 10^{-10}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3400:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 13: 44.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -9.6 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -9.6e-145)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 7.2e-197)
     (* 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 <= -9.6e-145) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 7.2e-197) {
		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 <= -9.6e-145) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 7.2e-197) {
		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 <= -9.6e-145:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 7.2e-197:
		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 <= -9.6e-145)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 7.2e-197)
		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 <= -9.6e-145)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 7.2e-197)
		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, -9.6e-145], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.2e-197], 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 < -9.60000000000000061e-145

   1. Initial program 60.2%

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

      1. associate-*l/ 60.2%

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

      2. *-lft-identity 60.2%

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

      3. +-commutative 60.2%

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

      4. unpow2 60.2%

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

      5. unpow2 60.2%

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

      6. hypot-def 79.9%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in B around -inf 42.8%

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

   if -9.60000000000000061e-145 < B < 7.1999999999999997e-197

   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. Step-by-step derivation

      1. associate-*l/ 58.4%

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

      2. *-lft-identity 58.4%

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

      3. +-commutative 58.4%

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

      4. unpow2 58.4%

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

      5. unpow2 58.4%

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

      6. hypot-def 77.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in C around inf 27.8%

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

      1. distribute-rgt1-in 27.8%

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

      2. metadata-eval 27.8%

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

      3. mul0-lft 27.8%

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

      4. metadata-eval 27.8%

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

   6. Simplified 27.8%

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

   if 7.1999999999999997e-197 < B

   1. Initial program 51.4%

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

      1. associate-*l/ 51.4%

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

      2. *-lft-identity 51.4%

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

      3. +-commutative 51.4%

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

      4. unpow2 51.4%

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

      5. unpow2 51.4%

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

      6. hypot-def 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in B around inf 46.5%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9.6 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 14: 46.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.5 \cdot 10^{+57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.5e+57)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 8.5e-101)
     (* (/ 180.0 PI) (atan (/ C B)))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.5e+57) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 8.5e-101) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / B));
	} 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 <= -2.5e+57) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 8.5e-101) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.5e+57:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 8.5e-101:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.5e+57)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 8.5e-101)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / B)));
	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 <= -2.5e+57)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 8.5e-101)
		tmp = (180.0 / pi) * atan((C / B));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.5e+57], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.5e-101], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.49999999999999986e57

   1. Initial program 42.8%

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

      1. associate-*l/ 42.8%

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

      2. *-lft-identity 42.8%

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

      3. +-commutative 42.8%

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

      4. unpow2 42.8%

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

      5. unpow2 42.8%

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

      6. hypot-def 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in B around -inf 59.2%

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

   if -2.49999999999999986e57 < B < 8.49999999999999941e-101

   1. Initial program 67.3%

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

      1. associate-*r/ 67.3%

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

      2. associate-*l/ 67.3%

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

      3. associate-*l/ 67.3%

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

      4. *-lft-identity 67.3%

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

      5. sub-neg 67.3%

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

      6. associate-+l- 65.6%

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

      7. sub-neg 65.6%

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

      8. remove-double-neg 65.6%

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

      9. +-commutative 65.6%

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

      10. unpow2 65.6%

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

      11. unpow2 65.6%

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

      12. hypot-def 69.5%

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

   3. Simplified 69.5%

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

   4. Taylor expanded in A around inf 59.2%

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

      1. *-commutative 59.2%

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

   6. Simplified 59.2%

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

   7. Taylor expanded in C around inf 38.2%

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

   if 8.49999999999999941e-101 < B

   1. Initial program 47.4%

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

      1. associate-*l/ 47.4%

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

      2. *-lft-identity 47.4%

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

      3. +-commutative 47.4%

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

      4. unpow2 47.4%

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

      5. unpow2 47.4%

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

      6. hypot-def 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in B around inf 53.3%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.5 \cdot 10^{+57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 15: 39.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -4.999999999999985e-310

   1. Initial program 59.0%

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

      1. associate-*l/ 59.0%

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

      2. *-lft-identity 59.0%

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

      3. +-commutative 59.0%

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

      4. unpow2 59.0%

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

      5. unpow2 59.0%

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

      6. hypot-def 78.2%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in B around -inf 35.0%

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

   if -4.999999999999985e-310 < B

   1. Initial program 53.5%

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

      1. associate-*l/ 53.5%

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

      2. *-lft-identity 53.5%

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

      3. +-commutative 53.5%

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

      4. unpow2 53.5%

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

      5. unpow2 53.5%

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

      6. hypot-def 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in B around inf 38.7%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 16: 20.8% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.0%

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

   1. associate-*l/ 56.0%

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

   2. *-lft-identity 56.0%

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

   3. +-commutative 56.0%

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

   4. unpow2 56.0%

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

   5. unpow2 56.0%

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

   6. hypot-def 76.7%

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

3. Simplified 76.7%

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

4. Taylor expanded in B around inf 22.1%

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

5. Final simplification 22.1%

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

Reproduce

herbie shell --seed 2023194 
(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)))