ABCF->ab-angle angle

Percentage Accurate: 54.1% → 88.8%

Time: 24.6s

Alternatives: 25

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: 54.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_1 := e^{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-29}:\\ \;\;\;\;2 \cdot \log \left(\sqrt{{t_1}^{\left(\frac{180}{\pi}\right)}}\right)\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{180}{2 \cdot \pi} \cdot \log t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
        (t_1 (exp (atan (/ (- (- C A) (hypot B (- C A))) B)))))
   (if (<= t_0 -1e-29)
     (* 2.0 (log (sqrt (pow t_1 (/ 180.0 PI)))))
     (if (<= t_0 0.0)
       (* (/ 180.0 PI) (atan (* B (/ -0.5 (- C A)))))
       (* 2.0 (* (/ 180.0 (* 2.0 PI)) (log t_1)))))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double t_1 = exp(atan((((C - A) - hypot(B, (C - A))) / B)));
	double tmp;
	if (t_0 <= -1e-29) {
		tmp = 2.0 * log(sqrt(pow(t_1, (180.0 / ((double) M_PI)))));
	} else if (t_0 <= 0.0) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / (C - A))));
	} else {
		tmp = 2.0 * ((180.0 / (2.0 * ((double) M_PI))) * log(t_1));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double t_1 = Math.exp(Math.atan((((C - A) - Math.hypot(B, (C - A))) / B)));
	double tmp;
	if (t_0 <= -1e-29) {
		tmp = 2.0 * Math.log(Math.sqrt(Math.pow(t_1, (180.0 / Math.PI))));
	} else if (t_0 <= 0.0) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / (C - A))));
	} else {
		tmp = 2.0 * ((180.0 / (2.0 * Math.PI)) * Math.log(t_1));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	t_1 = math.exp(math.atan((((C - A) - math.hypot(B, (C - A))) / B)))
	tmp = 0
	if t_0 <= -1e-29:
		tmp = 2.0 * math.log(math.sqrt(math.pow(t_1, (180.0 / math.pi))))
	elif t_0 <= 0.0:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / (C - A))))
	else:
		tmp = 2.0 * ((180.0 / (2.0 * math.pi)) * math.log(t_1))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	t_1 = exp(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(C - A))) / B)))
	tmp = 0.0
	if (t_0 <= -1e-29)
		tmp = Float64(2.0 * log(sqrt((t_1 ^ Float64(180.0 / pi)))));
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / Float64(C - A)))));
	else
		tmp = Float64(2.0 * Float64(Float64(180.0 / Float64(2.0 * pi)) * log(t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	t_1 = exp(atan((((C - A) - hypot(B, (C - A))) / B)));
	tmp = 0.0;
	if (t_0 <= -1e-29)
		tmp = 2.0 * log(sqrt((t_1 ^ (180.0 / pi))));
	elseif (t_0 <= 0.0)
		tmp = (180.0 / pi) * atan((B * (-0.5 / (C - A))));
	else
		tmp = 2.0 * ((180.0 / (2.0 * pi)) * log(t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$0, -1e-29], N[(2.0 * N[Log[N[Sqrt[N[Power[t$95$1, N[(180.0 / Pi), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(180.0 / N[(2.0 * Pi), $MachinePrecision]), $MachinePrecision] * N[Log[t$95$1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -9.99999999999999943e-30

   1. Initial program 66.1%

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

   3. Simplified 87.2%

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

      1. div-sub 84.7%

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

   5. Applied egg-rr 84.7%

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

      1. add-log-exp 84.8%

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

      2. *-commutative 84.8%

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

      3. exp-prod 84.7%

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

      4. sub-div 87.2%

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

   7. Applied egg-rr 87.2%

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

      1. add-sqr-sqrt 87.2%

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

      2. log-prod 87.2%

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

   9. Applied egg-rr 87.2%

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

   11. Simplified 91.2%

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

   if -9.99999999999999943e-30 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 0.0

   1. Initial program 9.7%

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

   3. Simplified 9.2%

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

   4. Taylor expanded in B around 0 99.6%

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

      1. associate-*r/ 99.6%

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

   6. Simplified 99.6%

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

      1. div-inv 99.6%

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

      2. *-commutative 99.6%

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

   8. Applied egg-rr 99.6%

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

      1. add-exp-log 92.4%

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

      2. log-rec 92.4%

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

   10. Applied egg-rr 92.4%

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

       1. expm1-log1p-u 92.4%

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

       2. expm1-udef 9.7%

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

       3. associate-*l* 9.7%

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

       4. exp-neg 9.7%

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

       5. add-exp-log 9.7%

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

   12. Applied egg-rr 9.7%

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

       1. expm1-def 99.6%

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

       2. expm1-log1p 99.6%

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

       3. associate-*r/ 99.6%

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

       4. metadata-eval 99.6%

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

   14. Simplified 99.6%

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

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

   1. Initial program 55.4%

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

   3. Simplified 78.7%

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

      1. div-sub 74.1%

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

   5. Applied egg-rr 74.1%

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

      1. add-log-exp 75.9%

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

      2. *-commutative 75.9%

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

      3. exp-prod 75.3%

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

      4. sub-div 79.8%

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

   7. Applied egg-rr 79.8%

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

      1. sqr-pow 79.8%

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

      2. log-prod 79.8%

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

   9. Applied egg-rr 79.8%

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

   11. Simplified 84.3%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -1 \cdot 10^{-29}:\\ \;\;\;\;2 \cdot \log \left(\sqrt{{\left(e^{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}\right)}^{\left(\frac{180}{\pi}\right)}}\right)\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{180}{2 \cdot \pi} \cdot \log \left(e^{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}\right)\right)\\ \end{array} \]

Alternative 2: 88.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-29} \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;2 \cdot \left(\frac{180}{2 \cdot \pi} \cdot \log \left(e^{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (or (<= t_0 -1e-29) (not (<= t_0 0.0)))
     (*
      2.0
      (*
       (/ 180.0 (* 2.0 PI))
       (log (exp (atan (/ (- (- C A) (hypot B (- C A))) B))))))
     (* (/ 180.0 PI) (atan (* B (/ -0.5 (- C A))))))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -1e-29) || !(t_0 <= 0.0)) {
		tmp = 2.0 * ((180.0 / (2.0 * ((double) M_PI))) * log(exp(atan((((C - A) - hypot(B, (C - A))) / B)))));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / (C - A))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -1e-29) || !(t_0 <= 0.0)) {
		tmp = 2.0 * ((180.0 / (2.0 * Math.PI)) * Math.log(Math.exp(Math.atan((((C - A) - Math.hypot(B, (C - A))) / B)))));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / (C - A))));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if (t_0 <= -1e-29) or not (t_0 <= 0.0):
		tmp = 2.0 * ((180.0 / (2.0 * math.pi)) * math.log(math.exp(math.atan((((C - A) - math.hypot(B, (C - A))) / B)))))
	else:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / (C - A))))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if ((t_0 <= -1e-29) || !(t_0 <= 0.0))
		tmp = Float64(2.0 * Float64(Float64(180.0 / Float64(2.0 * pi)) * log(exp(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(C - A))) / B))))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / Float64(C - A)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if ((t_0 <= -1e-29) || ~((t_0 <= 0.0)))
		tmp = 2.0 * ((180.0 / (2.0 * pi)) * log(exp(atan((((C - A) - hypot(B, (C - A))) / B)))));
	else
		tmp = (180.0 / pi) * atan((B * (-0.5 / (C - A))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e-29], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(2.0 * N[(N[(180.0 / N[(2.0 * Pi), $MachinePrecision]), $MachinePrecision] * N[Log[N[Exp[N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -9.99999999999999943e-30 or 0.0 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 61.0%

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

   3. Simplified 83.1%

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

      1. div-sub 79.6%

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

   5. Applied egg-rr 79.6%

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

      1. add-log-exp 80.5%

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

      2. *-commutative 80.5%

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

      3. exp-prod 80.2%

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

      4. sub-div 83.7%

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

   7. Applied egg-rr 83.7%

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

      1. sqr-pow 83.7%

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

      2. log-prod 83.7%

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

   9. Applied egg-rr 83.7%

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

   11. Simplified 87.9%

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

   if -9.99999999999999943e-30 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 0.0

   1. Initial program 9.7%

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

   3. Simplified 9.2%

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

   4. Taylor expanded in B around 0 99.6%

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

      1. associate-*r/ 99.6%

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

   6. Simplified 99.6%

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

      1. div-inv 99.6%

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

      2. *-commutative 99.6%

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

   8. Applied egg-rr 99.6%

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

      1. add-exp-log 92.4%

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

      2. log-rec 92.4%

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

   10. Applied egg-rr 92.4%

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

       1. expm1-log1p-u 92.4%

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

       2. expm1-udef 9.7%

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

       3. associate-*l* 9.7%

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

       4. exp-neg 9.7%

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

       5. add-exp-log 9.7%

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

   12. Applied egg-rr 9.7%

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

       1. expm1-def 99.6%

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

       2. expm1-log1p 99.6%

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

       3. associate-*r/ 99.6%

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

       4. metadata-eval 99.6%

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

   14. Simplified 99.6%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -1 \cdot 10^{-29} \lor \neg \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0\right):\\ \;\;\;\;2 \cdot \left(\frac{180}{2 \cdot \pi} \cdot \log \left(e^{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \end{array} \]

Alternative 3: 81.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{+130}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9e+130)
   (* (/ 180.0 PI) (atan (* B (/ 0.5 A))))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9e+130) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / A)));
	} 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 <= -9e+130) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / A)));
	} 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 <= -9e+130:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / A)))
	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 <= -9e+130)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / A))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -9e+130)
		tmp = (180.0 / pi) * atan((B * (0.5 / A)));
	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, -9e+130], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -9.00000000000000078e130

   1. Initial program 8.5%

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

   3. Simplified 8.5%

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

   4. Taylor expanded in A around -inf 90.9%

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

      1. associate-*r/ 90.9%

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

   6. Simplified 90.9%

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

      1. clear-num 90.7%

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

      2. inv-pow 90.7%

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

      3. associate-/l* 90.8%

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

   8. Applied egg-rr 90.8%

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

      1. unpow-1 90.8%

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

      2. associate-/r/ 90.8%

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

   10. Simplified 90.8%

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

   11. Taylor expanded in A around 0 90.9%

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

       1. associate-*r/ 90.8%

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

       2. associate-*r/ 90.8%

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

       3. *-commutative 90.8%

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

       4. associate-*r/ 90.8%

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

       5. associate-*l/ 91.0%

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

   13. Simplified 91.0%

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

   if -9.00000000000000078e130 < A

   1. Initial program 62.7%

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

   3. Simplified 84.7%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9 \cdot 10^{+130}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 81.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{+130}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.15e+130)
   (* (/ 180.0 PI) (atan (* B (/ 0.5 A))))
   (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B (- C A)))) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+130) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / A)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(B, (C - A)))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+130) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / A)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, (C - A)))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.15e+130:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / A)))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(B, (C - A)))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.15e+130)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / A))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(B, Float64(C - A)))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.15e+130)
		tmp = (180.0 / pi) * atan((B * (0.5 / A)));
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(B, (C - A)))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.15e+130], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.15000000000000011e130

   1. Initial program 8.5%

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

   3. Simplified 8.5%

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

   4. Taylor expanded in A around -inf 90.9%

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

      1. associate-*r/ 90.9%

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

   6. Simplified 90.9%

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

      1. clear-num 90.7%

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

      2. inv-pow 90.7%

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

      3. associate-/l* 90.8%

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

   8. Applied egg-rr 90.8%

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

      1. unpow-1 90.8%

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

      2. associate-/r/ 90.8%

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

   10. Simplified 90.8%

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

   11. Taylor expanded in A around 0 90.9%

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

       1. associate-*r/ 90.8%

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

       2. associate-*r/ 90.8%

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

       3. *-commutative 90.8%

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

       4. associate-*r/ 90.8%

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

       5. associate-*l/ 91.0%

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

   13. Simplified 91.0%

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

   if -1.15000000000000011e130 < A

   1. Initial program 62.7%

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

   3. Simplified 84.7%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{+130}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right)\\ \end{array} \]

Alternative 5: 78.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3 \cdot 10^{+127}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq 9.2 \cdot 10^{-97}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3e+127)
   (* (/ 180.0 PI) (atan (* B (/ 0.5 A))))
   (if (<= A 9.2e-97)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (* 180.0 (/ (atan (/ (- (- A) (hypot B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3e+127) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / A)));
	} else if (A <= 9.2e-97) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3e+127) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / A)));
	} else if (A <= 9.2e-97) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(B, A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3e+127:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / A)))
	elif A <= 9.2e-97:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = 180.0 * (math.atan(((-A - math.hypot(B, A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3e+127)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / A))));
	elseif (A <= 9.2e-97)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(B, A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3e+127)
		tmp = (180.0 / pi) * atan((B * (0.5 / A)));
	elseif (A <= 9.2e-97)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3e+127], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9.2e-97], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.0000000000000002e127

   1. Initial program 8.5%

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

   3. Simplified 8.5%

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

   4. Taylor expanded in A around -inf 90.9%

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

      1. associate-*r/ 90.9%

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

   6. Simplified 90.9%

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

      1. clear-num 90.7%

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

      2. inv-pow 90.7%

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

      3. associate-/l* 90.8%

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

   8. Applied egg-rr 90.8%

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

      1. unpow-1 90.8%

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

      2. associate-/r/ 90.8%

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

   10. Simplified 90.8%

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

   11. Taylor expanded in A around 0 90.9%

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

       1. associate-*r/ 90.8%

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

       2. associate-*r/ 90.8%

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

       3. *-commutative 90.8%

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

       4. associate-*r/ 90.8%

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

       5. associate-*l/ 91.0%

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

   13. Simplified 91.0%

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

   if -3.0000000000000002e127 < A < 9.19999999999999976e-97

   1. Initial program 53.6%

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

   3. Simplified 80.8%

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

      1. add-log-exp 80.8%

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

   5. Applied egg-rr 80.8%

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

   6. Taylor expanded in A around 0 51.7%

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

      1. unpow2 51.7%

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

      2. unpow2 51.7%

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

      3. hypot-def 79.1%

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

   8. Simplified 79.1%

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

   if 9.19999999999999976e-97 < A

   1. Initial program 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in C around 0 79.3%

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

      1. associate-*r/ 79.3%

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

      2. mul-1-neg 79.3%

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

      3. +-commutative 79.3%

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

      4. unpow2 79.3%

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

      5. unpow2 79.3%

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

      6. hypot-def 90.4%

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

   6. Simplified 90.4%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3 \cdot 10^{+127}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq 9.2 \cdot 10^{-97}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 6: 73.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{+127}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.1e+127)
   (* (/ 180.0 PI) (atan (* B (/ 0.5 A))))
   (if (<= A 3.5e-94)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.1e+127) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / A)));
	} else if (A <= 3.5e-94) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.1e+127) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / A)));
	} else if (A <= 3.5e-94) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.1e+127:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / A)))
	elif A <= 3.5e-94:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.1e+127)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / A))));
	elseif (A <= 3.5e-94)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.1e+127)
		tmp = (180.0 / pi) * atan((B * (0.5 / A)));
	elseif (A <= 3.5e-94)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.1e+127], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.5e-94], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.09999999999999992e127

   1. Initial program 8.5%

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

   3. Simplified 8.5%

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

   4. Taylor expanded in A around -inf 90.9%

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

      1. associate-*r/ 90.9%

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

   6. Simplified 90.9%

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

      1. clear-num 90.7%

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

      2. inv-pow 90.7%

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

      3. associate-/l* 90.8%

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

   8. Applied egg-rr 90.8%

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

      1. unpow-1 90.8%

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

      2. associate-/r/ 90.8%

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

   10. Simplified 90.8%

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

   11. Taylor expanded in A around 0 90.9%

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

       1. associate-*r/ 90.8%

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

       2. associate-*r/ 90.8%

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

       3. *-commutative 90.8%

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

       4. associate-*r/ 90.8%

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

       5. associate-*l/ 91.0%

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

   13. Simplified 91.0%

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

   if -2.09999999999999992e127 < A < 3.49999999999999998e-94

   1. Initial program 53.9%

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

   3. Simplified 53.9%

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

   4. Taylor expanded in A around 0 52.0%

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

      1. unpow2 52.0%

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

      2. unpow2 52.0%

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

      3. hypot-def 79.2%

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

   6. Simplified 79.2%

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

   if 3.49999999999999998e-94 < A

   1. Initial program 79.1%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in B around inf 85.8%

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

      1. +-commutative 85.8%

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

      2. associate--r+ 85.8%

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

      3. div-sub 85.9%

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

   6. Simplified 85.9%

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

   7. Taylor expanded in C around 0 86.0%

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

      1. associate-*r/ 86.0%

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

      2. neg-mul-1 86.0%

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

   9. Simplified 86.0%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{+127}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 73.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.4 \cdot 10^{+129}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.4e+129)
   (* (/ 180.0 PI) (atan (* B (/ 0.5 A))))
   (if (<= A 3.5e-94)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.4e+129) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / A)));
	} else if (A <= 3.5e-94) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.4e+129) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / A)));
	} else if (A <= 3.5e-94) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.4e+129:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / A)))
	elif A <= 3.5e-94:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.4e+129)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / A))));
	elseif (A <= 3.5e-94)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.4e+129)
		tmp = (180.0 / pi) * atan((B * (0.5 / A)));
	elseif (A <= 3.5e-94)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.4e+129], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.5e-94], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.4000000000000002e129

   1. Initial program 8.5%

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

   3. Simplified 8.5%

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

   4. Taylor expanded in A around -inf 90.9%

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

      1. associate-*r/ 90.9%

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

   6. Simplified 90.9%

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

      1. clear-num 90.7%

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

      2. inv-pow 90.7%

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

      3. associate-/l* 90.8%

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

   8. Applied egg-rr 90.8%

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

      1. unpow-1 90.8%

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

      2. associate-/r/ 90.8%

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

   10. Simplified 90.8%

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

   11. Taylor expanded in A around 0 90.9%

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

       1. associate-*r/ 90.8%

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

       2. associate-*r/ 90.8%

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

       3. *-commutative 90.8%

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

       4. associate-*r/ 90.8%

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

       5. associate-*l/ 91.0%

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

   13. Simplified 91.0%

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

   if -5.4000000000000002e129 < A < 3.49999999999999998e-94

   1. Initial program 53.9%

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

   3. Simplified 80.9%

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

      1. add-log-exp 80.9%

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

   5. Applied egg-rr 80.9%

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

   6. Taylor expanded in A around 0 52.0%

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

      1. unpow2 52.0%

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

      2. unpow2 52.0%

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

      3. hypot-def 79.2%

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

   8. Simplified 79.2%

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

   if 3.49999999999999998e-94 < A

   1. Initial program 79.1%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in B around inf 85.8%

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

      1. +-commutative 85.8%

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

      2. associate--r+ 85.8%

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

      3. div-sub 85.9%

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

   6. Simplified 85.9%

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

   7. Taylor expanded in C around 0 86.0%

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

      1. associate-*r/ 86.0%

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

      2. neg-mul-1 86.0%

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

   9. Simplified 86.0%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.4 \cdot 10^{+129}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq 3.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 47.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;B \leq -3 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2.9 \cdot 10^{+20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -7 \cdot 10^{-203}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 1.32 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-13}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan 1.0) PI))))
   (if (<= B -3e+69)
     t_0
     (if (<= B -2.9e+20)
       (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
       (if (<= B -1e-63)
         t_0
         (if (<= B -7e-203)
           (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
           (if (<= B 1.32e-216)
             (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
             (if (<= B 4.6e-13)
               (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
               (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(1.0) / ((double) M_PI));
	double tmp;
	if (B <= -3e+69) {
		tmp = t_0;
	} else if (B <= -2.9e+20) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (B <= -1e-63) {
		tmp = t_0;
	} else if (B <= -7e-203) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else if (B <= 1.32e-216) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (B <= 4.6e-13) {
		tmp = 180.0 * (atan(((A * -2.0) / 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 t_0 = 180.0 * (Math.atan(1.0) / Math.PI);
	double tmp;
	if (B <= -3e+69) {
		tmp = t_0;
	} else if (B <= -2.9e+20) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (B <= -1e-63) {
		tmp = t_0;
	} else if (B <= -7e-203) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else if (B <= 1.32e-216) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (B <= 4.6e-13) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(1.0) / math.pi)
	tmp = 0
	if B <= -3e+69:
		tmp = t_0
	elif B <= -2.9e+20:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif B <= -1e-63:
		tmp = t_0
	elif B <= -7e-203:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	elif B <= 1.32e-216:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif B <= 4.6e-13:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(1.0) / pi))
	tmp = 0.0
	if (B <= -3e+69)
		tmp = t_0;
	elseif (B <= -2.9e+20)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (B <= -1e-63)
		tmp = t_0;
	elseif (B <= -7e-203)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	elseif (B <= 1.32e-216)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (B <= 4.6e-13)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(1.0) / pi);
	tmp = 0.0;
	if (B <= -3e+69)
		tmp = t_0;
	elseif (B <= -2.9e+20)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (B <= -1e-63)
		tmp = t_0;
	elseif (B <= -7e-203)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	elseif (B <= 1.32e-216)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (B <= 4.6e-13)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3e+69], t$95$0, If[LessEqual[B, -2.9e+20], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1e-63], t$95$0, If[LessEqual[B, -7e-203], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.32e-216], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.6e-13], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -2.99999999999999983e69 or -2.9e20 < B < -1.00000000000000007e-63

   1. Initial program 52.9%

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

   3. Simplified 52.9%

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

   4. Taylor expanded in B around -inf 64.1%

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

   if -2.99999999999999983e69 < B < -2.9e20

   1. Initial program 45.3%

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

   3. Simplified 45.3%

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

   4. Taylor expanded in A around -inf 72.1%

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

      1. associate-*r/ 72.1%

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

   6. Simplified 72.1%

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

   if -1.00000000000000007e-63 < B < -7.0000000000000003e-203

   1. Initial program 44.1%

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

   3. Simplified 63.8%

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

   4. Taylor expanded in B around 0 55.9%

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

      1. associate-*r/ 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in C around inf 55.9%

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

   if -7.0000000000000003e-203 < B < 1.31999999999999997e-216

   1. Initial program 62.9%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in C around -inf 55.0%

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

   if 1.31999999999999997e-216 < B < 4.59999999999999958e-13

   1. Initial program 75.6%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in A around inf 48.9%

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

      1. associate-*r/ 48.9%

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

      2. *-commutative 48.9%

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

   6. Simplified 48.9%

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

   if 4.59999999999999958e-13 < B

   1. Initial program 49.7%

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

   3. Simplified 49.7%

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

   4. Taylor expanded in B around inf 67.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3 \cdot 10^{+69}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.9 \cdot 10^{+20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7 \cdot 10^{-203}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 1.32 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.6 \cdot 10^{-13}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 9: 47.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;B \leq -3 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2.9 \cdot 10^{+20}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq -2.6 \cdot 10^{-61}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-203}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-214}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan 1.0) PI))))
   (if (<= B -3e+69)
     t_0
     (if (<= B -2.9e+20)
       (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
       (if (<= B -2.6e-61)
         t_0
         (if (<= B -1.25e-203)
           (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
           (if (<= B 1.9e-214)
             (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
             (if (<= B 5e-15)
               (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
               (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(1.0) / ((double) M_PI));
	double tmp;
	if (B <= -3e+69) {
		tmp = t_0;
	} else if (B <= -2.9e+20) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (B <= -2.6e-61) {
		tmp = t_0;
	} else if (B <= -1.25e-203) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else if (B <= 1.9e-214) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (B <= 5e-15) {
		tmp = 180.0 * (atan(((A * -2.0) / 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 t_0 = 180.0 * (Math.atan(1.0) / Math.PI);
	double tmp;
	if (B <= -3e+69) {
		tmp = t_0;
	} else if (B <= -2.9e+20) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (B <= -2.6e-61) {
		tmp = t_0;
	} else if (B <= -1.25e-203) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else if (B <= 1.9e-214) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (B <= 5e-15) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(1.0) / math.pi)
	tmp = 0
	if B <= -3e+69:
		tmp = t_0
	elif B <= -2.9e+20:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif B <= -2.6e-61:
		tmp = t_0
	elif B <= -1.25e-203:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	elif B <= 1.9e-214:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif B <= 5e-15:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(1.0) / pi))
	tmp = 0.0
	if (B <= -3e+69)
		tmp = t_0;
	elseif (B <= -2.9e+20)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (B <= -2.6e-61)
		tmp = t_0;
	elseif (B <= -1.25e-203)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	elseif (B <= 1.9e-214)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (B <= 5e-15)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(1.0) / pi);
	tmp = 0.0;
	if (B <= -3e+69)
		tmp = t_0;
	elseif (B <= -2.9e+20)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (B <= -2.6e-61)
		tmp = t_0;
	elseif (B <= -1.25e-203)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	elseif (B <= 1.9e-214)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (B <= 5e-15)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3e+69], t$95$0, If[LessEqual[B, -2.9e+20], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.6e-61], t$95$0, If[LessEqual[B, -1.25e-203], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.9e-214], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5e-15], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -2.99999999999999983e69 or -2.9e20 < B < -2.6000000000000001e-61

   1. Initial program 52.9%

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

   3. Simplified 52.9%

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

   4. Taylor expanded in B around -inf 64.1%

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

   if -2.99999999999999983e69 < B < -2.9e20

   1. Initial program 45.3%

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

   3. Simplified 44.7%

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

      1. add-log-exp 45.0%

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

   5. Applied egg-rr 45.0%

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

   6. Taylor expanded in A around -inf 72.2%

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

   if -2.6000000000000001e-61 < B < -1.25e-203

   1. Initial program 44.1%

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

   3. Simplified 63.8%

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

   4. Taylor expanded in B around 0 55.9%

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

      1. associate-*r/ 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in C around inf 55.9%

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

   if -1.25e-203 < B < 1.9000000000000001e-214

   1. Initial program 62.9%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in C around -inf 55.0%

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

   if 1.9000000000000001e-214 < B < 4.99999999999999999e-15

   1. Initial program 75.6%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in A around inf 48.9%

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

      1. associate-*r/ 48.9%

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

      2. *-commutative 48.9%

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

   6. Simplified 48.9%

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

   if 4.99999999999999999e-15 < B

   1. Initial program 49.7%

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

   3. Simplified 49.7%

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

   4. Taylor expanded in B around inf 67.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3 \cdot 10^{+69}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.9 \cdot 10^{+20}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq -2.6 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-203}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-214}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 10: 47.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;B \leq -3.1 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.8 \cdot 10^{+18}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;B \leq -3.75 \cdot 10^{-62}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3.1 \cdot 10^{-203}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-213}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-13}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan 1.0) PI))))
   (if (<= B -3.1e+69)
     t_0
     (if (<= B -1.8e+18)
       (* (/ 180.0 PI) (atan (* B (/ 0.5 A))))
       (if (<= B -3.75e-62)
         t_0
         (if (<= B -3.1e-203)
           (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
           (if (<= B 1.9e-213)
             (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
             (if (<= B 6.2e-13)
               (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
               (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(1.0) / ((double) M_PI));
	double tmp;
	if (B <= -3.1e+69) {
		tmp = t_0;
	} else if (B <= -1.8e+18) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / A)));
	} else if (B <= -3.75e-62) {
		tmp = t_0;
	} else if (B <= -3.1e-203) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else if (B <= 1.9e-213) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (B <= 6.2e-13) {
		tmp = 180.0 * (atan(((A * -2.0) / 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 t_0 = 180.0 * (Math.atan(1.0) / Math.PI);
	double tmp;
	if (B <= -3.1e+69) {
		tmp = t_0;
	} else if (B <= -1.8e+18) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / A)));
	} else if (B <= -3.75e-62) {
		tmp = t_0;
	} else if (B <= -3.1e-203) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else if (B <= 1.9e-213) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (B <= 6.2e-13) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(1.0) / math.pi)
	tmp = 0
	if B <= -3.1e+69:
		tmp = t_0
	elif B <= -1.8e+18:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / A)))
	elif B <= -3.75e-62:
		tmp = t_0
	elif B <= -3.1e-203:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	elif B <= 1.9e-213:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif B <= 6.2e-13:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(1.0) / pi))
	tmp = 0.0
	if (B <= -3.1e+69)
		tmp = t_0;
	elseif (B <= -1.8e+18)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / A))));
	elseif (B <= -3.75e-62)
		tmp = t_0;
	elseif (B <= -3.1e-203)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	elseif (B <= 1.9e-213)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (B <= 6.2e-13)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(1.0) / pi);
	tmp = 0.0;
	if (B <= -3.1e+69)
		tmp = t_0;
	elseif (B <= -1.8e+18)
		tmp = (180.0 / pi) * atan((B * (0.5 / A)));
	elseif (B <= -3.75e-62)
		tmp = t_0;
	elseif (B <= -3.1e-203)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	elseif (B <= 1.9e-213)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (B <= 6.2e-13)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3.1e+69], t$95$0, If[LessEqual[B, -1.8e+18], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.75e-62], t$95$0, If[LessEqual[B, -3.1e-203], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.9e-213], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.2e-13], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -3.0999999999999998e69 or -1.8e18 < B < -3.75000000000000015e-62

   1. Initial program 52.9%

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

   3. Simplified 52.9%

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

   4. Taylor expanded in B around -inf 64.1%

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

   if -3.0999999999999998e69 < B < -1.8e18

   1. Initial program 45.3%

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

   3. Simplified 45.3%

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

   4. Taylor expanded in A around -inf 72.1%

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

      1. associate-*r/ 72.1%

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

   6. Simplified 72.1%

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

      1. clear-num 72.1%

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

      2. inv-pow 72.1%

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

      3. associate-/l* 72.2%

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

   8. Applied egg-rr 72.2%

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

      1. unpow-1 72.2%

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

      2. associate-/r/ 72.2%

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

   10. Simplified 72.2%

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

   11. Taylor expanded in A around 0 72.1%

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

       1. associate-*r/ 72.2%

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

       2. associate-*r/ 72.2%

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

       3. *-commutative 72.2%

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

       4. associate-*r/ 72.4%

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

       5. associate-*l/ 72.4%

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

   13. Simplified 72.4%

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

   if -3.75000000000000015e-62 < B < -3.09999999999999977e-203

   1. Initial program 44.1%

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

   3. Simplified 63.8%

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

   4. Taylor expanded in B around 0 55.9%

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

      1. associate-*r/ 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in C around inf 55.9%

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

   if -3.09999999999999977e-203 < B < 1.9e-213

   1. Initial program 62.9%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in C around -inf 55.0%

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

   if 1.9e-213 < B < 6.1999999999999998e-13

   1. Initial program 75.6%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in A around inf 48.9%

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

      1. associate-*r/ 48.9%

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

      2. *-commutative 48.9%

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

   6. Simplified 48.9%

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

   if 6.1999999999999998e-13 < B

   1. Initial program 49.7%

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

   3. Simplified 49.7%

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

   4. Taylor expanded in B around inf 67.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.1 \cdot 10^{+69}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.8 \cdot 10^{+18}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;B \leq -3.75 \cdot 10^{-62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.1 \cdot 10^{-203}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 1.9 \cdot 10^{-213}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-13}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11: 47.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;B \leq -4.5 \cdot 10^{+70}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-62}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2.7 \cdot 10^{-207}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan 1.0) PI))))
   (if (<= B -4.5e+70)
     t_0
     (if (<= B -2.5e+19)
       (* (/ 180.0 PI) (atan (* B (/ 0.5 A))))
       (if (<= B -7.5e-62)
         t_0
         (if (<= B -2.7e-207)
           (* (/ 180.0 PI) (atan (/ (* B -0.5) C)))
           (if (<= B 4.2e-216)
             (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
             (if (<= B 8e-15)
               (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
               (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(1.0) / ((double) M_PI));
	double tmp;
	if (B <= -4.5e+70) {
		tmp = t_0;
	} else if (B <= -2.5e+19) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / A)));
	} else if (B <= -7.5e-62) {
		tmp = t_0;
	} else if (B <= -2.7e-207) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	} else if (B <= 4.2e-216) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (B <= 8e-15) {
		tmp = 180.0 * (atan(((A * -2.0) / 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 t_0 = 180.0 * (Math.atan(1.0) / Math.PI);
	double tmp;
	if (B <= -4.5e+70) {
		tmp = t_0;
	} else if (B <= -2.5e+19) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / A)));
	} else if (B <= -7.5e-62) {
		tmp = t_0;
	} else if (B <= -2.7e-207) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	} else if (B <= 4.2e-216) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (B <= 8e-15) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(1.0) / math.pi)
	tmp = 0
	if B <= -4.5e+70:
		tmp = t_0
	elif B <= -2.5e+19:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / A)))
	elif B <= -7.5e-62:
		tmp = t_0
	elif B <= -2.7e-207:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	elif B <= 4.2e-216:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif B <= 8e-15:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(1.0) / pi))
	tmp = 0.0
	if (B <= -4.5e+70)
		tmp = t_0;
	elseif (B <= -2.5e+19)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / A))));
	elseif (B <= -7.5e-62)
		tmp = t_0;
	elseif (B <= -2.7e-207)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	elseif (B <= 4.2e-216)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (B <= 8e-15)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(1.0) / pi);
	tmp = 0.0;
	if (B <= -4.5e+70)
		tmp = t_0;
	elseif (B <= -2.5e+19)
		tmp = (180.0 / pi) * atan((B * (0.5 / A)));
	elseif (B <= -7.5e-62)
		tmp = t_0;
	elseif (B <= -2.7e-207)
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	elseif (B <= 4.2e-216)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (B <= 8e-15)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -4.5e+70], t$95$0, If[LessEqual[B, -2.5e+19], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7.5e-62], t$95$0, If[LessEqual[B, -2.7e-207], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.2e-216], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8e-15], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if B < -4.4999999999999999e70 or -2.5e19 < B < -7.5000000000000003e-62

   1. Initial program 52.9%

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

   3. Simplified 52.9%

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

   4. Taylor expanded in B around -inf 64.1%

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

   if -4.4999999999999999e70 < B < -2.5e19

   1. Initial program 45.3%

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

   3. Simplified 45.3%

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

   4. Taylor expanded in A around -inf 72.1%

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

      1. associate-*r/ 72.1%

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

   6. Simplified 72.1%

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

      1. clear-num 72.1%

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

      2. inv-pow 72.1%

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

      3. associate-/l* 72.2%

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

   8. Applied egg-rr 72.2%

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

      1. unpow-1 72.2%

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

      2. associate-/r/ 72.2%

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

   10. Simplified 72.2%

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

   11. Taylor expanded in A around 0 72.1%

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

       1. associate-*r/ 72.2%

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

       2. associate-*r/ 72.2%

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

       3. *-commutative 72.2%

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

       4. associate-*r/ 72.4%

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

       5. associate-*l/ 72.4%

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

   13. Simplified 72.4%

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

   if -7.5000000000000003e-62 < B < -2.7e-207

   1. Initial program 44.1%

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

   3. Simplified 63.8%

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

   4. Taylor expanded in B around 0 55.9%

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

      1. associate-*r/ 55.9%

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

   6. Simplified 55.9%

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

      1. div-inv 56.0%

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

      2. *-commutative 56.0%

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

   8. Applied egg-rr 56.0%

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

   9. Taylor expanded in C around inf 55.9%

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

       1. associate-*r/ 55.9%

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

       2. *-commutative 55.9%

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

   11. Simplified 55.9%

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

   if -2.7e-207 < B < 4.2000000000000003e-216

   1. Initial program 62.9%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in C around -inf 55.0%

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

   if 4.2000000000000003e-216 < B < 8.0000000000000006e-15

   1. Initial program 75.6%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in A around inf 48.9%

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

      1. associate-*r/ 48.9%

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

      2. *-commutative 48.9%

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

   6. Simplified 48.9%

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

   if 8.0000000000000006e-15 < B

   1. Initial program 49.7%

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

   3. Simplified 49.7%

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

   4. Taylor expanded in B around inf 67.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.5 \cdot 10^{+70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.7 \cdot 10^{-207}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12: 47.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;B \leq -3 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3.2 \cdot 10^{+20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-55}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.75 \cdot 10^{-213}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan 1.0) PI))))
   (if (<= B -3e+69)
     t_0
     (if (<= B -3.2e+20)
       (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
       (if (<= B -1.25e-55)
         t_0
         (if (<= B 2.75e-213)
           (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
           (if (<= B 4.8e-14)
             (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
             (* 180.0 (/ (atan -1.0) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(1.0) / ((double) M_PI));
	double tmp;
	if (B <= -3e+69) {
		tmp = t_0;
	} else if (B <= -3.2e+20) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (B <= -1.25e-55) {
		tmp = t_0;
	} else if (B <= 2.75e-213) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (B <= 4.8e-14) {
		tmp = 180.0 * (atan(((A * -2.0) / 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 t_0 = 180.0 * (Math.atan(1.0) / Math.PI);
	double tmp;
	if (B <= -3e+69) {
		tmp = t_0;
	} else if (B <= -3.2e+20) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (B <= -1.25e-55) {
		tmp = t_0;
	} else if (B <= 2.75e-213) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (B <= 4.8e-14) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(1.0) / math.pi)
	tmp = 0
	if B <= -3e+69:
		tmp = t_0
	elif B <= -3.2e+20:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif B <= -1.25e-55:
		tmp = t_0
	elif B <= 2.75e-213:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif B <= 4.8e-14:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(1.0) / pi))
	tmp = 0.0
	if (B <= -3e+69)
		tmp = t_0;
	elseif (B <= -3.2e+20)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (B <= -1.25e-55)
		tmp = t_0;
	elseif (B <= 2.75e-213)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (B <= 4.8e-14)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(1.0) / pi);
	tmp = 0.0;
	if (B <= -3e+69)
		tmp = t_0;
	elseif (B <= -3.2e+20)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (B <= -1.25e-55)
		tmp = t_0;
	elseif (B <= 2.75e-213)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (B <= 4.8e-14)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3e+69], t$95$0, If[LessEqual[B, -3.2e+20], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.25e-55], t$95$0, If[LessEqual[B, 2.75e-213], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.8e-14], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.99999999999999983e69 or -3.2e20 < B < -1.25e-55

   1. Initial program 52.2%

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

   3. Simplified 52.2%

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

   4. Taylor expanded in B around -inf 64.7%

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

   if -2.99999999999999983e69 < B < -3.2e20

   1. Initial program 45.3%

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

   3. Simplified 45.3%

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

   4. Taylor expanded in A around -inf 72.1%

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

      1. associate-*r/ 72.1%

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

   6. Simplified 72.1%

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

   if -1.25e-55 < B < 2.75000000000000004e-213

   1. Initial program 55.2%

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

   3. Simplified 55.1%

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

   4. Taylor expanded in C around -inf 39.8%

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

   if 2.75000000000000004e-213 < B < 4.8e-14

   1. Initial program 75.6%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in A around inf 48.9%

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

      1. associate-*r/ 48.9%

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

      2. *-commutative 48.9%

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

   6. Simplified 48.9%

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

   if 4.8e-14 < B

   1. Initial program 49.7%

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

   3. Simplified 49.7%

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

   4. Taylor expanded in B around inf 67.8%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3 \cdot 10^{+69}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.2 \cdot 10^{+20}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.25 \cdot 10^{-55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.75 \cdot 10^{-213}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 13: 47.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;B \leq -3 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.3 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan 1.0) PI))))
   (if (<= B -3e+69)
     t_0
     (if (<= B -2.3e+19)
       (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
       (if (<= B -4e-57)
         t_0
         (if (<= B 4.3e-32)
           (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
           (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(1.0) / ((double) M_PI));
	double tmp;
	if (B <= -3e+69) {
		tmp = t_0;
	} else if (B <= -2.3e+19) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (B <= -4e-57) {
		tmp = t_0;
	} else if (B <= 4.3e-32) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(1.0) / Math.PI);
	double tmp;
	if (B <= -3e+69) {
		tmp = t_0;
	} else if (B <= -2.3e+19) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (B <= -4e-57) {
		tmp = t_0;
	} else if (B <= 4.3e-32) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(1.0) / math.pi)
	tmp = 0
	if B <= -3e+69:
		tmp = t_0
	elif B <= -2.3e+19:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif B <= -4e-57:
		tmp = t_0
	elif B <= 4.3e-32:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(1.0) / pi))
	tmp = 0.0
	if (B <= -3e+69)
		tmp = t_0;
	elseif (B <= -2.3e+19)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (B <= -4e-57)
		tmp = t_0;
	elseif (B <= 4.3e-32)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(1.0) / pi);
	tmp = 0.0;
	if (B <= -3e+69)
		tmp = t_0;
	elseif (B <= -2.3e+19)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (B <= -4e-57)
		tmp = t_0;
	elseif (B <= 4.3e-32)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3e+69], t$95$0, If[LessEqual[B, -2.3e+19], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -4e-57], t$95$0, If[LessEqual[B, 4.3e-32], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.99999999999999983e69 or -2.3e19 < B < -3.99999999999999982e-57

   1. Initial program 52.2%

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

   3. Simplified 52.2%

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

   4. Taylor expanded in B around -inf 64.7%

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

   if -2.99999999999999983e69 < B < -2.3e19

   1. Initial program 45.3%

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

   3. Simplified 45.3%

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

   4. Taylor expanded in A around -inf 72.1%

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

      1. associate-*r/ 72.1%

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

   6. Simplified 72.1%

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

   if -3.99999999999999982e-57 < B < 4.2999999999999999e-32

   1. Initial program 62.7%

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

   3. Simplified 62.6%

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

   4. Taylor expanded in C around -inf 38.0%

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

   if 4.2999999999999999e-32 < B

   1. Initial program 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in B around inf 66.3%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3 \cdot 10^{+69}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -4 \cdot 10^{-57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.3 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 14: 51.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{if}\;B \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.05 \cdot 10^{-201}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{-216}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (+ B C) B)))))
   (if (<= B -6.5e-102)
     t_0
     (if (<= B -1.05e-201)
       (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
       (if (<= B 5.6e-216)
         t_0
         (if (<= B 2.4e-15)
           (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
           (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	double tmp;
	if (B <= -6.5e-102) {
		tmp = t_0;
	} else if (B <= -1.05e-201) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else if (B <= 5.6e-216) {
		tmp = t_0;
	} else if (B <= 2.4e-15) {
		tmp = 180.0 * (atan(((A * -2.0) / 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 t_0 = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	double tmp;
	if (B <= -6.5e-102) {
		tmp = t_0;
	} else if (B <= -1.05e-201) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else if (B <= 5.6e-216) {
		tmp = t_0;
	} else if (B <= 2.4e-15) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} 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(((B + C) / B))
	tmp = 0
	if B <= -6.5e-102:
		tmp = t_0
	elif B <= -1.05e-201:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	elif B <= 5.6e-216:
		tmp = t_0
	elif B <= 2.4e-15:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	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(B + C) / B)))
	tmp = 0.0
	if (B <= -6.5e-102)
		tmp = t_0;
	elseif (B <= -1.05e-201)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	elseif (B <= 5.6e-216)
		tmp = t_0;
	elseif (B <= 2.4e-15)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(((B + C) / B));
	tmp = 0.0;
	if (B <= -6.5e-102)
		tmp = t_0;
	elseif (B <= -1.05e-201)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	elseif (B <= 5.6e-216)
		tmp = t_0;
	elseif (B <= 2.4e-15)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	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[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -6.5e-102], t$95$0, If[LessEqual[B, -1.05e-201], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.6e-216], t$95$0, If[LessEqual[B, 2.4e-15], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -6.5000000000000003e-102 or -1.05000000000000006e-201 < B < 5.6e-216

   1. Initial program 56.6%

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

   3. Simplified 76.3%

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

      1. add-log-exp 77.1%

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

   5. Applied egg-rr 77.1%

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

   6. Taylor expanded in A around 0 47.8%

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

      1. unpow2 47.8%

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

      2. unpow2 47.8%

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

      3. hypot-def 66.6%

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

   8. Simplified 66.6%

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

   9. Taylor expanded in B around -inf 61.3%

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

       1. +-commutative 61.3%

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

   11. Simplified 61.3%

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

   if -6.5000000000000003e-102 < B < -1.05000000000000006e-201

   1. Initial program 30.7%

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

   3. Simplified 56.2%

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

   4. Taylor expanded in B around 0 67.9%

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

      1. associate-*r/ 67.9%

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

   6. Simplified 67.9%

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

   7. Taylor expanded in C around inf 67.9%

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

   if 5.6e-216 < B < 2.39999999999999995e-15

   1. Initial program 75.6%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in A around inf 48.9%

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

      1. associate-*r/ 48.9%

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

      2. *-commutative 48.9%

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

   6. Simplified 48.9%

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

   if 2.39999999999999995e-15 < B

   1. Initial program 49.7%

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

   3. Simplified 49.7%

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

   4. Taylor expanded in B around inf 67.8%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;B \leq -1.05 \cdot 10^{-201}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 5.6 \cdot 10^{-216}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 15: 54.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{if}\;B \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-202}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-217}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-133}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (+ B C) B)))))
   (if (<= B -6.5e-102)
     t_0
     (if (<= B -8.5e-202)
       (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
       (if (<= B 9.2e-217)
         t_0
         (if (<= B 1.45e-133)
           (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
           (* (/ 180.0 PI) (atan (/ (- C B) B)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	double tmp;
	if (B <= -6.5e-102) {
		tmp = t_0;
	} else if (B <= -8.5e-202) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else if (B <= 9.2e-217) {
		tmp = t_0;
	} else if (B <= 1.45e-133) {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	double tmp;
	if (B <= -6.5e-102) {
		tmp = t_0;
	} else if (B <= -8.5e-202) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else if (B <= 9.2e-217) {
		tmp = t_0;
	} else if (B <= 1.45e-133) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(((B + C) / B))
	tmp = 0
	if B <= -6.5e-102:
		tmp = t_0
	elif B <= -8.5e-202:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	elif B <= 9.2e-217:
		tmp = t_0
	elif B <= 1.45e-133:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)))
	tmp = 0.0
	if (B <= -6.5e-102)
		tmp = t_0;
	elseif (B <= -8.5e-202)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	elseif (B <= 9.2e-217)
		tmp = t_0;
	elseif (B <= 1.45e-133)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(((B + C) / B));
	tmp = 0.0;
	if (B <= -6.5e-102)
		tmp = t_0;
	elseif (B <= -8.5e-202)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	elseif (B <= 9.2e-217)
		tmp = t_0;
	elseif (B <= 1.45e-133)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	else
		tmp = (180.0 / pi) * atan(((C - B) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -6.5e-102], t$95$0, If[LessEqual[B, -8.5e-202], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.2e-217], t$95$0, If[LessEqual[B, 1.45e-133], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -6.5000000000000003e-102 or -8.49999999999999963e-202 < B < 9.20000000000000019e-217

   1. Initial program 56.6%

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

   3. Simplified 76.3%

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

      1. add-log-exp 77.1%

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

   5. Applied egg-rr 77.1%

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

   6. Taylor expanded in A around 0 47.8%

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

      1. unpow2 47.8%

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

      2. unpow2 47.8%

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

      3. hypot-def 66.6%

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

   8. Simplified 66.6%

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

   9. Taylor expanded in B around -inf 61.3%

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

       1. +-commutative 61.3%

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

   11. Simplified 61.3%

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

   if -6.5000000000000003e-102 < B < -8.49999999999999963e-202

   1. Initial program 30.7%

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

   3. Simplified 56.2%

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

   4. Taylor expanded in B around 0 67.9%

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

      1. associate-*r/ 67.9%

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

   6. Simplified 67.9%

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

   7. Taylor expanded in C around inf 67.9%

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

   if 9.20000000000000019e-217 < B < 1.4499999999999999e-133

   1. Initial program 76.1%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in A around inf 57.0%

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

      1. associate-*r/ 57.0%

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

      2. *-commutative 57.0%

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

   6. Simplified 57.0%

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

   if 1.4499999999999999e-133 < B

   1. Initial program 57.4%

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

   3. Simplified 80.5%

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

      1. add-log-exp 80.7%

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

   5. Applied egg-rr 80.7%

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

   6. Taylor expanded in A around 0 49.2%

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

      1. unpow2 49.2%

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

      2. unpow2 49.2%

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

      3. hypot-def 69.9%

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

   8. Simplified 69.9%

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

   9. Taylor expanded in C around 0 67.6%

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

       1. mul-1-neg 67.6%

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

       2. unsub-neg 67.6%

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

   11. Simplified 67.6%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;B \leq -8.5 \cdot 10^{-202}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-217}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-133}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]

Alternative 16: 62.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -6.2 \cdot 10^{-102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.35 \cdot 10^{-200}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-72}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B -6.2e-102)
     t_0
     (if (<= B -1.35e-200)
       (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
       (if (<= B 1.2e-72) t_0 (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (B <= -6.2e-102) {
		tmp = t_0;
	} else if (B <= -1.35e-200) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else if (B <= 1.2e-72) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= -6.2e-102) {
		tmp = t_0;
	} else if (B <= -1.35e-200) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else if (B <= 1.2e-72) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= -6.2e-102:
		tmp = t_0
	elif B <= -1.35e-200:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	elif B <= 1.2e-72:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= -6.2e-102)
		tmp = t_0;
	elseif (B <= -1.35e-200)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	elseif (B <= 1.2e-72)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= -6.2e-102)
		tmp = t_0;
	elseif (B <= -1.35e-200)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	elseif (B <= 1.2e-72)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -6.2e-102], t$95$0, If[LessEqual[B, -1.35e-200], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.2e-72], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -6.20000000000000026e-102 or -1.3500000000000001e-200 < B < 1.2e-72

   1. Initial program 60.7%

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

   3. Simplified 60.6%

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

   4. Taylor expanded in B around -inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. div-sub 71.1%

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

   6. Simplified 71.1%

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

   if -6.20000000000000026e-102 < B < -1.3500000000000001e-200

   1. Initial program 27.0%

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

   3. Simplified 53.6%

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

   4. Taylor expanded in B around 0 71.8%

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

      1. associate-*r/ 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in C around inf 66.4%

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

   if 1.2e-72 < B

   1. Initial program 54.5%

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

   3. Simplified 54.4%

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

   4. Taylor expanded in B around inf 78.1%

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

      1. +-commutative 78.1%

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

      2. associate--r+ 78.1%

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

      3. div-sub 78.1%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in C around 0 73.9%

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

      1. associate-*r/ 73.9%

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

      2. neg-mul-1 73.9%

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

   9. Simplified 73.9%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.2 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.35 \cdot 10^{-200}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 17: 65.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -6.4 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.1 \cdot 10^{-199}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t_0 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -6.4e-102)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B -3.1e-199)
       (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
       (* 180.0 (/ (atan (+ t_0 -1.0)) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -6.4e-102) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= -3.1e-199) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else {
		tmp = 180.0 * (atan((t_0 + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -6.4e-102) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= -3.1e-199) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else {
		tmp = 180.0 * (Math.atan((t_0 + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -6.4e-102:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= -3.1e-199:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	else:
		tmp = 180.0 * (math.atan((t_0 + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -6.4e-102)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= -3.1e-199)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -6.4e-102)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= -3.1e-199)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	else
		tmp = 180.0 * (atan((t_0 + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -6.4e-102], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.1e-199], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -6.39999999999999973e-102

   1. Initial program 53.8%

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

   3. Simplified 53.7%

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

   4. Taylor expanded in B around -inf 75.5%

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

      1. associate--l+ 75.5%

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

      2. div-sub 75.5%

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

   6. Simplified 75.5%

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

   if -6.39999999999999973e-102 < B < -3.10000000000000012e-199

   1. Initial program 27.0%

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

   3. Simplified 53.6%

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

   4. Taylor expanded in B around 0 71.8%

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

      1. associate-*r/ 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in C around inf 66.4%

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

   if -3.10000000000000012e-199 < B

   1. Initial program 61.6%

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

   3. Simplified 61.5%

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

   4. Taylor expanded in B around inf 71.0%

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

      1. +-commutative 71.0%

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

      2. associate--r+ 71.0%

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

      3. div-sub 73.0%

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

   6. Simplified 73.0%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.4 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3.1 \cdot 10^{-199}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 18: 66.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -6.4 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-200}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t_0 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -6.4e-102)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B -3e-200)
       (* 180.0 (/ (atan (/ (* B -0.5) (- C A))) PI))
       (* 180.0 (/ (atan (+ t_0 -1.0)) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -6.4e-102) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= -3e-200) {
		tmp = 180.0 * (atan(((B * -0.5) / (C - A))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((t_0 + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -6.4e-102) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= -3e-200) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / (C - A))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((t_0 + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -6.4e-102:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= -3e-200:
		tmp = 180.0 * (math.atan(((B * -0.5) / (C - A))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((t_0 + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -6.4e-102)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= -3e-200)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / Float64(C - A))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -6.4e-102)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= -3e-200)
		tmp = 180.0 * (atan(((B * -0.5) / (C - A))) / pi);
	else
		tmp = 180.0 * (atan((t_0 + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -6.4e-102], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3e-200], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -6.39999999999999973e-102

   1. Initial program 53.8%

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

   3. Simplified 53.7%

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

   4. Taylor expanded in B around -inf 75.5%

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

      1. associate--l+ 75.5%

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

      2. div-sub 75.5%

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

   6. Simplified 75.5%

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

   if -6.39999999999999973e-102 < B < -2.99999999999999995e-200

   1. Initial program 27.0%

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

   3. Simplified 53.6%

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

   4. Taylor expanded in B around 0 71.8%

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

      1. associate-*r/ 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in B around 0 71.4%

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

      1. *-commutative 71.4%

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

      2. associate-*l/ 71.4%

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

   9. Simplified 71.4%

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

   if -2.99999999999999995e-200 < B

   1. Initial program 61.6%

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

   3. Simplified 61.5%

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

   4. Taylor expanded in B around inf 71.0%

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

      1. +-commutative 71.0%

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

      2. associate--r+ 71.0%

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

      3. div-sub 73.0%

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

   6. Simplified 73.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.4 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -3 \cdot 10^{-200}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 19: 66.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -6.8 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{elif}\;B \leq -5.5 \cdot 10^{-201}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t_0 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -6.8e-102)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B -5.5e-201)
       (* (/ 180.0 PI) (atan (* B (/ -0.5 (- C A)))))
       (* 180.0 (/ (atan (+ t_0 -1.0)) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -6.8e-102) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= -5.5e-201) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / (C - A))));
	} else {
		tmp = 180.0 * (atan((t_0 + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -6.8e-102) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= -5.5e-201) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / (C - A))));
	} else {
		tmp = 180.0 * (Math.atan((t_0 + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -6.8e-102:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= -5.5e-201:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / (C - A))))
	else:
		tmp = 180.0 * (math.atan((t_0 + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -6.8e-102)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= -5.5e-201)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / Float64(C - A)))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -6.8e-102)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= -5.5e-201)
		tmp = (180.0 / pi) * atan((B * (-0.5 / (C - A))));
	else
		tmp = 180.0 * (atan((t_0 + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -6.8e-102], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -5.5e-201], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -6.80000000000000026e-102

   1. Initial program 53.8%

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

   3. Simplified 53.7%

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

   4. Taylor expanded in B around -inf 75.5%

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

      1. associate--l+ 75.5%

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

      2. div-sub 75.5%

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

   6. Simplified 75.5%

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

   if -6.80000000000000026e-102 < B < -5.50000000000000034e-201

   1. Initial program 27.0%

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

   3. Simplified 53.6%

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

   4. Taylor expanded in B around 0 71.8%

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

      1. associate-*r/ 71.8%

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

   6. Simplified 71.8%

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

      1. div-inv 71.9%

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

      2. *-commutative 71.9%

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

   8. Applied egg-rr 71.9%

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

      1. add-exp-log 68.0%

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

      2. log-rec 68.0%

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

   10. Applied egg-rr 68.0%

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

       1. expm1-log1p-u 68.0%

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

       2. expm1-udef 36.8%

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

       3. associate-*l* 36.8%

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

       4. exp-neg 36.8%

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

       5. add-exp-log 37.5%

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

   12. Applied egg-rr 37.5%

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

       1. expm1-def 71.9%

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

       2. expm1-log1p 71.9%

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

       3. associate-*r/ 71.9%

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

       4. metadata-eval 71.9%

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

   14. Simplified 71.9%

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

   if -5.50000000000000034e-201 < B

   1. Initial program 61.6%

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

   3. Simplified 61.5%

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

   4. Taylor expanded in B around inf 71.0%

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

      1. +-commutative 71.0%

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

      2. associate--r+ 71.0%

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

      3. div-sub 73.0%

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

   6. Simplified 73.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -5.5 \cdot 10^{-201}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]

Alternative 20: 66.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -6.2 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.05 \cdot 10^{-199}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(t_0 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -6.2e-102)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B -1.05e-199)
       (* (/ 180.0 PI) (atan (* B (/ -0.5 (- C A)))))
       (* (/ 180.0 PI) (atan (+ t_0 -1.0)))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -6.2e-102) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= -1.05e-199) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / (C - A))));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((t_0 + -1.0));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -6.2e-102) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= -1.05e-199) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / (C - A))));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((t_0 + -1.0));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -6.2e-102:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= -1.05e-199:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / (C - A))))
	else:
		tmp = (180.0 / math.pi) * math.atan((t_0 + -1.0))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -6.2e-102)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= -1.05e-199)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / Float64(C - A)))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(t_0 + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -6.2e-102)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= -1.05e-199)
		tmp = (180.0 / pi) * atan((B * (-0.5 / (C - A))));
	else
		tmp = (180.0 / pi) * atan((t_0 + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -6.2e-102], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.05e-199], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -6.20000000000000026e-102

   1. Initial program 53.8%

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

   3. Simplified 53.7%

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

   4. Taylor expanded in B around -inf 75.5%

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

      1. associate--l+ 75.5%

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

      2. div-sub 75.5%

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

   6. Simplified 75.5%

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

   if -6.20000000000000026e-102 < B < -1.05000000000000001e-199

   1. Initial program 27.0%

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

   3. Simplified 53.6%

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

   4. Taylor expanded in B around 0 71.8%

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

      1. associate-*r/ 71.8%

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

   6. Simplified 71.8%

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

      1. div-inv 71.9%

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

      2. *-commutative 71.9%

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

   8. Applied egg-rr 71.9%

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

      1. add-exp-log 68.0%

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

      2. log-rec 68.0%

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

   10. Applied egg-rr 68.0%

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

       1. expm1-log1p-u 68.0%

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

       2. expm1-udef 36.8%

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

       3. associate-*l* 36.8%

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

       4. exp-neg 36.8%

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

       5. add-exp-log 37.5%

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

   12. Applied egg-rr 37.5%

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

       1. expm1-def 71.9%

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

       2. expm1-log1p 71.9%

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

       3. associate-*r/ 71.9%

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

       4. metadata-eval 71.9%

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

   14. Simplified 71.9%

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

   if -1.05000000000000001e-199 < B

   1. Initial program 61.6%

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

   3. Simplified 78.1%

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

      1. add-log-exp 78.1%

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

   5. Applied egg-rr 78.1%

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

   6. Taylor expanded in B around inf 71.0%

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

      1. +-commutative 71.0%

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

      2. associate--r+ 71.0%

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

      3. div-sub 73.0%

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

   8. Simplified 73.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.2 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq -1.05 \cdot 10^{-199}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]

Alternative 21: 47.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.3 \cdot 10^{-58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-30}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.3e-58)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.6e-30)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.3e-58) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.6e-30) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.3e-58) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.6e-30) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.3e-58:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.6e-30:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.3e-58)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.6e-30)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.3e-58)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.6e-30)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.3e-58], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.6e-30], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.30000000000000026e-58

   1. Initial program 51.6%

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

   3. Simplified 51.6%

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

   4. Taylor expanded in B around -inf 59.7%

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

   if -3.30000000000000026e-58 < B < 2.59999999999999987e-30

   1. Initial program 62.7%

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

   3. Simplified 62.6%

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

   4. Taylor expanded in C around -inf 38.0%

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

   if 2.59999999999999987e-30 < B

   1. Initial program 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in B around inf 66.3%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.3 \cdot 10^{-58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-30}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 22: 58.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -7.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;C \leq 380:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -7.5e-86)
   (* (/ 180.0 PI) (atan (/ (+ B C) B)))
   (if (<= C 380.0)
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))
     (* (/ 180.0 PI) (atan (/ (* B -0.5) C))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -7.5e-86) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B + C) / B));
	} else if (C <= 380.0) {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -7.5e-86) {
		tmp = (180.0 / Math.PI) * Math.atan(((B + C) / B));
	} else if (C <= 380.0) {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -7.5e-86:
		tmp = (180.0 / math.pi) * math.atan(((B + C) / B))
	elif C <= 380.0:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -7.5e-86)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B + C) / B)));
	elseif (C <= 380.0)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -7.5e-86)
		tmp = (180.0 / pi) * atan(((B + C) / B));
	elseif (C <= 380.0)
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	else
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -7.5e-86], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B + C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 380.0], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -7.50000000000000055e-86

   1. Initial program 78.8%

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

   3. Simplified 90.8%

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

      1. add-log-exp 90.7%

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

   5. Applied egg-rr 90.7%

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

   6. Taylor expanded in A around 0 76.5%

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

      1. unpow2 76.5%

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

      2. unpow2 76.5%

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

      3. hypot-def 87.0%

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

   8. Simplified 87.0%

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

   9. Taylor expanded in B around -inf 78.2%

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

       1. +-commutative 78.2%

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

   11. Simplified 78.2%

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

   if -7.50000000000000055e-86 < C < 380

   1. Initial program 61.9%

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

   3. Simplified 61.8%

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

   4. Taylor expanded in B around inf 58.7%

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

      1. +-commutative 58.7%

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

      2. associate--r+ 58.7%

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

      3. div-sub 58.7%

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

   6. Simplified 58.7%

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

   7. Taylor expanded in C around 0 57.5%

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

      1. associate-*r/ 57.5%

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

      2. neg-mul-1 57.5%

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

   9. Simplified 57.5%

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

   if 380 < C

   1. Initial program 18.7%

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

   3. Simplified 47.7%

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

   4. Taylor expanded in B around 0 74.5%

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

      1. associate-*r/ 74.5%

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

   6. Simplified 74.5%

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

      1. div-inv 74.5%

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

      2. *-commutative 74.5%

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

   8. Applied egg-rr 74.5%

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

   9. Taylor expanded in C around inf 65.3%

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

       1. associate-*r/ 65.3%

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

       2. *-commutative 65.3%

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

   11. Simplified 65.3%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -7.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{elif}\;C \leq 380:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \]

Alternative 23: 44.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-166}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7.2e-65)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 5e-166)
     (* (/ 180.0 PI) (atan 0.0))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.2e-65) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 5e-166) {
		tmp = (180.0 / ((double) M_PI)) * atan(0.0);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.2e-65) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 5e-166) {
		tmp = (180.0 / Math.PI) * Math.atan(0.0);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7.2e-65:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 5e-166:
		tmp = (180.0 / math.pi) * math.atan(0.0)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -7.2e-65)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 5e-166)
		tmp = Float64(Float64(180.0 / pi) * atan(0.0));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -7.2e-65)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 5e-166)
		tmp = (180.0 / pi) * atan(0.0);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7.2e-65], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5e-166], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -7.1999999999999996e-65

   1. Initial program 52.8%

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

   3. Simplified 52.8%

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

   4. Taylor expanded in B around -inf 58.6%

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

   if -7.1999999999999996e-65 < B < 5e-166

   1. Initial program 55.5%

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

   3. Simplified 67.9%

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

      1. add-log-exp 70.2%

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

   5. Applied egg-rr 70.2%

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

   6. Taylor expanded in C around inf 28.1%

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

      1. distribute-rgt1-in 28.1%

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

      2. metadata-eval 28.1%

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

      3. associate-*r/ 12.9%

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

      4. mul0-lft 28.1%

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

      5. metadata-eval 28.1%

         \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{0} \]

   8. Simplified 28.1%

      \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{0} \]

   if 5e-166 < B

   1. Initial program 60.3%

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

   3. Simplified 60.2%

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

   4. Taylor expanded in B around inf 51.9%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-166}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 24: 40.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8.8 \cdot 10^{-303}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8.8e-303)
   (* 180.0 (/ (atan 1.0) PI))
   (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.8e-303) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.8e-303) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -8.8e-303:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -8.8e-303)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -8.8e-303)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -8.8e-303], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -8.80000000000000055e-303

   1. Initial program 52.1%

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

   3. Simplified 52.0%

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

   4. Taylor expanded in B around -inf 43.2%

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

   if -8.80000000000000055e-303 < B

   1. Initial program 60.5%

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

   3. Simplified 60.5%

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

   4. Taylor expanded in B around inf 41.1%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.8 \cdot 10^{-303}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 25: 20.4% 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 56.5%

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

3. Simplified 56.5%

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

4. Taylor expanded in B around inf 22.7%

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

5. Final simplification 22.7%

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

Reproduce

herbie shell --seed 2023271 
(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)))