ABCF->ab-angle angle

Percentage Accurate: 53.0% → 88.3%

Time: 17.4s

Alternatives: 15

Speedup: 2.4×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.0% 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: 88.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -0.5 \lor \neg \left(t_0 \leq 0\right):\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (or (<= t_0 -0.5) (not (<= t_0 0.0)))
     (* (atan (/ (- (- C A) (hypot B (- C A))) B)) (/ 180.0 PI))
     (/ (atan (/ B (/ (- C A) -0.5))) (* PI 0.005555555555555556)))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -0.5) || !(t_0 <= 0.0)) {
		tmp = atan((((C - A) - hypot(B, (C - A))) / B)) * (180.0 / ((double) M_PI));
	} else {
		tmp = atan((B / ((C - A) / -0.5))) / (((double) M_PI) * 0.005555555555555556);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if ((t_0 <= -0.5) || !(t_0 <= 0.0)) {
		tmp = Math.atan((((C - A) - Math.hypot(B, (C - A))) / B)) * (180.0 / Math.PI);
	} else {
		tmp = Math.atan((B / ((C - A) / -0.5))) / (Math.PI * 0.005555555555555556);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if (t_0 <= -0.5) or not (t_0 <= 0.0):
		tmp = math.atan((((C - A) - math.hypot(B, (C - A))) / B)) * (180.0 / math.pi)
	else:
		tmp = math.atan((B / ((C - A) / -0.5))) / (math.pi * 0.005555555555555556)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if ((t_0 <= -0.5) || !(t_0 <= 0.0))
		tmp = Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(C - A))) / B)) * Float64(180.0 / pi));
	else
		tmp = Float64(atan(Float64(B / Float64(Float64(C - A) / -0.5))) / Float64(pi * 0.005555555555555556));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if ((t_0 <= -0.5) || ~((t_0 <= 0.0)))
		tmp = atan((((C - A) - hypot(B, (C - A))) / B)) * (180.0 / pi);
	else
		tmp = atan((B / ((C - A) / -0.5))) / (pi * 0.005555555555555556);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -0.5], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(B / N[(N[(C - A), $MachinePrecision] / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 55.3%

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

      1. associate-*r/ 55.3%

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

      2. associate-*l/ 55.3%

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

      3. *-commutative 55.3%

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

   3. Simplified 83.2%

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

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

   1. Initial program 10.0%

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

      1. associate-*r/ 10.0%

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

      2. associate-*l/ 10.0%

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

      3. *-commutative 10.0%

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

   3. Simplified 10.0%

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

   4. Taylor expanded in B around 0 98.7%

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

      1. associate-*r/ 98.7%

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

   6. Simplified 98.7%

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

      1. add-log-exp 10.6%

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

      2. *-commutative 10.6%

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

   8. Applied egg-rr 10.6%

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

      1. clear-num 10.6%

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

      2. un-div-inv 10.6%

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

      3. add-log-exp 98.8%

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

      4. *-commutative 98.8%

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

      5. *-un-lft-identity 98.8%

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

      6. times-frac 98.7%

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

      7. metadata-eval 98.7%

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

      8. div-inv 98.7%

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

      9. metadata-eval 98.7%

         \[\leadsto \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot \color{blue}{0.005555555555555556}} \]

   10. Applied egg-rr 98.7%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}} \]
   11. Step-by-step derivation

       1. *-commutative 98.7%

          \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{C - A} \cdot -0.5\right)}}{\pi \cdot 0.005555555555555556} \]

       2. associate-/r/ 98.8%

          \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{\frac{C - A}{-0.5}}\right)}}{\pi \cdot 0.005555555555555556} \]

   12. Simplified 98.8%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.5 \lor \neg \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0\right):\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 2: 75.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)\\ \mathbf{if}\;C \leq -5 \cdot 10^{+21}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{-298}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 2.6 \cdot 10^{-268}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;C \leq 10^{+24}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (- (- A) (hypot A B)) B)))))
   (if (<= C -5e+21)
     (* (/ 180.0 PI) (atan (/ (+ C (- B A)) B)))
     (if (<= C 4.6e-298)
       t_0
       (if (<= C 2.6e-268)
         (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
         (if (<= C 1e+24)
           t_0
           (/ (atan (/ B (/ (- C A) -0.5))) (* PI 0.005555555555555556))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((-A - hypot(A, B)) / B));
	double tmp;
	if (C <= -5e+21) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C + (B - A)) / B));
	} else if (C <= 4.6e-298) {
		tmp = t_0;
	} else if (C <= 2.6e-268) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (C <= 1e+24) {
		tmp = t_0;
	} else {
		tmp = atan((B / ((C - A) / -0.5))) / (((double) M_PI) * 0.005555555555555556);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(((-A - Math.hypot(A, B)) / B));
	double tmp;
	if (C <= -5e+21) {
		tmp = (180.0 / Math.PI) * Math.atan(((C + (B - A)) / B));
	} else if (C <= 4.6e-298) {
		tmp = t_0;
	} else if (C <= 2.6e-268) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (C <= 1e+24) {
		tmp = t_0;
	} else {
		tmp = Math.atan((B / ((C - A) / -0.5))) / (Math.PI * 0.005555555555555556);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(((-A - math.hypot(A, B)) / B))
	tmp = 0
	if C <= -5e+21:
		tmp = (180.0 / math.pi) * math.atan(((C + (B - A)) / B))
	elif C <= 4.6e-298:
		tmp = t_0
	elif C <= 2.6e-268:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif C <= 1e+24:
		tmp = t_0
	else:
		tmp = math.atan((B / ((C - A) / -0.5))) / (math.pi * 0.005555555555555556)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(-A) - hypot(A, B)) / B)))
	tmp = 0.0
	if (C <= -5e+21)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + Float64(B - A)) / B)));
	elseif (C <= 4.6e-298)
		tmp = t_0;
	elseif (C <= 2.6e-268)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (C <= 1e+24)
		tmp = t_0;
	else
		tmp = Float64(atan(Float64(B / Float64(Float64(C - A) / -0.5))) / Float64(pi * 0.005555555555555556));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(((-A - hypot(A, B)) / B));
	tmp = 0.0;
	if (C <= -5e+21)
		tmp = (180.0 / pi) * atan(((C + (B - A)) / B));
	elseif (C <= 4.6e-298)
		tmp = t_0;
	elseif (C <= 2.6e-268)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (C <= 1e+24)
		tmp = t_0;
	else
		tmp = atan((B / ((C - A) / -0.5))) / (pi * 0.005555555555555556);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[((-A) - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -5e+21], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.6e-298], t$95$0, If[LessEqual[C, 2.6e-268], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1e+24], t$95$0, N[(N[ArcTan[N[(B / N[(N[(C - A), $MachinePrecision] / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -5e21

   1. Initial program 72.9%

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

      1. associate-*r/ 72.9%

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

      2. associate-*l/ 72.9%

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

      3. associate-*l/ 72.9%

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

      4. *-lft-identity 72.9%

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

      5. sub-neg 72.9%

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

      6. associate-+l- 72.9%

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

      7. sub-neg 72.9%

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

      8. remove-double-neg 72.9%

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

      9. +-commutative 72.9%

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

      10. unpow2 72.9%

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

      11. unpow2 72.9%

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

      12. hypot-def 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in B around -inf 85.2%

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

      1. neg-mul-1 85.2%

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

      2. unsub-neg 85.2%

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

   6. Simplified 85.2%

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

   if -5e21 < C < 4.6000000000000001e-298 or 2.60000000000000002e-268 < C < 9.9999999999999998e23

   1. Initial program 56.8%

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

      1. associate-*r/ 56.8%

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

      2. associate-*l/ 56.8%

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

      3. *-commutative 56.8%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in C around 0 55.1%

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

      1. mul-1-neg 55.1%

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

      2. +-commutative 55.1%

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

      3. unpow2 55.1%

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

      4. unpow2 55.1%

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

      5. hypot-def 80.7%

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

   6. Simplified 80.7%

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

   if 4.6000000000000001e-298 < C < 2.60000000000000002e-268

   1. Initial program 25.7%

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

      1. associate-*r/ 25.7%

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

      2. associate-*l/ 25.7%

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

      3. *-commutative 25.7%

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

   3. Simplified 36.5%

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

   4. Taylor expanded in A around -inf 81.6%

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

   if 9.9999999999999998e23 < C

   1. Initial program 19.5%

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

      1. associate-*r/ 19.5%

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

      2. associate-*l/ 19.5%

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

      3. *-commutative 19.5%

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

   3. Simplified 45.4%

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

   4. Taylor expanded in B around 0 78.3%

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

      1. associate-*r/ 78.3%

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

   6. Simplified 78.3%

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

      1. add-log-exp 24.4%

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

      2. *-commutative 24.4%

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

   8. Applied egg-rr 24.4%

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

      1. clear-num 24.4%

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

      2. un-div-inv 24.4%

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

      3. add-log-exp 78.3%

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

      4. *-commutative 78.3%

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

      5. *-un-lft-identity 78.3%

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

      6. times-frac 78.3%

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

      7. metadata-eval 78.3%

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

      8. div-inv 78.3%

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

      9. metadata-eval 78.3%

         \[\leadsto \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot \color{blue}{0.005555555555555556}} \]

   10. Applied egg-rr 78.3%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}} \]
   11. Step-by-step derivation

       1. *-commutative 78.3%

          \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{C - A} \cdot -0.5\right)}}{\pi \cdot 0.005555555555555556} \]

       2. associate-/r/ 78.3%

          \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{\frac{C - A}{-0.5}}\right)}}{\pi \cdot 0.005555555555555556} \]

   12. Simplified 78.3%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -5 \cdot 10^{+21}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{-298}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)\\ \mathbf{elif}\;C \leq 2.6 \cdot 10^{-268}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;C \leq 10^{+24}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]

Alternative 3: 45.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{if}\;B \leq -1.02 \cdot 10^{-75}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-187}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-131}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-131}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-32} \lor \neg \left(B \leq 8.5 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))))
   (if (<= B -1.02e-75)
     (* (/ 180.0 PI) (atan 1.0))
     (if (<= B 2.3e-187)
       (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
       (if (<= B 5e-131)
         t_0
         (if (<= B 7.8e-131)
           (* (/ 180.0 PI) (atan (/ 0.0 B)))
           (if (or (<= B 3.3e-32) (not (<= B 8.5e+53)))
             (* (/ 180.0 PI) (atan -1.0))
             t_0)))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	double tmp;
	if (B <= -1.02e-75) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 2.3e-187) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (B <= 5e-131) {
		tmp = t_0;
	} else if (B <= 7.8e-131) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.0 / B));
	} else if ((B <= 3.3e-32) || !(B <= 8.5e+53)) {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	double tmp;
	if (B <= -1.02e-75) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 2.3e-187) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (B <= 5e-131) {
		tmp = t_0;
	} else if (B <= 7.8e-131) {
		tmp = (180.0 / Math.PI) * Math.atan((0.0 / B));
	} else if ((B <= 3.3e-32) || !(B <= 8.5e+53)) {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	tmp = 0
	if B <= -1.02e-75:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 2.3e-187:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif B <= 5e-131:
		tmp = t_0
	elif B <= 7.8e-131:
		tmp = (180.0 / math.pi) * math.atan((0.0 / B))
	elif (B <= 3.3e-32) or not (B <= 8.5e+53):
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))))
	tmp = 0.0
	if (B <= -1.02e-75)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 2.3e-187)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (B <= 5e-131)
		tmp = t_0;
	elseif (B <= 7.8e-131)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.0 / B)));
	elseif ((B <= 3.3e-32) || !(B <= 8.5e+53))
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan((-0.5 * (B / C)));
	tmp = 0.0;
	if (B <= -1.02e-75)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 2.3e-187)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (B <= 5e-131)
		tmp = t_0;
	elseif (B <= 7.8e-131)
		tmp = (180.0 / pi) * atan((0.0 / B));
	elseif ((B <= 3.3e-32) || ~((B <= 8.5e+53)))
		tmp = (180.0 / pi) * atan(-1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.02e-75], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.3e-187], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5e-131], t$95$0, If[LessEqual[B, 7.8e-131], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 3.3e-32], N[Not[LessEqual[B, 8.5e+53]], $MachinePrecision]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.01999999999999997e-75

   1. Initial program 50.5%

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

      1. associate-*r/ 50.4%

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

      2. associate-*l/ 50.5%

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

      3. *-commutative 50.5%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in B around -inf 55.7%

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

   if -1.01999999999999997e-75 < B < 2.29999999999999998e-187

   1. Initial program 54.0%

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

      1. associate-*r/ 54.0%

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

      2. associate-*l/ 54.0%

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

      3. *-commutative 54.0%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in A around -inf 36.0%

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

   if 2.29999999999999998e-187 < B < 5.0000000000000004e-131 or 3.30000000000000025e-32 < B < 8.5000000000000002e53

   1. Initial program 45.4%

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

      1. associate-*r/ 45.4%

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

      2. associate-*l/ 45.4%

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

      3. *-commutative 45.4%

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

   3. Simplified 49.6%

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

   4. Taylor expanded in B around 0 57.4%

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

      1. associate-*r/ 57.4%

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

   6. Simplified 57.4%

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

   7. Taylor expanded in C around inf 53.8%

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

   if 5.0000000000000004e-131 < B < 7.80000000000000039e-131

   1. Initial program 3.1%

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

      1. associate-*r/ 3.1%

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

      2. associate-*l/ 3.1%

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

      3. *-commutative 3.1%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in C around inf 100.0%

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

      1. distribute-rgt1-in 100.0%

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

      2. metadata-eval 100.0%

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

      3. mul0-lft 100.0%

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

      4. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

   if 7.80000000000000039e-131 < B < 3.30000000000000025e-32 or 8.5000000000000002e53 < B

   1. Initial program 45.1%

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

      1. associate-*r/ 45.1%

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

      2. associate-*l/ 45.1%

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

      3. *-commutative 45.1%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in B around inf 60.3%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.02 \cdot 10^{-75}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 2.3 \cdot 10^{-187}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-131}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-131}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-32} \lor \neg \left(B \leq 8.5 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \end{array} \]

Alternative 4: 45.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{if}\;B \leq -1.55 \cdot 10^{-76}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-186}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-130}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-33} \lor \neg \left(B \leq 1.1 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))))
   (if (<= B -1.55e-76)
     (* (/ 180.0 PI) (atan 1.0))
     (if (<= B 3.9e-186)
       (* (/ 180.0 PI) (atan (/ (* B 0.5) A)))
       (if (<= B 5.8e-133)
         t_0
         (if (<= B 6.8e-130)
           (* (/ 180.0 PI) (atan (/ 0.0 B)))
           (if (or (<= B 3.1e-33) (not (<= B 1.1e+55)))
             (* (/ 180.0 PI) (atan -1.0))
             t_0)))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	double tmp;
	if (B <= -1.55e-76) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 3.9e-186) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * 0.5) / A));
	} else if (B <= 5.8e-133) {
		tmp = t_0;
	} else if (B <= 6.8e-130) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.0 / B));
	} else if ((B <= 3.1e-33) || !(B <= 1.1e+55)) {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	double tmp;
	if (B <= -1.55e-76) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 3.9e-186) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * 0.5) / A));
	} else if (B <= 5.8e-133) {
		tmp = t_0;
	} else if (B <= 6.8e-130) {
		tmp = (180.0 / Math.PI) * Math.atan((0.0 / B));
	} else if ((B <= 3.1e-33) || !(B <= 1.1e+55)) {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	tmp = 0
	if B <= -1.55e-76:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 3.9e-186:
		tmp = (180.0 / math.pi) * math.atan(((B * 0.5) / A))
	elif B <= 5.8e-133:
		tmp = t_0
	elif B <= 6.8e-130:
		tmp = (180.0 / math.pi) * math.atan((0.0 / B))
	elif (B <= 3.1e-33) or not (B <= 1.1e+55):
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))))
	tmp = 0.0
	if (B <= -1.55e-76)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 3.9e-186)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * 0.5) / A)));
	elseif (B <= 5.8e-133)
		tmp = t_0;
	elseif (B <= 6.8e-130)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.0 / B)));
	elseif ((B <= 3.1e-33) || !(B <= 1.1e+55))
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan((-0.5 * (B / C)));
	tmp = 0.0;
	if (B <= -1.55e-76)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 3.9e-186)
		tmp = (180.0 / pi) * atan(((B * 0.5) / A));
	elseif (B <= 5.8e-133)
		tmp = t_0;
	elseif (B <= 6.8e-130)
		tmp = (180.0 / pi) * atan((0.0 / B));
	elseif ((B <= 3.1e-33) || ~((B <= 1.1e+55)))
		tmp = (180.0 / pi) * atan(-1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.55e-76], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.9e-186], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.8e-133], t$95$0, If[LessEqual[B, 6.8e-130], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 3.1e-33], N[Not[LessEqual[B, 1.1e+55]], $MachinePrecision]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -1.54999999999999985e-76

   1. Initial program 50.5%

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

      1. associate-*r/ 50.4%

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

      2. associate-*l/ 50.5%

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

      3. *-commutative 50.5%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in B around -inf 55.7%

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

   if -1.54999999999999985e-76 < B < 3.9000000000000001e-186

   1. Initial program 54.0%

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

      1. associate-*r/ 54.0%

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

      2. associate-*l/ 54.0%

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

      3. *-commutative 54.0%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in A around -inf 36.0%

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

      1. associate-*r/ 36.0%

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

   6. Applied egg-rr 36.0%

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

   if 3.9000000000000001e-186 < B < 5.7999999999999997e-133 or 3.09999999999999997e-33 < B < 1.10000000000000005e55

   1. Initial program 45.4%

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

      1. associate-*r/ 45.4%

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

      2. associate-*l/ 45.4%

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

      3. *-commutative 45.4%

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

   3. Simplified 49.6%

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

   4. Taylor expanded in B around 0 57.4%

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

      1. associate-*r/ 57.4%

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

   6. Simplified 57.4%

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

   7. Taylor expanded in C around inf 53.8%

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

   if 5.7999999999999997e-133 < B < 6.8000000000000001e-130

   1. Initial program 3.1%

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

      1. associate-*r/ 3.1%

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

      2. associate-*l/ 3.1%

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

      3. *-commutative 3.1%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in C around inf 100.0%

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

      1. distribute-rgt1-in 100.0%

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

      2. metadata-eval 100.0%

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

      3. mul0-lft 100.0%

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

      4. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

   if 6.8000000000000001e-130 < B < 3.09999999999999997e-33 or 1.10000000000000005e55 < B

   1. Initial program 45.1%

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

      1. associate-*r/ 45.1%

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

      2. associate-*l/ 45.1%

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

      3. *-commutative 45.1%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in B around inf 60.3%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.55 \cdot 10^{-76}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-186}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{-133}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 6.8 \cdot 10^{-130}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-33} \lor \neg \left(B \leq 1.1 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \end{array} \]

Alternative 5: 47.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{if}\;C \leq -1.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;C \leq -6 \cdot 10^{-191}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 4.3 \cdot 10^{-224}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;C \leq 4.7 \cdot 10^{-11}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;C \leq 10^{+22}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan -1.0))))
   (if (<= C -1.2e-32)
     (* (/ 180.0 PI) (atan (/ (* C 2.0) B)))
     (if (<= C -6e-191)
       t_0
       (if (<= C 4.3e-224)
         (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
         (if (<= C 4.7e-11)
           (* (/ 180.0 PI) (atan 1.0))
           (if (<= C 1e+22) t_0 (* (/ 180.0 PI) (atan (* -0.5 (/ B C)))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(-1.0);
	double tmp;
	if (C <= -1.2e-32) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C * 2.0) / B));
	} else if (C <= -6e-191) {
		tmp = t_0;
	} else if (C <= 4.3e-224) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (C <= 4.7e-11) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (C <= 1e+22) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(-1.0);
	double tmp;
	if (C <= -1.2e-32) {
		tmp = (180.0 / Math.PI) * Math.atan(((C * 2.0) / B));
	} else if (C <= -6e-191) {
		tmp = t_0;
	} else if (C <= 4.3e-224) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (C <= 4.7e-11) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (C <= 1e+22) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(-1.0)
	tmp = 0
	if C <= -1.2e-32:
		tmp = (180.0 / math.pi) * math.atan(((C * 2.0) / B))
	elif C <= -6e-191:
		tmp = t_0
	elif C <= 4.3e-224:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif C <= 4.7e-11:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif C <= 1e+22:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(-1.0))
	tmp = 0.0
	if (C <= -1.2e-32)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C * 2.0) / B)));
	elseif (C <= -6e-191)
		tmp = t_0;
	elseif (C <= 4.3e-224)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (C <= 4.7e-11)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (C <= 1e+22)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(-1.0);
	tmp = 0.0;
	if (C <= -1.2e-32)
		tmp = (180.0 / pi) * atan(((C * 2.0) / B));
	elseif (C <= -6e-191)
		tmp = t_0;
	elseif (C <= 4.3e-224)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (C <= 4.7e-11)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (C <= 1e+22)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.2e-32], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -6e-191], t$95$0, If[LessEqual[C, 4.3e-224], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.7e-11], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1e+22], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -1.2000000000000001e-32

   1. Initial program 69.5%

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

      1. associate-*r/ 69.5%

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

      2. associate-*l/ 69.5%

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

      3. *-commutative 69.5%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in C around -inf 60.0%

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

   if -1.2000000000000001e-32 < C < -6.0000000000000001e-191 or 4.69999999999999993e-11 < C < 1e22

   1. Initial program 59.6%

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

      1. associate-*r/ 59.6%

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

      2. associate-*l/ 59.6%

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

      3. *-commutative 59.6%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in B around inf 43.6%

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

   if -6.0000000000000001e-191 < C < 4.3e-224

   1. Initial program 46.7%

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

      1. associate-*r/ 46.7%

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

      2. associate-*l/ 46.7%

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

      3. *-commutative 46.7%

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

   3. Simplified 66.6%

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

   4. Taylor expanded in A around -inf 46.0%

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

   if 4.3e-224 < C < 4.69999999999999993e-11

   1. Initial program 57.9%

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

      1. associate-*r/ 57.9%

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

      2. associate-*l/ 57.9%

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

      3. *-commutative 57.9%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in B around -inf 38.6%

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

   if 1e22 < C

   1. Initial program 19.5%

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

      1. associate-*r/ 19.5%

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

      2. associate-*l/ 19.5%

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

      3. *-commutative 19.5%

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

   3. Simplified 45.4%

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

   4. Taylor expanded in B around 0 78.3%

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

      1. associate-*r/ 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in C around inf 68.5%

      \[\leadsto \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C}\right)} \cdot \frac{180}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;C \leq -6 \cdot 10^{-191}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{elif}\;C \leq 4.3 \cdot 10^{-224}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;C \leq 4.7 \cdot 10^{-11}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;C \leq 10^{+22}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \end{array} \]

Alternative 6: 64.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{if}\;B \leq -3.4 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -15000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -2.3 \cdot 10^{-288}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A)))))
        (t_1 (* (/ 180.0 PI) (atan (/ (+ C (- B A)) B)))))
   (if (<= B -3.4e+28)
     t_1
     (if (<= B -15000000000.0)
       t_0
       (if (<= B -7.5e-73)
         t_1
         (if (<= B -2.3e-288)
           t_0
           (* (/ 180.0 PI) (atan (/ (- C (+ B A)) B)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	double t_1 = (180.0 / ((double) M_PI)) * atan(((C + (B - A)) / B));
	double tmp;
	if (B <= -3.4e+28) {
		tmp = t_1;
	} else if (B <= -15000000000.0) {
		tmp = t_0;
	} else if (B <= -7.5e-73) {
		tmp = t_1;
	} else if (B <= -2.3e-288) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (B + A)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	double t_1 = (180.0 / Math.PI) * Math.atan(((C + (B - A)) / B));
	double tmp;
	if (B <= -3.4e+28) {
		tmp = t_1;
	} else if (B <= -15000000000.0) {
		tmp = t_0;
	} else if (B <= -7.5e-73) {
		tmp = t_1;
	} else if (B <= -2.3e-288) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (B + A)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	t_1 = (180.0 / math.pi) * math.atan(((C + (B - A)) / B))
	tmp = 0
	if B <= -3.4e+28:
		tmp = t_1
	elif B <= -15000000000.0:
		tmp = t_0
	elif B <= -7.5e-73:
		tmp = t_1
	elif B <= -2.3e-288:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (B + A)) / B))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))))
	t_1 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + Float64(B - A)) / B)))
	tmp = 0.0
	if (B <= -3.4e+28)
		tmp = t_1;
	elseif (B <= -15000000000.0)
		tmp = t_0;
	elseif (B <= -7.5e-73)
		tmp = t_1;
	elseif (B <= -2.3e-288)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(B + A)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	t_1 = (180.0 / pi) * atan(((C + (B - A)) / B));
	tmp = 0.0;
	if (B <= -3.4e+28)
		tmp = t_1;
	elseif (B <= -15000000000.0)
		tmp = t_0;
	elseif (B <= -7.5e-73)
		tmp = t_1;
	elseif (B <= -2.3e-288)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan(((C - (B + A)) / 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 * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -3.4e+28], t$95$1, If[LessEqual[B, -15000000000.0], t$95$0, If[LessEqual[B, -7.5e-73], t$95$1, If[LessEqual[B, -2.3e-288], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.4e28 or -1.5e10 < B < -7.5e-73

   1. Initial program 53.8%

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

      1. associate-*r/ 53.8%

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

      2. associate-*l/ 53.8%

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

      3. associate-*l/ 53.8%

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

      4. *-lft-identity 53.8%

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

      5. sub-neg 53.8%

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

      6. associate-+l- 53.8%

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

      7. sub-neg 53.8%

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

      8. remove-double-neg 53.8%

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

      9. +-commutative 53.8%

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

      10. unpow2 53.8%

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

      11. unpow2 53.8%

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

      12. hypot-def 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in B around -inf 80.5%

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

      1. neg-mul-1 80.5%

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

      2. unsub-neg 80.5%

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

   6. Simplified 80.5%

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

   if -3.4e28 < B < -1.5e10 or -7.5e-73 < B < -2.3e-288

   1. Initial program 36.9%

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

      1. associate-*r/ 36.9%

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

      2. associate-*l/ 36.9%

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

      3. *-commutative 36.9%

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

   3. Simplified 56.9%

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

   4. Taylor expanded in B around 0 66.9%

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

      1. associate-*r/ 66.9%

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

   6. Simplified 66.9%

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

   if -2.3e-288 < B

   1. Initial program 51.0%

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

      1. associate-*r/ 51.0%

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

      2. associate-*l/ 51.0%

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

      3. associate-*l/ 51.0%

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

      4. *-lft-identity 51.0%

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

      5. sub-neg 51.0%

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

      6. associate-+l- 50.9%

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

      7. sub-neg 50.9%

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

      8. remove-double-neg 50.9%

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

      9. +-commutative 50.9%

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

      10. unpow2 50.9%

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

      11. unpow2 50.9%

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

      12. hypot-def 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in B around inf 65.7%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.4 \cdot 10^{+28}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{elif}\;B \leq -15000000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;B \leq -7.5 \cdot 10^{-73}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{elif}\;B \leq -2.3 \cdot 10^{-288}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \]

Alternative 7: 64.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{if}\;B \leq -1.56 \cdot 10^{+28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1100000000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{-74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{-288}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (+ C (- B A)) B)))))
   (if (<= B -1.56e+28)
     t_0
     (if (<= B -1100000000000.0)
       (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
       (if (<= B -1.3e-74)
         t_0
         (if (<= B -1.4e-288)
           (/ (atan (/ B (/ (- C A) -0.5))) (* PI 0.005555555555555556))
           (* (/ 180.0 PI) (atan (/ (- C (+ B A)) B)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((C + (B - A)) / B));
	double tmp;
	if (B <= -1.56e+28) {
		tmp = t_0;
	} else if (B <= -1100000000000.0) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else if (B <= -1.3e-74) {
		tmp = t_0;
	} else if (B <= -1.4e-288) {
		tmp = atan((B / ((C - A) / -0.5))) / (((double) M_PI) * 0.005555555555555556);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (B + A)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(((C + (B - A)) / B));
	double tmp;
	if (B <= -1.56e+28) {
		tmp = t_0;
	} else if (B <= -1100000000000.0) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else if (B <= -1.3e-74) {
		tmp = t_0;
	} else if (B <= -1.4e-288) {
		tmp = Math.atan((B / ((C - A) / -0.5))) / (Math.PI * 0.005555555555555556);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (B + A)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(((C + (B - A)) / B))
	tmp = 0
	if B <= -1.56e+28:
		tmp = t_0
	elif B <= -1100000000000.0:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	elif B <= -1.3e-74:
		tmp = t_0
	elif B <= -1.4e-288:
		tmp = math.atan((B / ((C - A) / -0.5))) / (math.pi * 0.005555555555555556)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (B + A)) / B))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + Float64(B - A)) / B)))
	tmp = 0.0
	if (B <= -1.56e+28)
		tmp = t_0;
	elseif (B <= -1100000000000.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	elseif (B <= -1.3e-74)
		tmp = t_0;
	elseif (B <= -1.4e-288)
		tmp = Float64(atan(Float64(B / Float64(Float64(C - A) / -0.5))) / Float64(pi * 0.005555555555555556));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(B + A)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(((C + (B - A)) / B));
	tmp = 0.0;
	if (B <= -1.56e+28)
		tmp = t_0;
	elseif (B <= -1100000000000.0)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	elseif (B <= -1.3e-74)
		tmp = t_0;
	elseif (B <= -1.4e-288)
		tmp = atan((B / ((C - A) / -0.5))) / (pi * 0.005555555555555556);
	else
		tmp = (180.0 / pi) * atan(((C - (B + A)) / 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[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.56e+28], t$95$0, If[LessEqual[B, -1100000000000.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.3e-74], t$95$0, If[LessEqual[B, -1.4e-288], N[(N[ArcTan[N[(B / N[(N[(C - A), $MachinePrecision] / -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.5599999999999999e28 or -1.1e12 < B < -1.3e-74

   1. Initial program 53.8%

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

      1. associate-*r/ 53.8%

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

      2. associate-*l/ 53.8%

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

      3. associate-*l/ 53.8%

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

      4. *-lft-identity 53.8%

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

      5. sub-neg 53.8%

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

      6. associate-+l- 53.8%

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

      7. sub-neg 53.8%

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

      8. remove-double-neg 53.8%

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

      9. +-commutative 53.8%

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

      10. unpow2 53.8%

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

      11. unpow2 53.8%

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

      12. hypot-def 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in B around -inf 80.5%

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

      1. neg-mul-1 80.5%

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

      2. unsub-neg 80.5%

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

   6. Simplified 80.5%

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

   if -1.5599999999999999e28 < B < -1.1e12

   1. Initial program 25.2%

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

      1. associate-*r/ 25.2%

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

      2. associate-*l/ 25.2%

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

      3. *-commutative 25.2%

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

   3. Simplified 26.2%

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

   4. Taylor expanded in B around 0 79.8%

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

      1. associate-*r/ 79.8%

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

   6. Simplified 79.8%

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

   if -1.3e-74 < B < -1.4e-288

   1. Initial program 39.6%

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

      1. associate-*r/ 39.6%

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

      2. associate-*l/ 39.6%

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

      3. *-commutative 39.6%

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

   3. Simplified 64.2%

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

   4. Taylor expanded in B around 0 63.9%

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

      1. associate-*r/ 63.9%

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

   6. Simplified 63.9%

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

      1. add-log-exp 28.5%

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

      2. *-commutative 28.5%

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

   8. Applied egg-rr 28.5%

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

      1. clear-num 28.5%

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

      2. un-div-inv 28.5%

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

      3. add-log-exp 63.9%

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

      4. *-commutative 63.9%

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

      5. *-un-lft-identity 63.9%

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

      6. times-frac 63.9%

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

      7. metadata-eval 63.9%

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

      8. div-inv 63.9%

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

      9. metadata-eval 63.9%

         \[\leadsto \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot \color{blue}{0.005555555555555556}} \]

   10. Applied egg-rr 63.9%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi \cdot 0.005555555555555556}} \]
   11. Step-by-step derivation

       1. *-commutative 63.9%

          \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{C - A} \cdot -0.5\right)}}{\pi \cdot 0.005555555555555556} \]

       2. associate-/r/ 63.9%

          \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B}{\frac{C - A}{-0.5}}\right)}}{\pi \cdot 0.005555555555555556} \]

   12. Simplified 63.9%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}} \]

   if -1.4e-288 < B

   1. Initial program 51.0%

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

      1. associate-*r/ 51.0%

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

      2. associate-*l/ 51.0%

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

      3. associate-*l/ 51.0%

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

      4. *-lft-identity 51.0%

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

      5. sub-neg 51.0%

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

      6. associate-+l- 50.9%

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

      7. sub-neg 50.9%

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

      8. remove-double-neg 50.9%

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

      9. +-commutative 50.9%

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

      10. unpow2 50.9%

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

      11. unpow2 50.9%

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

      12. hypot-def 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in B around inf 65.7%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.56 \cdot 10^{+28}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{elif}\;B \leq -1100000000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;B \leq -1.3 \cdot 10^{-74}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{-288}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{\frac{C - A}{-0.5}}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \]

Alternative 8: 45.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.05 \cdot 10^{-74}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-105} \lor \neg \left(B \leq 4.7 \cdot 10^{-31}\right) \land B \leq 8.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.05e-74)
   (* (/ 180.0 PI) (atan 1.0))
   (if (or (<= B 1.7e-105) (and (not (<= B 4.7e-31)) (<= B 8.5e+53)))
     (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.05e-74) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if ((B <= 1.7e-105) || (!(B <= 4.7e-31) && (B <= 8.5e+53))) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.05e-74) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if ((B <= 1.7e-105) || (!(B <= 4.7e-31) && (B <= 8.5e+53))) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.05e-74:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif (B <= 1.7e-105) or (not (B <= 4.7e-31) and (B <= 8.5e+53)):
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.05e-74)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif ((B <= 1.7e-105) || (!(B <= 4.7e-31) && (B <= 8.5e+53)))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.05e-74)
		tmp = (180.0 / pi) * atan(1.0);
	elseif ((B <= 1.7e-105) || (~((B <= 4.7e-31)) && (B <= 8.5e+53)))
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.05e-74], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[B, 1.7e-105], And[N[Not[LessEqual[B, 4.7e-31]], $MachinePrecision], LessEqual[B, 8.5e+53]]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.05e-74

   1. Initial program 51.0%

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

      1. associate-*r/ 51.0%

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

      2. associate-*l/ 51.0%

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

      3. *-commutative 51.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in B around -inf 56.2%

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

   if -1.05e-74 < B < 1.69999999999999996e-105 or 4.69999999999999987e-31 < B < 8.5000000000000002e53

   1. Initial program 50.5%

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

      1. associate-*r/ 50.5%

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

      2. associate-*l/ 50.5%

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

      3. *-commutative 50.5%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in B around 0 53.9%

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

      1. associate-*r/ 53.9%

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

   6. Simplified 53.9%

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

   7. Taylor expanded in C around inf 35.2%

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

   if 1.69999999999999996e-105 < B < 4.69999999999999987e-31 or 8.5000000000000002e53 < B

   1. Initial program 44.9%

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

      1. associate-*r/ 44.9%

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

      2. associate-*l/ 44.9%

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

      3. *-commutative 44.9%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in B around inf 61.8%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.05 \cdot 10^{-74}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-105} \lor \neg \left(B \leq 4.7 \cdot 10^{-31}\right) \land B \leq 8.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 9: 51.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{if}\;A \leq -9.5 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{-264}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.15 \cdot 10^{-302}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-57}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan -1.0))))
   (if (<= A -9.5e-216)
     (* 180.0 (/ (atan (/ (* B -0.5) (- C A))) PI))
     (if (<= A -2.3e-264)
       t_0
       (if (<= A -2.15e-302)
         (* (/ 180.0 PI) (atan (/ (* C 2.0) B)))
         (if (<= A 3e-57) t_0 (* (/ 180.0 PI) (atan (/ (* A -2.0) B)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(-1.0);
	double tmp;
	if (A <= -9.5e-216) {
		tmp = 180.0 * (atan(((B * -0.5) / (C - A))) / ((double) M_PI));
	} else if (A <= -2.3e-264) {
		tmp = t_0;
	} else if (A <= -2.15e-302) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C * 2.0) / B));
	} else if (A <= 3e-57) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((A * -2.0) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(-1.0);
	double tmp;
	if (A <= -9.5e-216) {
		tmp = 180.0 * (Math.atan(((B * -0.5) / (C - A))) / Math.PI);
	} else if (A <= -2.3e-264) {
		tmp = t_0;
	} else if (A <= -2.15e-302) {
		tmp = (180.0 / Math.PI) * Math.atan(((C * 2.0) / B));
	} else if (A <= 3e-57) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((A * -2.0) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(-1.0)
	tmp = 0
	if A <= -9.5e-216:
		tmp = 180.0 * (math.atan(((B * -0.5) / (C - A))) / math.pi)
	elif A <= -2.3e-264:
		tmp = t_0
	elif A <= -2.15e-302:
		tmp = (180.0 / math.pi) * math.atan(((C * 2.0) / B))
	elif A <= 3e-57:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan(((A * -2.0) / B))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(-1.0))
	tmp = 0.0
	if (A <= -9.5e-216)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / Float64(C - A))) / pi));
	elseif (A <= -2.3e-264)
		tmp = t_0;
	elseif (A <= -2.15e-302)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C * 2.0) / B)));
	elseif (A <= 3e-57)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A * -2.0) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(-1.0);
	tmp = 0.0;
	if (A <= -9.5e-216)
		tmp = 180.0 * (atan(((B * -0.5) / (C - A))) / pi);
	elseif (A <= -2.3e-264)
		tmp = t_0;
	elseif (A <= -2.15e-302)
		tmp = (180.0 / pi) * atan(((C * 2.0) / B));
	elseif (A <= 3e-57)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan(((A * -2.0) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -9.5e-216], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.3e-264], t$95$0, If[LessEqual[A, -2.15e-302], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3e-57], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -9.49999999999999943e-216

   1. Initial program 28.0%

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

      1. associate-*r/ 28.0%

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

      2. associate-*l/ 28.0%

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

      3. *-commutative 28.0%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in B around 0 64.7%

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

      1. associate-*r/ 64.7%

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

   6. Simplified 64.7%

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

   7. Taylor expanded in B around 0 64.6%

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

      1. associate-*r/ 64.6%

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

      2. associate-*r/ 64.7%

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

      3. *-commutative 64.7%

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

      4. associate-*r/ 64.6%

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

   9. Simplified 64.6%

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

   if -9.49999999999999943e-216 < A < -2.30000000000000012e-264 or -2.1500000000000001e-302 < A < 3.00000000000000001e-57

   1. Initial program 60.3%

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

      1. associate-*r/ 60.3%

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

      2. associate-*l/ 60.3%

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

      3. *-commutative 60.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in B around inf 44.0%

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

   if -2.30000000000000012e-264 < A < -2.1500000000000001e-302

   1. Initial program 50.3%

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

      1. associate-*r/ 50.3%

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

      2. associate-*l/ 50.3%

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

      3. *-commutative 50.3%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in C around -inf 47.0%

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

   if 3.00000000000000001e-57 < A

   1. Initial program 70.6%

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

      1. associate-*r/ 70.6%

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

      2. associate-*l/ 70.6%

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

      3. *-commutative 70.6%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in A around inf 64.5%

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

      1. *-commutative 64.5%

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

   6. Simplified 64.5%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{-216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.3 \cdot 10^{-264}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{elif}\;A \leq -2.15 \cdot 10^{-302}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-57}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \]

Alternative 10: 51.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{if}\;A \leq -2.7 \cdot 10^{-222}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq -1.95 \cdot 10^{-263}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -2.5 \cdot 10^{-302}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;A \leq 3.9 \cdot 10^{-58}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan -1.0))))
   (if (<= A -2.7e-222)
     (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
     (if (<= A -1.95e-263)
       t_0
       (if (<= A -2.5e-302)
         (* (/ 180.0 PI) (atan (/ (* C 2.0) B)))
         (if (<= A 3.9e-58) t_0 (* (/ 180.0 PI) (atan (/ (* A -2.0) B)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(-1.0);
	double tmp;
	if (A <= -2.7e-222) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else if (A <= -1.95e-263) {
		tmp = t_0;
	} else if (A <= -2.5e-302) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C * 2.0) / B));
	} else if (A <= 3.9e-58) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((A * -2.0) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(-1.0);
	double tmp;
	if (A <= -2.7e-222) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else if (A <= -1.95e-263) {
		tmp = t_0;
	} else if (A <= -2.5e-302) {
		tmp = (180.0 / Math.PI) * Math.atan(((C * 2.0) / B));
	} else if (A <= 3.9e-58) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((A * -2.0) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(-1.0)
	tmp = 0
	if A <= -2.7e-222:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	elif A <= -1.95e-263:
		tmp = t_0
	elif A <= -2.5e-302:
		tmp = (180.0 / math.pi) * math.atan(((C * 2.0) / B))
	elif A <= 3.9e-58:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan(((A * -2.0) / B))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(-1.0))
	tmp = 0.0
	if (A <= -2.7e-222)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	elseif (A <= -1.95e-263)
		tmp = t_0;
	elseif (A <= -2.5e-302)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C * 2.0) / B)));
	elseif (A <= 3.9e-58)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A * -2.0) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(-1.0);
	tmp = 0.0;
	if (A <= -2.7e-222)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	elseif (A <= -1.95e-263)
		tmp = t_0;
	elseif (A <= -2.5e-302)
		tmp = (180.0 / pi) * atan(((C * 2.0) / B));
	elseif (A <= 3.9e-58)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan(((A * -2.0) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -2.7e-222], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -1.95e-263], t$95$0, If[LessEqual[A, -2.5e-302], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.9e-58], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -2.7e-222

   1. Initial program 28.0%

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

      1. associate-*r/ 28.0%

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

      2. associate-*l/ 28.0%

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

      3. *-commutative 28.0%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in B around 0 64.7%

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

      1. associate-*r/ 64.7%

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

   6. Simplified 64.7%

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

   if -2.7e-222 < A < -1.94999999999999985e-263 or -2.50000000000000017e-302 < A < 3.89999999999999992e-58

   1. Initial program 60.3%

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

      1. associate-*r/ 60.3%

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

      2. associate-*l/ 60.3%

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

      3. *-commutative 60.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in B around inf 44.0%

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

   if -1.94999999999999985e-263 < A < -2.50000000000000017e-302

   1. Initial program 50.3%

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

      1. associate-*r/ 50.3%

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

      2. associate-*l/ 50.3%

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

      3. *-commutative 50.3%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in C around -inf 47.0%

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

   if 3.89999999999999992e-58 < A

   1. Initial program 70.6%

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

      1. associate-*r/ 70.6%

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

      2. associate-*l/ 70.6%

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

      3. *-commutative 70.6%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in A around inf 64.5%

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

      1. *-commutative 64.5%

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

   6. Simplified 64.5%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.7 \cdot 10^{-222}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq -1.95 \cdot 10^{-263}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{elif}\;A \leq -2.5 \cdot 10^{-302}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C \cdot 2}{B}\right)\\ \mathbf{elif}\;A \leq 3.9 \cdot 10^{-58}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \]

Alternative 11: 46.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.3 \cdot 10^{-75}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-287}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-98}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.3e-75)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B -8.2e-287)
     (* (/ 180.0 PI) (atan (/ (* B 0.5) A)))
     (if (<= B 1.3e-98)
       (* (/ 180.0 PI) (atan (/ (* A -2.0) B)))
       (* (/ 180.0 PI) (atan -1.0))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.3e-75) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= -8.2e-287) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * 0.5) / A));
	} else if (B <= 1.3e-98) {
		tmp = (180.0 / ((double) M_PI)) * atan(((A * -2.0) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.3e-75) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= -8.2e-287) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * 0.5) / A));
	} else if (B <= 1.3e-98) {
		tmp = (180.0 / Math.PI) * Math.atan(((A * -2.0) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.3e-75:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= -8.2e-287:
		tmp = (180.0 / math.pi) * math.atan(((B * 0.5) / A))
	elif B <= 1.3e-98:
		tmp = (180.0 / math.pi) * math.atan(((A * -2.0) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.3e-75)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= -8.2e-287)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * 0.5) / A)));
	elseif (B <= 1.3e-98)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A * -2.0) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.3e-75)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= -8.2e-287)
		tmp = (180.0 / pi) * atan(((B * 0.5) / A));
	elseif (B <= 1.3e-98)
		tmp = (180.0 / pi) * atan(((A * -2.0) / B));
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.3e-75], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -8.2e-287], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.3e-98], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.3e-75

   1. Initial program 50.5%

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

      1. associate-*r/ 50.4%

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

      2. associate-*l/ 50.5%

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

      3. *-commutative 50.5%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in B around -inf 55.7%

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

   if -2.3e-75 < B < -8.2000000000000004e-287

   1. Initial program 41.6%

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

      1. associate-*r/ 41.6%

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

      2. associate-*l/ 41.6%

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

      3. *-commutative 41.6%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in A around -inf 40.6%

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

      1. associate-*r/ 40.6%

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

   6. Applied egg-rr 40.6%

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

   if -8.2000000000000004e-287 < B < 1.30000000000000007e-98

   1. Initial program 60.9%

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

      1. associate-*r/ 60.9%

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

      2. associate-*l/ 60.9%

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

      3. *-commutative 60.9%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in A around inf 44.3%

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

      1. *-commutative 44.3%

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

   6. Simplified 44.3%

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

   if 1.30000000000000007e-98 < B

   1. Initial program 44.6%

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

      1. associate-*r/ 44.6%

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

      2. associate-*l/ 44.6%

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

      3. *-commutative 44.6%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in B around inf 55.1%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.3 \cdot 10^{-75}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -8.2 \cdot 10^{-287}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-98}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 12: 61.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{-217}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9.5e-217)
   (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
   (* (/ 180.0 PI) (atan (/ (- C (+ B A)) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.5e-217) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (B + A)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.5e-217) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (B + A)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -9.5e-217:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (B + A)) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -9.5e-217)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(B + A)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -9.5e-217)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	else
		tmp = (180.0 / pi) * atan(((C - (B + A)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -9.5e-217], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -9.5000000000000001e-217

   1. Initial program 28.0%

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

      1. associate-*r/ 28.0%

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

      2. associate-*l/ 28.0%

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

      3. *-commutative 28.0%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in B around 0 64.7%

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

      1. associate-*r/ 64.7%

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

   6. Simplified 64.7%

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

   if -9.5000000000000001e-217 < A

   1. Initial program 64.5%

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

      1. associate-*r/ 64.5%

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

      2. associate-*l/ 64.5%

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

      3. associate-*l/ 64.5%

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

      4. *-lft-identity 64.5%

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

      5. sub-neg 64.5%

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

      6. associate-+l- 64.5%

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

      7. sub-neg 64.5%

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

      8. remove-double-neg 64.5%

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

      9. +-commutative 64.5%

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

      10. unpow2 64.5%

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

      11. unpow2 64.5%

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

      12. hypot-def 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in B around inf 66.5%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{-217}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \]

Alternative 13: 44.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.7 \cdot 10^{-142}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-198}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.7e-142)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 1.15e-198)
     (* (/ 180.0 PI) (atan (/ 0.0 B)))
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.7e-142) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 1.15e-198) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.0 / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.7e-142) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 1.15e-198) {
		tmp = (180.0 / Math.PI) * Math.atan((0.0 / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.7e-142:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 1.15e-198:
		tmp = (180.0 / math.pi) * math.atan((0.0 / B))
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.7e-142)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 1.15e-198)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.0 / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.7e-142)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 1.15e-198)
		tmp = (180.0 / pi) * atan((0.0 / B));
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.7e-142], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.15e-198], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.69999999999999986e-142

   1. Initial program 49.7%

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

      1. associate-*r/ 49.7%

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

      2. associate-*l/ 49.7%

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

      3. *-commutative 49.7%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in B around -inf 51.2%

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

   if -3.69999999999999986e-142 < B < 1.15000000000000007e-198

   1. Initial program 56.5%

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

      1. associate-*r/ 56.5%

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

      2. associate-*l/ 56.5%

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

      3. *-commutative 56.5%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in C around inf 30.4%

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

      1. distribute-rgt1-in 30.4%

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

      2. metadata-eval 30.4%

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

      3. mul0-lft 30.4%

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

      4. metadata-eval 30.4%

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

   6. Simplified 30.4%

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

   if 1.15000000000000007e-198 < B

   1. Initial program 45.1%

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

      1. associate-*r/ 45.1%

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

      2. associate-*l/ 45.1%

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

      3. *-commutative 45.1%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in B around inf 47.7%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.7 \cdot 10^{-142}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-198}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 14: 39.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-310) (* (/ 180.0 PI) (atan 1.0)) (* (/ 180.0 PI) (atan -1.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5e-310:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5e-310)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5e-310)
		tmp = (180.0 / pi) * atan(1.0);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5e-310], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -4.999999999999985e-310

   1. Initial program 49.2%

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

      1. associate-*r/ 49.2%

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

      2. associate-*l/ 49.2%

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

      3. *-commutative 49.2%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in B around -inf 41.7%

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

   if -4.999999999999985e-310 < B

   1. Initial program 49.3%

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

      1. associate-*r/ 49.3%

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

      2. associate-*l/ 49.3%

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

      3. *-commutative 49.3%

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

   3. Simplified 72.4%

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

   4. Taylor expanded in B around inf 41.8%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]

Alternative 15: 21.1% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 49.3%

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

   1. associate-*r/ 49.3%

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

   2. associate-*l/ 49.3%

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

   3. *-commutative 49.3%

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

3. Simplified 73.4%

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

4. Taylor expanded in B around inf 20.8%

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

5. Final simplification 20.8%

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

Reproduce

herbie shell --seed 2023230 
(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)))