ABCF->ab-angle angle

Percentage Accurate: 53.6% → 82.4%

Time: 17.3s

Alternatives: 18

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: 53.6% 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: 82.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_1 := \left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)\\ \mathbf{if}\;t_0 \leq -0.05:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{t_1}{B}\right)}}\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{1}{B} \cdot t_1\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
        (t_1 (- (- C A) (hypot (- A C) B))))
   (if (<= t_0 -0.05)
     (* 180.0 (/ 1.0 (/ PI (atan (/ t_1 B)))))
     (if (<= t_0 0.0)
       (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
       (/ 180.0 (/ PI (atan (* (/ 1.0 B) t_1))))))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double t_1 = (C - A) - hypot((A - C), B);
	double tmp;
	if (t_0 <= -0.05) {
		tmp = 180.0 * (1.0 / (((double) M_PI) / atan((t_1 / B))));
	} else if (t_0 <= 0.0) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((1.0 / B) * t_1)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double t_1 = (C - A) - Math.hypot((A - C), B);
	double tmp;
	if (t_0 <= -0.05) {
		tmp = 180.0 * (1.0 / (Math.PI / Math.atan((t_1 / B))));
	} else if (t_0 <= 0.0) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((1.0 / B) * t_1)));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	t_1 = (C - A) - math.hypot((A - C), B)
	tmp = 0
	if t_0 <= -0.05:
		tmp = 180.0 * (1.0 / (math.pi / math.atan((t_1 / B))))
	elif t_0 <= 0.0:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = 180.0 / (math.pi / math.atan(((1.0 / B) * t_1)))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	t_1 = Float64(Float64(C - A) - hypot(Float64(A - C), B))
	tmp = 0.0
	if (t_0 <= -0.05)
		tmp = Float64(180.0 * Float64(1.0 / Float64(pi / atan(Float64(t_1 / B)))));
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(1.0 / B) * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	t_1 = (C - A) - hypot((A - C), B);
	tmp = 0.0;
	if (t_0 <= -0.05)
		tmp = 180.0 * (1.0 / (pi / atan((t_1 / B))));
	elseif (t_0 <= 0.0)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 / (pi / atan(((1.0 / B) * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.05], N[(180.0 * N[(1.0 / N[(Pi / N[ArcTan[N[(t$95$1 / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.050000000000000003

   1. Initial program 64.5%

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

   3. Applied egg-rr 86.1%

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

      1. div-inv 86.1%

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

   5. Applied egg-rr 86.1%

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

   if -0.050000000000000003 < (*.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 14.7%

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

   3. Applied egg-rr 14.7%

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

   4. Taylor expanded in A around -inf 45.8%

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

      1. expm1-log1p-u 45.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}}\right)\right)} \]

      2. expm1-udef 14.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}}\right)} - 1} \]

      3. associate-/r/ 14.3%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}\right)} - 1 \]

      4. *-un-lft-identity 14.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{\color{blue}{1 \cdot B}}\right)\right)} - 1 \]

      5. times-frac 14.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{0.5}{1} \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)}\right)} - 1 \]

      6. metadata-eval 14.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\color{blue}{0.5} \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)} - 1 \]

   6. Applied egg-rr 14.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 45.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)\right)} \]

      2. expm1-log1p 45.8%

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

      3. associate-/l/ 49.9%

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

      4. unpow2 49.9%

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

      5. times-frac 65.3%

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

      6. *-inverses 65.3%

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

   8. Simplified 65.3%

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

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

   1. Initial program 67.9%

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

   3. Applied egg-rr 90.9%

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

      1. div-inv 90.9%

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

   5. Applied egg-rr 90.9%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.05:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)\right)\right)}}\\ \end{array} \]

Alternative 2: 77.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.7 \cdot 10^{+23}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 7 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\left(A + \mathsf{hypot}\left(A, B\right)\right) \cdot \frac{-1}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.7e+23)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (if (<= A 7e-67)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (/ 180.0 (/ PI (atan (* (+ A (hypot A B)) (/ -1.0 B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.7e+23) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (A <= 7e-67) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((A + hypot(A, B)) * (-1.0 / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.7e+23) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (A <= 7e-67) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((A + Math.hypot(A, B)) * (-1.0 / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.7e+23:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif A <= 7e-67:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan(((A + math.hypot(A, B)) * (-1.0 / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.7e+23)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (A <= 7e-67)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(A + hypot(A, B)) * Float64(-1.0 / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.7e+23)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (A <= 7e-67)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 / (pi / atan(((A + hypot(A, B)) * (-1.0 / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.7e+23], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 7e-67], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] * N[(-1.0 / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.6999999999999999e23

   1. Initial program 24.0%

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

   3. Applied egg-rr 46.7%

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

   4. Taylor expanded in A around -inf 57.0%

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

      1. expm1-log1p-u 54.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}}\right)\right)} \]

      2. expm1-udef 23.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}}\right)} - 1} \]

      3. associate-/r/ 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}\right)} - 1 \]

      4. *-un-lft-identity 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{\color{blue}{1 \cdot B}}\right)\right)} - 1 \]

      5. times-frac 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{0.5}{1} \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)}\right)} - 1 \]

      6. metadata-eval 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\color{blue}{0.5} \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)} - 1 \]

   6. Applied egg-rr 23.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 54.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)\right)} \]

      2. expm1-log1p 57.0%

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

      3. associate-/l/ 58.4%

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

      4. unpow2 58.4%

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

      5. times-frac 72.0%

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

      6. *-inverses 72.0%

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

   8. Simplified 72.0%

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

   if -2.6999999999999999e23 < A < 7.0000000000000001e-67

   1. Initial program 62.8%

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

   2. Taylor expanded in A around 0 61.4%

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

      1. unpow2 61.4%

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

      2. unpow2 61.4%

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

      3. hypot-def 78.9%

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

   4. Simplified 78.9%

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

   if 7.0000000000000001e-67 < A

   1. Initial program 75.5%

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

   3. Applied egg-rr 93.8%

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

      1. div-inv 93.8%

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

   5. Applied egg-rr 93.8%

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

   6. Taylor expanded in C around 0 72.8%

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

      1. distribute-lft-in 72.8%

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

      2. +-commutative 72.8%

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

      3. unpow2 72.8%

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

      4. unpow2 72.8%

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

      5. hypot-def 86.7%

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

      6. neg-mul-1 86.7%

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

      7. sub-neg 86.7%

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

      8. neg-mul-1 86.7%

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

      9. hypot-def 72.8%

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

      10. unpow2 72.8%

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

      11. unpow2 72.8%

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

      12. +-commutative 72.8%

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

      13. unpow2 72.8%

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

      14. unpow2 72.8%

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

      15. hypot-def 86.7%

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

   8. Simplified 86.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.7 \cdot 10^{+23}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 7 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\left(A + \mathsf{hypot}\left(A, B\right)\right) \cdot \frac{-1}{B}\right)}}\\ \end{array} \]

Alternative 3: 80.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.6e+22)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.6e+22) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.6e+22) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.6e+22:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.6e+22)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.6e+22)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.6e+22], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -8.6000000000000004e22

   1. Initial program 24.0%

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

   3. Applied egg-rr 46.7%

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

   4. Taylor expanded in A around -inf 57.0%

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

      1. expm1-log1p-u 54.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}}\right)\right)} \]

      2. expm1-udef 23.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}}\right)} - 1} \]

      3. associate-/r/ 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}\right)} - 1 \]

      4. *-un-lft-identity 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{\color{blue}{1 \cdot B}}\right)\right)} - 1 \]

      5. times-frac 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{0.5}{1} \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)}\right)} - 1 \]

      6. metadata-eval 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\color{blue}{0.5} \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)} - 1 \]

   6. Applied egg-rr 23.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 54.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)\right)} \]

      2. expm1-log1p 57.0%

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

      3. associate-/l/ 58.4%

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

      4. unpow2 58.4%

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

      5. times-frac 72.0%

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

      6. *-inverses 72.0%

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

   8. Simplified 72.0%

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

   if -8.6000000000000004e22 < A

   1. Initial program 68.1%

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

   3. Simplified 85.9%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.6 \cdot 10^{+22}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 80.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.9 \cdot 10^{+23}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.9e+23)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (/ 180.0 (/ PI (atan (/ (- (- C A) (hypot (- A C) B)) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.9e+23) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((C - A) - hypot((A - C), B)) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.9e+23) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((C - A) - Math.hypot((A - C), B)) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.9e+23:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	else:
		tmp = 180.0 / (math.pi / math.atan((((C - A) - math.hypot((A - C), B)) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.9e+23)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.9e+23)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	else
		tmp = 180.0 / (pi / atan((((C - A) - hypot((A - C), B)) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.9e+23], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -4.9000000000000003e23

   1. Initial program 24.0%

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

   3. Applied egg-rr 46.7%

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

   4. Taylor expanded in A around -inf 57.0%

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

      1. expm1-log1p-u 54.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}}\right)\right)} \]

      2. expm1-udef 23.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}}\right)} - 1} \]

      3. associate-/r/ 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}\right)} - 1 \]

      4. *-un-lft-identity 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{\color{blue}{1 \cdot B}}\right)\right)} - 1 \]

      5. times-frac 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{0.5}{1} \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)}\right)} - 1 \]

      6. metadata-eval 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\color{blue}{0.5} \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)} - 1 \]

   6. Applied egg-rr 23.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 54.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)\right)} \]

      2. expm1-log1p 57.0%

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

      3. associate-/l/ 58.4%

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

      4. unpow2 58.4%

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

      5. times-frac 72.0%

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

      6. *-inverses 72.0%

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

   8. Simplified 72.0%

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

   if -4.9000000000000003e23 < A

   1. Initial program 68.1%

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

   3. Applied egg-rr 85.9%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.9 \cdot 10^{+23}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}}\\ \end{array} \]

Alternative 5: 77.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.32 \cdot 10^{+23}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.32e+23)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (if (<= A 2e-67)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (/ (- (- A) (hypot B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.32e+23) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (A <= 2e-67) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.32e+23) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (A <= 2e-67) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot(B, A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.32e+23:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif A <= 2e-67:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((-A - math.hypot(B, A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.32e+23)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (A <= 2e-67)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(B, A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.32e+23)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (A <= 2e-67)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((-A - hypot(B, A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.32e+23], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2e-67], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.3199999999999999e23

   1. Initial program 24.0%

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

   3. Applied egg-rr 46.7%

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

   4. Taylor expanded in A around -inf 57.0%

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

      1. expm1-log1p-u 54.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}}\right)\right)} \]

      2. expm1-udef 23.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}}\right)} - 1} \]

      3. associate-/r/ 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}\right)} - 1 \]

      4. *-un-lft-identity 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{\color{blue}{1 \cdot B}}\right)\right)} - 1 \]

      5. times-frac 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{0.5}{1} \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)}\right)} - 1 \]

      6. metadata-eval 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\color{blue}{0.5} \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)} - 1 \]

   6. Applied egg-rr 23.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 54.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)\right)} \]

      2. expm1-log1p 57.0%

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

      3. associate-/l/ 58.4%

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

      4. unpow2 58.4%

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

      5. times-frac 72.0%

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

      6. *-inverses 72.0%

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

   8. Simplified 72.0%

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

   if -1.3199999999999999e23 < A < 1.99999999999999989e-67

   1. Initial program 62.8%

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

   2. Taylor expanded in A around 0 61.4%

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

      1. unpow2 61.4%

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

      2. unpow2 61.4%

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

      3. hypot-def 78.9%

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

   4. Simplified 78.9%

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

   if 1.99999999999999989e-67 < A

   1. Initial program 75.5%

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

   2. Taylor expanded in C around 0 72.8%

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

      1. associate-*r/ 72.8%

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

      2. mul-1-neg 72.8%

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

      3. +-commutative 72.8%

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

      4. unpow2 72.8%

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

      5. unpow2 72.8%

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

      6. hypot-def 86.7%

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

   4. Simplified 86.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.32 \cdot 10^{+23}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(B, A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 6: 77.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 2.5 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.8e+21)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (if (<= A 2.5e-67)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (/ 180.0 (/ PI (atan (/ (- (- A) (hypot A B)) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.8e+21) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (A <= 2.5e-67) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((-A - hypot(A, B)) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.8e+21) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (A <= 2.5e-67) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((-A - Math.hypot(A, B)) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.8e+21:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif A <= 2.5e-67:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan(((-A - math.hypot(A, B)) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.8e+21)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (A <= 2.5e-67)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(-A) - hypot(A, B)) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.8e+21)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (A <= 2.5e-67)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 / (pi / atan(((-A - hypot(A, B)) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.8e+21], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.5e-67], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[((-A) - N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.8e21

   1. Initial program 24.0%

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

   3. Applied egg-rr 46.7%

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

   4. Taylor expanded in A around -inf 57.0%

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

      1. expm1-log1p-u 54.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}}\right)\right)} \]

      2. expm1-udef 23.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}}\right)} - 1} \]

      3. associate-/r/ 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}\right)} - 1 \]

      4. *-un-lft-identity 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{\color{blue}{1 \cdot B}}\right)\right)} - 1 \]

      5. times-frac 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{0.5}{1} \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)}\right)} - 1 \]

      6. metadata-eval 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\color{blue}{0.5} \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)} - 1 \]

   6. Applied egg-rr 23.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 54.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)\right)} \]

      2. expm1-log1p 57.0%

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

      3. associate-/l/ 58.4%

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

      4. unpow2 58.4%

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

      5. times-frac 72.0%

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

      6. *-inverses 72.0%

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

   8. Simplified 72.0%

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

   if -5.8e21 < A < 2.4999999999999999e-67

   1. Initial program 62.8%

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

   2. Taylor expanded in A around 0 61.4%

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

      1. unpow2 61.4%

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

      2. unpow2 61.4%

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

      3. hypot-def 78.9%

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

   4. Simplified 78.9%

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

   if 2.4999999999999999e-67 < A

   1. Initial program 75.5%

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

   3. Applied egg-rr 93.8%

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

   4. Taylor expanded in C around 0 72.8%

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

      1. distribute-lft-in 72.8%

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

      2. +-commutative 72.8%

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

      3. unpow2 72.8%

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

      4. unpow2 72.8%

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

      5. hypot-def 86.7%

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

      6. neg-mul-1 86.7%

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

      7. sub-neg 86.7%

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

      8. neg-mul-1 86.7%

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

      9. hypot-def 72.8%

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

      10. unpow2 72.8%

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

      11. unpow2 72.8%

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

      12. +-commutative 72.8%

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

      13. unpow2 72.8%

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

      14. unpow2 72.8%

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

      15. hypot-def 86.7%

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

   6. Simplified 86.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 2.5 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A, B\right)}{B}\right)}}\\ \end{array} \]

Alternative 7: 74.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.3 \cdot 10^{+23}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 8.6 \cdot 10^{-72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.3e+23)
   (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
   (if (<= A 8.6e-72)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.3e+23) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (A <= 8.6e-72) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.3e+23) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (A <= 8.6e-72) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.3e+23:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif A <= 8.6e-72:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.3e+23)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (A <= 8.6e-72)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.3e+23)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (A <= 8.6e-72)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.3e+23], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 8.6e-72], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.3000000000000001e23

   1. Initial program 24.0%

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

   3. Applied egg-rr 46.7%

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

   4. Taylor expanded in A around -inf 57.0%

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

      1. expm1-log1p-u 54.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}}\right)\right)} \]

      2. expm1-udef 23.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}}\right)} - 1} \]

      3. associate-/r/ 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{B}\right)}\right)} - 1 \]

      4. *-un-lft-identity 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5 \cdot \frac{{B}^{2}}{A}}{\color{blue}{1 \cdot B}}\right)\right)} - 1 \]

      5. times-frac 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{0.5}{1} \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)}\right)} - 1 \]

      6. metadata-eval 23.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(\color{blue}{0.5} \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)} - 1 \]

   6. Applied egg-rr 23.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 54.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{\frac{{B}^{2}}{A}}{B}\right)\right)\right)} \]

      2. expm1-log1p 57.0%

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

      3. associate-/l/ 58.4%

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

      4. unpow2 58.4%

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

      5. times-frac 72.0%

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

      6. *-inverses 72.0%

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

   8. Simplified 72.0%

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

   if -5.3000000000000001e23 < A < 8.5999999999999998e-72

   1. Initial program 61.9%

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

   2. Taylor expanded in A around 0 60.4%

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

      1. unpow2 60.4%

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

      2. unpow2 60.4%

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

      3. hypot-def 78.3%

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

   4. Simplified 78.3%

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

   if 8.5999999999999998e-72 < A

   1. Initial program 76.3%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in B around inf 79.9%

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

      1. +-commutative 79.9%

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

   6. Simplified 79.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.3 \cdot 10^{+23}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;A \leq 8.6 \cdot 10^{-72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 48.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{-144}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.15 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6e-145)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 1.8e-252)
     (* 180.0 (/ (atan (/ C B)) PI))
     (if (<= A 1e-144)
       (* 180.0 (/ (atan 1.0) PI))
       (if (<= A 1.15e-61)
         (* 180.0 (/ (atan -1.0) PI))
         (* 180.0 (/ (atan (* (/ A B) -2.0)) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6e-145) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 1.8e-252) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (A <= 1e-144) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 1.15e-61) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6e-145) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 1.8e-252) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (A <= 1e-144) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 1.15e-61) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6e-145:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 1.8e-252:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif A <= 1e-144:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 1.15e-61:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6e-145)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 1.8e-252)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (A <= 1e-144)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 1.15e-61)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6e-145)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 1.8e-252)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (A <= 1e-144)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 1.15e-61)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6e-145], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.8e-252], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1e-144], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.15e-61], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -5.99999999999999985e-145

   1. Initial program 31.9%

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

   2. Taylor expanded in A around -inf 62.2%

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

   if -5.99999999999999985e-145 < A < 1.80000000000000011e-252

   1. Initial program 68.5%

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

   3. Simplified 84.7%

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

      1. add-sqr-sqrt 80.5%

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

      2. pow2 80.5%

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

      3. hypot-udef 64.2%

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

      4. unpow2 64.2%

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

      5. unpow2 64.2%

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

      6. +-commutative 64.2%

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

      7. unpow2 64.2%

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

      8. unpow2 64.2%

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

      9. hypot-def 80.5%

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

   5. Applied egg-rr 80.5%

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

   6. Taylor expanded in C around inf 49.1%

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

   if 1.80000000000000011e-252 < A < 9.9999999999999995e-145

   1. Initial program 55.7%

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

   2. Taylor expanded in B around -inf 44.9%

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

   if 9.9999999999999995e-145 < A < 1.14999999999999996e-61

   1. Initial program 76.1%

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

   2. Taylor expanded in B around inf 54.8%

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

   if 1.14999999999999996e-61 < A

   1. Initial program 75.9%

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

   2. Taylor expanded in A around inf 67.4%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.8 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{-144}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.15 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \]

Alternative 9: 48.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.8 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-249}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.22 \cdot 10^{-141}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.8e-145)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 1.2e-249)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= A 1.22e-141)
       (* 180.0 (/ (atan 1.0) PI))
       (if (<= A 1.25e-54)
         (* 180.0 (/ (atan -1.0) PI))
         (* 180.0 (/ (atan (* (/ A B) -2.0)) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.8e-145) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 1.2e-249) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (A <= 1.22e-141) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (A <= 1.25e-54) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.8e-145) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 1.2e-249) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (A <= 1.22e-141) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (A <= 1.25e-54) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.8e-145:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 1.2e-249:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif A <= 1.22e-141:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif A <= 1.25e-54:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.8e-145)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 1.2e-249)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (A <= 1.22e-141)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (A <= 1.25e-54)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.8e-145)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 1.2e-249)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (A <= 1.22e-141)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (A <= 1.25e-54)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.8e-145], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.2e-249], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.22e-141], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.25e-54], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -6.7999999999999998e-145

   1. Initial program 31.9%

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

   2. Taylor expanded in A around -inf 62.2%

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

   if -6.7999999999999998e-145 < A < 1.20000000000000006e-249

   1. Initial program 68.5%

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

   2. Taylor expanded in C around -inf 49.4%

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

   if 1.20000000000000006e-249 < A < 1.22e-141

   1. Initial program 55.7%

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

   2. Taylor expanded in B around -inf 44.9%

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

   if 1.22e-141 < A < 1.25000000000000004e-54

   1. Initial program 76.1%

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

   2. Taylor expanded in B around inf 54.8%

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

   if 1.25000000000000004e-54 < A

   1. Initial program 75.9%

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

   2. Taylor expanded in A around inf 67.4%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.8 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-249}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.22 \cdot 10^{-141}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1.25 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \]

Alternative 10: 59.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.3 \cdot 10^{-143}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.9 \cdot 10^{-231} \lor \neg \left(A \leq 1.45 \cdot 10^{-169}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.3e-143)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (if (or (<= A 3.9e-231) (not (<= A 1.45e-169)))
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI))
     (* 180.0 (/ (atan 1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.3e-143) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if ((A <= 3.9e-231) || !(A <= 1.45e-169)) {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.3e-143) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if ((A <= 3.9e-231) || !(A <= 1.45e-169)) {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.3e-143:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif (A <= 3.9e-231) or not (A <= 1.45e-169):
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.3e-143)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif ((A <= 3.9e-231) || !(A <= 1.45e-169))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.3e-143)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif ((A <= 3.9e-231) || ~((A <= 1.45e-169)))
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	else
		tmp = 180.0 * (atan(1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.3e-143], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[Or[LessEqual[A, 3.9e-231], N[Not[LessEqual[A, 1.45e-169]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.3000000000000001e-143

   1. Initial program 32.1%

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

   3. Applied egg-rr 52.4%

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

   4. Taylor expanded in A around -inf 47.1%

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

   5. Taylor expanded in B around 0 62.7%

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

      1. associate-*r/ 62.8%

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

   7. Simplified 62.8%

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

   if -3.3000000000000001e-143 < A < 3.8999999999999998e-231 or 1.4500000000000001e-169 < A

   1. Initial program 73.0%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in B around inf 71.2%

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

      1. +-commutative 71.2%

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

   6. Simplified 71.2%

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

   if 3.8999999999999998e-231 < A < 1.4500000000000001e-169

   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. Taylor expanded in B around -inf 53.8%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.3 \cdot 10^{-143}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.9 \cdot 10^{-231} \lor \neg \left(A \leq 1.45 \cdot 10^{-169}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \end{array} \]

Alternative 11: 53.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9.2 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.5 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.25 \cdot 10^{-169}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9.2e-145)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 2.5e-250)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= A 2.25e-169)
       (* 180.0 (/ (atan 1.0) PI))
       (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.2e-145) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 2.5e-250) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (A <= 2.25e-169) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.2e-145) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 2.5e-250) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (A <= 2.25e-169) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -9.2e-145:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 2.5e-250:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif A <= 2.25e-169:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -9.2e-145)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 2.5e-250)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (A <= 2.25e-169)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -9.2e-145)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 2.5e-250)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (A <= 2.25e-169)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -9.2e-145], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.5e-250], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.25e-169], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -9.20000000000000028e-145

   1. Initial program 31.9%

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

   2. Taylor expanded in A around -inf 62.2%

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

   if -9.20000000000000028e-145 < A < 2.50000000000000013e-250

   1. Initial program 68.5%

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

   2. Taylor expanded in C around -inf 49.4%

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

   if 2.50000000000000013e-250 < A < 2.2499999999999999e-169

   1. Initial program 53.4%

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

   2. Taylor expanded in B around -inf 51.4%

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

   if 2.2499999999999999e-169 < A

   1. Initial program 75.7%

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

   2. Taylor expanded in C around 0 68.8%

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

      1. associate-*r/ 68.8%

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

      2. mul-1-neg 68.8%

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

      3. +-commutative 68.8%

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

      4. unpow2 68.8%

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

      5. unpow2 68.8%

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

      6. hypot-def 82.9%

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

   4. Simplified 82.9%

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

   5. Taylor expanded in A around 0 72.0%

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

   6. Taylor expanded in A around 0 72.0%

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

      1. neg-mul-1 72.0%

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

      2. distribute-neg-frac 72.0%

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

      3. +-commutative 72.0%

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

      4. distribute-neg-in 72.0%

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

      5. neg-mul-1 72.0%

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

      6. sub-neg 72.0%

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

      7. sub-neg 72.0%

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

      8. neg-mul-1 72.0%

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

      9. distribute-neg-in 72.0%

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

      10. +-commutative 72.0%

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

      11. distribute-neg-in 72.0%

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

      12. mul-1-neg 72.0%

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

      13. sub-neg 72.0%

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

   8. Simplified 72.0%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -9.2 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.5 \cdot 10^{-250}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.25 \cdot 10^{-169}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 12: 53.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.9 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.85 \cdot 10^{-253}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-161}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.9e-145)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 1.85e-253)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= A 1.2e-161)
       (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
       (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.9e-145) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 1.85e-253) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (A <= 1.2e-161) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.9e-145) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 1.85e-253) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (A <= 1.2e-161) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.9e-145:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 1.85e-253:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif A <= 1.2e-161:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.9e-145)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 1.85e-253)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (A <= 1.2e-161)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.9e-145)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 1.85e-253)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (A <= 1.2e-161)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.9e-145], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.85e-253], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.2e-161], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -5.8999999999999998e-145

   1. Initial program 31.9%

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

   2. Taylor expanded in A around -inf 62.2%

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

   if -5.8999999999999998e-145 < A < 1.84999999999999988e-253

   1. Initial program 68.5%

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

   2. Taylor expanded in C around -inf 49.4%

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

   if 1.84999999999999988e-253 < A < 1.19999999999999999e-161

   1. Initial program 58.3%

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

   2. Taylor expanded in C around 0 46.1%

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

      1. associate-*r/ 46.1%

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

      2. mul-1-neg 46.1%

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

      3. +-commutative 46.1%

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

      4. unpow2 46.1%

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

      5. unpow2 46.1%

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

      6. hypot-def 67.5%

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

   4. Simplified 67.5%

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

   5. Taylor expanded in B around -inf 56.5%

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

      1. mul-1-neg 56.5%

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

      2. unsub-neg 56.5%

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

   7. Simplified 56.5%

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

   if 1.19999999999999999e-161 < A

   1. Initial program 75.2%

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

   2. Taylor expanded in C around 0 69.0%

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

      1. associate-*r/ 69.0%

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

      2. mul-1-neg 69.0%

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

      3. +-commutative 69.0%

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

      4. unpow2 69.0%

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

      5. unpow2 69.0%

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

      6. hypot-def 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in A around 0 72.4%

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

   6. Taylor expanded in A around 0 72.4%

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

      1. neg-mul-1 72.4%

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

      2. distribute-neg-frac 72.4%

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

      3. +-commutative 72.4%

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

      4. distribute-neg-in 72.4%

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

      5. neg-mul-1 72.4%

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

      6. sub-neg 72.4%

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

      7. sub-neg 72.4%

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

      8. neg-mul-1 72.4%

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

      9. distribute-neg-in 72.4%

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

      10. +-commutative 72.4%

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

      11. distribute-neg-in 72.4%

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

      12. mul-1-neg 72.4%

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

      13. sub-neg 72.4%

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

   8. Simplified 72.4%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.9 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.85 \cdot 10^{-253}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-161}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 13: 53.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -7.2 \cdot 10^{-145}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.7 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-157}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -7.2e-145)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (if (<= A 2.7e-252)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= A 1.2e-157)
       (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
       (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -7.2e-145) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= 2.7e-252) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (A <= 1.2e-157) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -7.2e-145) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= 2.7e-252) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (A <= 1.2e-157) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -7.2e-145:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= 2.7e-252:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif A <= 1.2e-157:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -7.2e-145)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= 2.7e-252)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (A <= 1.2e-157)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -7.2e-145)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= 2.7e-252)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (A <= 1.2e-157)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -7.2e-145], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 2.7e-252], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.2e-157], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -7.2000000000000001e-145

   1. Initial program 31.9%

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

   3. Applied egg-rr 53.0%

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

   4. Taylor expanded in A around -inf 46.7%

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

   5. Taylor expanded in B around 0 62.2%

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

      1. associate-*r/ 62.3%

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

   7. Simplified 62.3%

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

   if -7.2000000000000001e-145 < A < 2.69999999999999981e-252

   1. Initial program 68.5%

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

   2. Taylor expanded in C around -inf 49.4%

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

   if 2.69999999999999981e-252 < A < 1.2e-157

   1. Initial program 58.3%

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

   2. Taylor expanded in C around 0 46.1%

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

      1. associate-*r/ 46.1%

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

      2. mul-1-neg 46.1%

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

      3. +-commutative 46.1%

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

      4. unpow2 46.1%

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

      5. unpow2 46.1%

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

      6. hypot-def 67.5%

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

   4. Simplified 67.5%

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

   5. Taylor expanded in B around -inf 56.5%

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

      1. mul-1-neg 56.5%

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

      2. unsub-neg 56.5%

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

   7. Simplified 56.5%

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

   if 1.2e-157 < A

   1. Initial program 75.2%

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

   2. Taylor expanded in C around 0 69.0%

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

      1. associate-*r/ 69.0%

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

      2. mul-1-neg 69.0%

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

      3. +-commutative 69.0%

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

      4. unpow2 69.0%

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

      5. unpow2 69.0%

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

      6. hypot-def 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in A around 0 72.4%

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

   6. Taylor expanded in A around 0 72.4%

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

      1. neg-mul-1 72.4%

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

      2. distribute-neg-frac 72.4%

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

      3. +-commutative 72.4%

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

      4. distribute-neg-in 72.4%

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

      5. neg-mul-1 72.4%

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

      6. sub-neg 72.4%

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

      7. sub-neg 72.4%

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

      8. neg-mul-1 72.4%

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

      9. distribute-neg-in 72.4%

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

      10. +-commutative 72.4%

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

      11. distribute-neg-in 72.4%

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

      12. mul-1-neg 72.4%

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

      13. sub-neg 72.4%

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

   8. Simplified 72.4%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7.2 \cdot 10^{-145}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.7 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{-157}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 14: 63.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.4 \cdot 10^{-103}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2300000:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.4e-103)
   (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
   (if (<= B 2300000.0)
     (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.4e-103) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else if (B <= 2300000.0) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.4e-103) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else if (B <= 2300000.0) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((C - (B + A)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 1.4e-103:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	elif B <= 2300000.0:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((C - (B + A)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 1.4e-103)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	elseif (B <= 2300000.0)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 1.4e-103)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	elseif (B <= 2300000.0)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	else
		tmp = 180.0 * (atan(((C - (B + A)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 1.4e-103], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2300000.0], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 1.40000000000000011e-103

   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

   3. Simplified 73.9%

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

   4. Taylor expanded in B around -inf 67.5%

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

      1. neg-mul-1 67.5%

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

      2. unsub-neg 67.5%

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

   6. Simplified 67.5%

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

   if 1.40000000000000011e-103 < B < 2.3e6

   1. Initial program 38.8%

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

   3. Applied egg-rr 48.8%

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

   4. Taylor expanded in A around -inf 57.1%

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

   5. Taylor expanded in B around 0 61.0%

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

      1. associate-*r/ 61.1%

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

   7. Simplified 61.1%

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

   if 2.3e6 < B

   1. Initial program 58.2%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in B around inf 80.7%

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

      1. +-commutative 80.7%

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

   6. Simplified 80.7%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.4 \cdot 10^{-103}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2300000:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 15: 46.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.2 \cdot 10^{-81}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.2e-81)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.6e-61)
     (* 180.0 (/ (atan (/ C B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.2e-81) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.6e-61) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.2e-81) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.6e-61) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -6.2e-81:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.6e-61:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -6.2e-81)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.6e-61)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -6.2e-81)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.6e-61)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -6.2e-81], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.6e-61], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -6.19999999999999976e-81

   1. Initial program 58.3%

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

   2. Taylor expanded in B around -inf 58.9%

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

   if -6.19999999999999976e-81 < B < 1.6000000000000001e-61

   1. Initial program 61.5%

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

   3. Simplified 66.5%

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

      1. add-sqr-sqrt 60.9%

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

      2. pow2 60.9%

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

      3. hypot-udef 57.1%

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

      4. unpow2 57.1%

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

      5. unpow2 57.1%

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

      6. +-commutative 57.1%

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

      7. unpow2 57.1%

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

      8. unpow2 57.1%

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

      9. hypot-def 60.9%

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

   5. Applied egg-rr 60.9%

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

   6. Taylor expanded in C around inf 37.4%

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

   if 1.6000000000000001e-61 < B

   1. Initial program 53.7%

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

   2. Taylor expanded in B around inf 54.2%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.2 \cdot 10^{-81}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 16: 43.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.1 \cdot 10^{-130}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-226}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.1e-130)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 7.2e-226)
     (/ 180.0 (/ PI (atan 0.0)))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.1e-130) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 7.2e-226) {
		tmp = 180.0 / (((double) M_PI) / atan(0.0));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.1e-130) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 7.2e-226) {
		tmp = 180.0 / (Math.PI / Math.atan(0.0));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.1e-130:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 7.2e-226:
		tmp = 180.0 / (math.pi / math.atan(0.0))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.1e-130)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 7.2e-226)
		tmp = Float64(180.0 / Float64(pi / atan(0.0)));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.1e-130)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 7.2e-226)
		tmp = 180.0 / (pi / atan(0.0));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.1e-130], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.2e-226], N[(180.0 / N[(Pi / N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.0999999999999999e-130

   1. Initial program 62.4%

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

   2. Taylor expanded in B around -inf 53.4%

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

   if -1.0999999999999999e-130 < B < 7.19999999999999988e-226

   1. Initial program 55.7%

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

   3. Applied egg-rr 74.5%

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

      1. div-inv 74.5%

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

   5. Applied egg-rr 74.5%

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

   6. Taylor expanded in C around inf 28.6%

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

      1. associate-*r/ 28.6%

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

      2. distribute-rgt1-in 28.6%

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

      3. metadata-eval 28.6%

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

      4. mul0-lft 28.6%

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

      5. metadata-eval 28.6%

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

      6. div0 28.6%

         \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{0}}} \]

   8. Simplified 28.6%

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \color{blue}{0}}} \]

   if 7.19999999999999988e-226 < B

   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. Taylor expanded in B around inf 41.5%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.1 \cdot 10^{-130}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7.2 \cdot 10^{-226}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 17: 40.1% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if B < -4.999999999999985e-310

   1. Initial program 59.4%

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

   2. Taylor expanded in B around -inf 40.6%

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

   if -4.999999999999985e-310 < B

   1. Initial program 57.2%

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

   2. Taylor expanded in B around inf 37.0%

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

4. Final simplification 38.7%

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

Alternative 18: 20.6% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.3%

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

2. Taylor expanded in B around inf 20.1%

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

3. Final simplification 20.1%

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

Reproduce

herbie shell --seed 2023322 
(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)))