ABCF->ab-angle angle

Percentage Accurate: 54.4% → 82.6%

Time: 16.8s

Alternatives: 21

Speedup: 3.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.4% 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: 82.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -0.5 \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -0.5 or 0.0 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 64.2%

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

      1. associate-*l/ 64.2%

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

      2. *-lft-identity 64.2%

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

      3. +-commutative 64.2%

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

      4. unpow2 64.2%

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

      5. unpow2 64.2%

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

      6. hypot-define 93.5%

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

   3. Simplified 93.5%

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

   if -0.5 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 0.0

   1. Initial program 14.3%

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

   3. Taylor expanded in A around -inf 61.3%

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

      1. associate-*r/ 61.3%

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

   5. Simplified 61.3%

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

4. Final simplification 89.5%

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

Alternative 2: 79.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq 7.2 \cdot 10^{-121}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.8e+64)
   (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
   (if (<= A 7.2e-121)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (/ (atan (/ (- C (+ A (hypot B A))) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+64) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (A <= 7.2e-121) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (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 <= -1.8e+64) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (A <= 7.2e-121) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, A))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.8e+64:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif A <= 7.2e-121:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, A))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.8e+64)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= 7.2e-121)
		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(A + hypot(B, A))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.8e+64)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (A <= 7.2e-121)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, A))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.8e+64], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 7.2e-121], 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[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.80000000000000007e64

   1. Initial program 16.8%

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

      1. clear-num 16.8%

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

      2. un-div-inv 16.8%

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

      3. associate-*l/ 16.8%

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

      4. *-un-lft-identity 16.8%

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

      5. associate--l- 14.3%

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

      6. unpow2 14.3%

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

      7. unpow2 14.3%

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

      8. hypot-define 35.1%

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

   4. Applied egg-rr 35.1%

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

   5. Taylor expanded in A around -inf 79.1%

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

   if -1.80000000000000007e64 < A < 7.19999999999999967e-121

   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. Add Preprocessing

   3. Taylor expanded in A around 0 57.2%

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

      1. unpow2 57.2%

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

      2. unpow2 57.2%

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

      3. hypot-define 77.1%

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

   5. Simplified 77.1%

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

   if 7.19999999999999967e-121 < A

   1. Initial program 76.9%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in C around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. unpow2 75.6%

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

      3. unpow2 75.6%

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

      4. hypot-define 91.6%

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

   7. Simplified 91.6%

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

Alternative 3: 78.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{-81}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.2e+63)
   (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
   (if (<= A 2.8e-81)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* (/ 180.0 PI) (atan (/ (+ A (hypot B A)) (- B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.2e+63) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (A <= 2.8e-81) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((A + hypot(B, A)) / -B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.2e+63) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (A <= 2.8e-81) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((A + Math.hypot(B, A)) / -B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.2e+63:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif A <= 2.8e-81:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((A + math.hypot(B, A)) / -B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.2e+63)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= 2.8e-81)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A + hypot(B, A)) / Float64(-B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.2e+63)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (A <= 2.8e-81)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = (180.0 / pi) * atan(((A + hypot(B, A)) / -B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.2e+63], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.8e-81], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.2000000000000002e63

   1. Initial program 16.8%

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

      1. clear-num 16.8%

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

      2. un-div-inv 16.8%

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

      3. associate-*l/ 16.8%

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

      4. *-un-lft-identity 16.8%

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

      5. associate--l- 14.3%

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

      6. unpow2 14.3%

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

      7. unpow2 14.3%

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

      8. hypot-define 35.1%

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

   4. Applied egg-rr 35.1%

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

   5. Taylor expanded in A around -inf 79.1%

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

   if -5.2000000000000002e63 < A < 2.7999999999999999e-81

   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. Add Preprocessing

   3. Taylor expanded in A around 0 57.5%

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

      1. unpow2 57.5%

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

      2. unpow2 57.5%

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

      3. hypot-define 76.9%

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

   5. Simplified 76.9%

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

   if 2.7999999999999999e-81 < A

   1. Initial program 77.1%

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

   3. Taylor expanded in B around 0 77.1%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in C around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. +-commutative 74.8%

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

      3. unpow2 74.8%

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

      4. unpow2 74.8%

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

      5. hypot-undefine 91.4%

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

   8. Simplified 91.4%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq 2.8 \cdot 10^{-81}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.3 \cdot 10^{+64}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq 1.42 \cdot 10^{-81}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.3e+64)
   (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
   (if (<= A 1.42e-81)
     (* 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 <= -1.3e+64) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (A <= 1.42e-81) {
		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 <= -1.3e+64) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (A <= 1.42e-81) {
		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 <= -1.3e+64:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif A <= 1.42e-81:
		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 <= -1.3e+64)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= 1.42e-81)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.3e+64)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (A <= 1.42e-81)
		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, -1.3e+64], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.42e-81], 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 < -1.29999999999999998e64

   1. Initial program 16.8%

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

      1. clear-num 16.8%

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

      2. un-div-inv 16.8%

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

      3. associate-*l/ 16.8%

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

      4. *-un-lft-identity 16.8%

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

      5. associate--l- 14.3%

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

      6. unpow2 14.3%

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

      7. unpow2 14.3%

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

      8. hypot-define 35.1%

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

   4. Applied egg-rr 35.1%

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

   5. Taylor expanded in A around -inf 79.1%

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

   if -1.29999999999999998e64 < A < 1.42000000000000009e-81

   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. Add Preprocessing

   3. Taylor expanded in A around 0 57.5%

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

      1. unpow2 57.5%

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

      2. unpow2 57.5%

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

      3. hypot-define 76.9%

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

   5. Simplified 76.9%

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

   if 1.42000000000000009e-81 < A

   1. Initial program 77.1%

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

   3. Taylor expanded in C around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. distribute-neg-frac2 74.8%

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

      3. +-commutative 74.8%

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

      4. unpow2 74.8%

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

      5. unpow2 74.8%

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

      6. hypot-define 91.3%

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

   5. Simplified 91.3%

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

Alternative 5: 76.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.8 \cdot 10^{+63}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq 1.02 \cdot 10^{+107}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \left(\frac{1}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.8e+63)
   (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
   (if (<= A 1.02e+107)
     (* 180.0 (/ (atan (/ (- C (hypot B C)) B)) PI))
     (* 180.0 (* (/ 1.0 PI) (atan (- -1.0 (/ A B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.8e+63) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (A <= 1.02e+107) {
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * ((1.0 / ((double) M_PI)) * atan((-1.0 - (A / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.8e+63) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (A <= 1.02e+107) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(B, C)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * ((1.0 / Math.PI) * Math.atan((-1.0 - (A / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.8e+63:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif A <= 1.02e+107:
		tmp = 180.0 * (math.atan(((C - math.hypot(B, C)) / B)) / math.pi)
	else:
		tmp = 180.0 * ((1.0 / math.pi) * math.atan((-1.0 - (A / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.8e+63)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= 1.02e+107)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(B, C)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(Float64(1.0 / pi) * atan(Float64(-1.0 - Float64(A / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.8e+63)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (A <= 1.02e+107)
		tmp = 180.0 * (atan(((C - hypot(B, C)) / B)) / pi);
	else
		tmp = 180.0 * ((1.0 / pi) * atan((-1.0 - (A / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.8e+63], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.02e+107], 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[(1.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.7999999999999995e63

   1. Initial program 16.8%

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

      1. clear-num 16.8%

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

      2. un-div-inv 16.8%

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

      3. associate-*l/ 16.8%

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

      4. *-un-lft-identity 16.8%

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

      5. associate--l- 14.3%

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

      6. unpow2 14.3%

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

      7. unpow2 14.3%

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

      8. hypot-define 35.1%

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

   4. Applied egg-rr 35.1%

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

   5. Taylor expanded in A around -inf 79.1%

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

   if -8.7999999999999995e63 < A < 1.01999999999999994e107

   1. Initial program 62.1%

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

   3. Taylor expanded in A around 0 56.5%

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

      1. unpow2 56.5%

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

      2. unpow2 56.5%

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

      3. hypot-define 77.0%

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

   5. Simplified 77.0%

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

   if 1.01999999999999994e107 < A

   1. Initial program 79.4%

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

   3. Taylor expanded in B around inf 86.4%

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

      1. clear-num 86.4%

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

      2. associate-/r/ 86.4%

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

      3. associate-*r* 86.4%

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

      4. lft-mult-inverse 86.4%

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

      5. *-un-lft-identity 86.4%

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

   5. Applied egg-rr 86.4%

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

   6. Taylor expanded in C around 0 92.4%

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

      1. distribute-lft-in 92.4%

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

      2. metadata-eval 92.4%

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

      3. mul-1-neg 92.4%

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

      4. unsub-neg 92.4%

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

   8. Simplified 92.4%

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

Alternative 6: 81.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.16 \cdot 10^{+64}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.16e+64)
   (/ 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 <= -1.16e+64) {
		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 <= -1.16e+64) {
		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 <= -1.16e+64:
		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 <= -1.16e+64)
		tmp = Float64(180.0 / Float64(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 <= -1.16e+64)
		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, -1.16e+64], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $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 < -1.16e64

   1. Initial program 16.8%

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

      1. clear-num 16.8%

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

      2. un-div-inv 16.8%

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

      3. associate-*l/ 16.8%

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

      4. *-un-lft-identity 16.8%

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

      5. associate--l- 14.3%

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

      6. unpow2 14.3%

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

      7. unpow2 14.3%

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

      8. hypot-define 35.1%

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

   4. Applied egg-rr 35.1%

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

   5. Taylor expanded in A around -inf 79.1%

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

   if -1.16e64 < A

   1. Initial program 66.2%

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

   3. Simplified 86.1%

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

Alternative 7: 49.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ t_1 := \frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{if}\;B \leq -5 \cdot 10^{-66}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.6 \cdot 10^{-177}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 0.0052:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ C B)) PI)))
        (t_1 (/ 180.0 (/ PI (atan 0.0)))))
   (if (<= B -5e-66)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -3.6e-177)
       t_0
       (if (<= B 4.5e-246)
         t_1
         (if (<= B 1.2e-195)
           (* 180.0 (/ (atan (/ A (- B))) PI))
           (if (<= B 4.5e-153)
             t_1
             (if (<= B 0.0052)
               t_0
               (* 180.0 (/ (atan (- -1.0 (/ A B))) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double t_1 = 180.0 / (((double) M_PI) / atan(0.0));
	double tmp;
	if (B <= -5e-66) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -3.6e-177) {
		tmp = t_0;
	} else if (B <= 4.5e-246) {
		tmp = t_1;
	} else if (B <= 1.2e-195) {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	} else if (B <= 4.5e-153) {
		tmp = t_1;
	} else if (B <= 0.0052) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double t_1 = 180.0 / (Math.PI / Math.atan(0.0));
	double tmp;
	if (B <= -5e-66) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -3.6e-177) {
		tmp = t_0;
	} else if (B <= 4.5e-246) {
		tmp = t_1;
	} else if (B <= 1.2e-195) {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	} else if (B <= 4.5e-153) {
		tmp = t_1;
	} else if (B <= 0.0052) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((C / B)) / math.pi)
	t_1 = 180.0 / (math.pi / math.atan(0.0))
	tmp = 0
	if B <= -5e-66:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -3.6e-177:
		tmp = t_0
	elif B <= 4.5e-246:
		tmp = t_1
	elif B <= 1.2e-195:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	elif B <= 4.5e-153:
		tmp = t_1
	elif B <= 0.0052:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	t_1 = Float64(180.0 / Float64(pi / atan(0.0)))
	tmp = 0.0
	if (B <= -5e-66)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -3.6e-177)
		tmp = t_0;
	elseif (B <= 4.5e-246)
		tmp = t_1;
	elseif (B <= 1.2e-195)
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	elseif (B <= 4.5e-153)
		tmp = t_1;
	elseif (B <= 0.0052)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((C / B)) / pi);
	t_1 = 180.0 / (pi / atan(0.0));
	tmp = 0.0;
	if (B <= -5e-66)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -3.6e-177)
		tmp = t_0;
	elseif (B <= 4.5e-246)
		tmp = t_1;
	elseif (B <= 1.2e-195)
		tmp = 180.0 * (atan((A / -B)) / pi);
	elseif (B <= 4.5e-153)
		tmp = t_1;
	elseif (B <= 0.0052)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 / N[(Pi / N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -5e-66], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.6e-177], t$95$0, If[LessEqual[B, 4.5e-246], t$95$1, If[LessEqual[B, 1.2e-195], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.5e-153], t$95$1, If[LessEqual[B, 0.0052], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -4.99999999999999962e-66

   1. Initial program 63.7%

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

   3. Taylor expanded in B around -inf 62.6%

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

   if -4.99999999999999962e-66 < B < -3.59999999999999983e-177 or 4.5e-153 < B < 0.0051999999999999998

   1. Initial program 72.6%

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

   3. Taylor expanded in B around inf 68.0%

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

   4. Taylor expanded in C around inf 49.5%

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

   if -3.59999999999999983e-177 < B < 4.49999999999999999e-246 or 1.2e-195 < B < 4.5e-153

   1. Initial program 38.0%

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

      1. clear-num 38.0%

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

      2. un-div-inv 38.0%

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

      3. associate-*l/ 38.0%

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

      4. *-un-lft-identity 38.0%

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

      5. associate--l- 35.9%

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

      6. unpow2 35.9%

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

      7. unpow2 35.9%

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

      8. hypot-define 57.3%

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

   4. Applied egg-rr 57.3%

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

   5. Taylor expanded in C around inf 48.0%

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

   6. Taylor expanded in B around 0 50.5%

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

      1. associate-*r/ 50.5%

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

      2. distribute-rgt1-in 50.5%

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

      3. metadata-eval 50.5%

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

      4. mul0-lft 50.5%

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

      5. metadata-eval 50.5%

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

      6. div0 50.5%

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

   8. Simplified 50.5%

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

   if 4.49999999999999999e-246 < B < 1.2e-195

   1. Initial program 86.9%

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

   3. Taylor expanded in B around inf 71.8%

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

   4. Taylor expanded in A around inf 72.1%

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

      1. neg-mul-1 72.1%

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

      2. distribute-neg-frac2 72.1%

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

   6. Simplified 72.1%

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

   if 0.0051999999999999998 < B

   1. Initial program 51.0%

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

   3. Taylor expanded in B around inf 86.5%

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

   4. Taylor expanded in C around 0 84.2%

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

      1. distribute-lft-in 84.2%

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

      2. metadata-eval 84.2%

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

      3. neg-mul-1 84.2%

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

      4. unsub-neg 84.2%

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

   6. Simplified 84.2%

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

Alternative 8: 47.4% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ t_1 := \frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{if}\;B \leq -4 \cdot 10^{-67}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1 \cdot 10^{-175}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;B \leq 0.0055:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ C B)) PI)))
        (t_1 (/ 180.0 (/ PI (atan 0.0)))))
   (if (<= B -4e-67)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -1e-175)
       t_0
       (if (<= B 4.4e-245)
         t_1
         (if (<= B 1.2e-195)
           (* 180.0 (/ (atan (/ A (- B))) PI))
           (if (<= B 8.2e-153)
             t_1
             (if (<= B 0.0055) t_0 (* 180.0 (/ (atan -1.0) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double t_1 = 180.0 / (((double) M_PI) / atan(0.0));
	double tmp;
	if (B <= -4e-67) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -1e-175) {
		tmp = t_0;
	} else if (B <= 4.4e-245) {
		tmp = t_1;
	} else if (B <= 1.2e-195) {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	} else if (B <= 8.2e-153) {
		tmp = t_1;
	} else if (B <= 0.0055) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double t_1 = 180.0 / (Math.PI / Math.atan(0.0));
	double tmp;
	if (B <= -4e-67) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -1e-175) {
		tmp = t_0;
	} else if (B <= 4.4e-245) {
		tmp = t_1;
	} else if (B <= 1.2e-195) {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	} else if (B <= 8.2e-153) {
		tmp = t_1;
	} else if (B <= 0.0055) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((C / B)) / math.pi)
	t_1 = 180.0 / (math.pi / math.atan(0.0))
	tmp = 0
	if B <= -4e-67:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -1e-175:
		tmp = t_0
	elif B <= 4.4e-245:
		tmp = t_1
	elif B <= 1.2e-195:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	elif B <= 8.2e-153:
		tmp = t_1
	elif B <= 0.0055:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	t_1 = Float64(180.0 / Float64(pi / atan(0.0)))
	tmp = 0.0
	if (B <= -4e-67)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -1e-175)
		tmp = t_0;
	elseif (B <= 4.4e-245)
		tmp = t_1;
	elseif (B <= 1.2e-195)
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	elseif (B <= 8.2e-153)
		tmp = t_1;
	elseif (B <= 0.0055)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((C / B)) / pi);
	t_1 = 180.0 / (pi / atan(0.0));
	tmp = 0.0;
	if (B <= -4e-67)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -1e-175)
		tmp = t_0;
	elseif (B <= 4.4e-245)
		tmp = t_1;
	elseif (B <= 1.2e-195)
		tmp = 180.0 * (atan((A / -B)) / pi);
	elseif (B <= 8.2e-153)
		tmp = t_1;
	elseif (B <= 0.0055)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 / N[(Pi / N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -4e-67], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1e-175], t$95$0, If[LessEqual[B, 4.4e-245], t$95$1, If[LessEqual[B, 1.2e-195], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.2e-153], t$95$1, If[LessEqual[B, 0.0055], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -3.99999999999999977e-67

   1. Initial program 63.7%

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

   3. Taylor expanded in B around -inf 62.6%

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

   if -3.99999999999999977e-67 < B < -1e-175 or 8.2e-153 < B < 0.0054999999999999997

   1. Initial program 72.6%

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

   3. Taylor expanded in B around inf 68.0%

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

   4. Taylor expanded in C around inf 49.5%

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

   if -1e-175 < B < 4.39999999999999986e-245 or 1.2e-195 < B < 8.2e-153

   1. Initial program 38.0%

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

      1. clear-num 38.0%

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

      2. un-div-inv 38.0%

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

      3. associate-*l/ 38.0%

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

      4. *-un-lft-identity 38.0%

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

      5. associate--l- 35.9%

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

      6. unpow2 35.9%

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

      7. unpow2 35.9%

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

      8. hypot-define 57.3%

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

   4. Applied egg-rr 57.3%

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

   5. Taylor expanded in C around inf 48.0%

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

   6. Taylor expanded in B around 0 50.5%

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

      1. associate-*r/ 50.5%

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

      2. distribute-rgt1-in 50.5%

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

      3. metadata-eval 50.5%

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

      4. mul0-lft 50.5%

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

      5. metadata-eval 50.5%

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

      6. div0 50.5%

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

   8. Simplified 50.5%

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

   if 4.39999999999999986e-245 < B < 1.2e-195

   1. Initial program 86.9%

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

   3. Taylor expanded in B around inf 71.8%

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

   4. Taylor expanded in A around inf 72.1%

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

      1. neg-mul-1 72.1%

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

      2. distribute-neg-frac2 72.1%

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

   6. Simplified 72.1%

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

   if 0.0054999999999999997 < B

   1. Initial program 51.0%

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

   3. Taylor expanded in B around inf 69.8%

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

Alternative 9: 55.6% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{if}\;B \leq -2.75 \cdot 10^{-170}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-246}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-196}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-179}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 8200000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ 180.0 (/ PI (atan 0.0)))))
   (if (<= B -2.75e-170)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (if (<= B 4.5e-246)
       t_0
       (if (<= B 2.6e-196)
         (* 180.0 (/ (atan (/ A (- B))) PI))
         (if (<= B 9e-179)
           t_0
           (if (<= B 8200000.0)
             (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
             (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 / (((double) M_PI) / atan(0.0));
	double tmp;
	if (B <= -2.75e-170) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= 4.5e-246) {
		tmp = t_0;
	} else if (B <= 2.6e-196) {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	} else if (B <= 9e-179) {
		tmp = t_0;
	} else if (B <= 8200000.0) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 / (Math.PI / Math.atan(0.0));
	double tmp;
	if (B <= -2.75e-170) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= 4.5e-246) {
		tmp = t_0;
	} else if (B <= 2.6e-196) {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	} else if (B <= 9e-179) {
		tmp = t_0;
	} else if (B <= 8200000.0) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 / (math.pi / math.atan(0.0))
	tmp = 0
	if B <= -2.75e-170:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= 4.5e-246:
		tmp = t_0
	elif B <= 2.6e-196:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	elif B <= 9e-179:
		tmp = t_0
	elif B <= 8200000.0:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 / Float64(pi / atan(0.0)))
	tmp = 0.0
	if (B <= -2.75e-170)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= 4.5e-246)
		tmp = t_0;
	elseif (B <= 2.6e-196)
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	elseif (B <= 9e-179)
		tmp = t_0;
	elseif (B <= 8200000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 / (pi / atan(0.0));
	tmp = 0.0;
	if (B <= -2.75e-170)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= 4.5e-246)
		tmp = t_0;
	elseif (B <= 2.6e-196)
		tmp = 180.0 * (atan((A / -B)) / pi);
	elseif (B <= 9e-179)
		tmp = t_0;
	elseif (B <= 8200000.0)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 / N[(Pi / N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.75e-170], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.5e-246], t$95$0, If[LessEqual[B, 2.6e-196], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9e-179], t$95$0, If[LessEqual[B, 8200000.0], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[(C / 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 5 regimes

2. if B < -2.75000000000000009e-170

   1. Initial program 63.8%

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

   3. Taylor expanded in B around -inf 75.2%

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

   4. Taylor expanded in C around 0 66.3%

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

      1. sub-neg 66.3%

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

      2. metadata-eval 66.3%

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

      3. distribute-lft-in 66.3%

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

      4. metadata-eval 66.3%

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

      5. +-commutative 66.3%

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

      6. mul-1-neg 66.3%

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

      7. unsub-neg 66.3%

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

   6. Simplified 66.3%

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

   if -2.75000000000000009e-170 < B < 4.49999999999999999e-246 or 2.5999999999999998e-196 < B < 8.99999999999999984e-179

   1. Initial program 36.9%

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

      1. clear-num 36.9%

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

      2. un-div-inv 36.9%

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

      3. associate-*l/ 36.9%

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

      4. *-un-lft-identity 36.9%

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

      5. associate--l- 34.6%

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

      6. unpow2 34.6%

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

      7. unpow2 34.6%

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

      8. hypot-define 57.8%

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

   4. Applied egg-rr 57.8%

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

   5. Taylor expanded in C around inf 49.7%

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

   6. Taylor expanded in B around 0 50.4%

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

      1. associate-*r/ 50.4%

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

      2. distribute-rgt1-in 50.4%

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

      3. metadata-eval 50.4%

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

      4. mul0-lft 50.4%

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

      5. metadata-eval 50.4%

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

      6. div0 50.4%

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

   8. Simplified 50.4%

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

   if 4.49999999999999999e-246 < B < 2.5999999999999998e-196

   1. Initial program 86.9%

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

   3. Taylor expanded in B around inf 71.8%

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

   4. Taylor expanded in A around inf 72.1%

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

      1. neg-mul-1 72.1%

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

      2. distribute-neg-frac2 72.1%

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

   6. Simplified 72.1%

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

   if 8.99999999999999984e-179 < B < 8.2e6

   1. Initial program 77.1%

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

   3. Taylor expanded in B around inf 75.3%

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

   4. Taylor expanded in A around 0 60.7%

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

   if 8.2e6 < B

   1. Initial program 48.6%

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

   3. Taylor expanded in B around inf 85.8%

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

   4. Taylor expanded in C around 0 85.0%

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

      1. distribute-lft-in 85.0%

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

      2. metadata-eval 85.0%

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

      3. neg-mul-1 85.0%

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

      4. unsub-neg 85.0%

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

   6. Simplified 85.0%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.75 \cdot 10^{-170}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-246}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-196}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-179}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{elif}\;B \leq 8200000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.3% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{if}\;B \leq -2.7 \cdot 10^{-170}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-245}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-153}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 0.0052:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ 180.0 (/ PI (atan 0.0)))))
   (if (<= B -2.7e-170)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (if (<= B 4.4e-245)
       t_0
       (if (<= B 1.2e-195)
         (* 180.0 (/ (atan (/ A (- B))) PI))
         (if (<= B 4.5e-153)
           t_0
           (if (<= B 0.0052)
             (* 180.0 (/ (atan (/ C B)) PI))
             (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 / (((double) M_PI) / atan(0.0));
	double tmp;
	if (B <= -2.7e-170) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= 4.4e-245) {
		tmp = t_0;
	} else if (B <= 1.2e-195) {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	} else if (B <= 4.5e-153) {
		tmp = t_0;
	} else if (B <= 0.0052) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 / (Math.PI / Math.atan(0.0));
	double tmp;
	if (B <= -2.7e-170) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= 4.4e-245) {
		tmp = t_0;
	} else if (B <= 1.2e-195) {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	} else if (B <= 4.5e-153) {
		tmp = t_0;
	} else if (B <= 0.0052) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 / (math.pi / math.atan(0.0))
	tmp = 0
	if B <= -2.7e-170:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= 4.4e-245:
		tmp = t_0
	elif B <= 1.2e-195:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	elif B <= 4.5e-153:
		tmp = t_0
	elif B <= 0.0052:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 / Float64(pi / atan(0.0)))
	tmp = 0.0
	if (B <= -2.7e-170)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= 4.4e-245)
		tmp = t_0;
	elseif (B <= 1.2e-195)
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	elseif (B <= 4.5e-153)
		tmp = t_0;
	elseif (B <= 0.0052)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 / (pi / atan(0.0));
	tmp = 0.0;
	if (B <= -2.7e-170)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= 4.4e-245)
		tmp = t_0;
	elseif (B <= 1.2e-195)
		tmp = 180.0 * (atan((A / -B)) / pi);
	elseif (B <= 4.5e-153)
		tmp = t_0;
	elseif (B <= 0.0052)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 / N[(Pi / N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -2.7e-170], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.4e-245], t$95$0, If[LessEqual[B, 1.2e-195], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.5e-153], t$95$0, If[LessEqual[B, 0.0052], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.6999999999999999e-170

   1. Initial program 63.8%

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

   3. Taylor expanded in B around -inf 75.2%

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

   4. Taylor expanded in C around 0 66.3%

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

      1. sub-neg 66.3%

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

      2. metadata-eval 66.3%

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

      3. distribute-lft-in 66.3%

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

      4. metadata-eval 66.3%

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

      5. +-commutative 66.3%

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

      6. mul-1-neg 66.3%

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

      7. unsub-neg 66.3%

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

   6. Simplified 66.3%

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

   if -2.6999999999999999e-170 < B < 4.39999999999999986e-245 or 1.2e-195 < B < 4.5e-153

   1. Initial program 39.1%

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

      1. clear-num 39.1%

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

      2. un-div-inv 39.1%

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

      3. associate-*l/ 39.1%

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

      4. *-un-lft-identity 39.1%

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

      5. associate--l- 37.0%

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

      6. unpow2 37.0%

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

      7. unpow2 37.0%

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

      8. hypot-define 58.1%

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

   4. Applied egg-rr 58.1%

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

   5. Taylor expanded in C around inf 47.2%

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

   6. Taylor expanded in B around 0 49.6%

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

      1. associate-*r/ 49.6%

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

      2. distribute-rgt1-in 49.6%

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

      3. metadata-eval 49.6%

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

      4. mul0-lft 49.6%

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

      5. metadata-eval 49.6%

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

      6. div0 49.6%

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

   8. Simplified 49.6%

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

   if 4.39999999999999986e-245 < B < 1.2e-195

   1. Initial program 86.9%

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

   3. Taylor expanded in B around inf 71.8%

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

   4. Taylor expanded in A around inf 72.1%

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

      1. neg-mul-1 72.1%

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

      2. distribute-neg-frac2 72.1%

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

   6. Simplified 72.1%

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

   if 4.5e-153 < B < 0.0051999999999999998

   1. Initial program 77.4%

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

   3. Taylor expanded in B around inf 75.2%

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

   4. Taylor expanded in C around inf 54.3%

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

   if 0.0051999999999999998 < B

   1. Initial program 51.0%

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

   3. Taylor expanded in B around inf 86.5%

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

   4. Taylor expanded in C around 0 84.2%

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

      1. distribute-lft-in 84.2%

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

      2. metadata-eval 84.2%

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

      3. neg-mul-1 84.2%

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

      4. unsub-neg 84.2%

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

   6. Simplified 84.2%

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

Alternative 11: 63.9% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.5 \cdot 10^{-178}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-290}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.5e-178)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= B 1.1e-290)
     (* (/ 180.0 PI) (atan (/ (* B -0.5) C)))
     (if (<= B 9e-244)
       (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
       (* 180.0 (/ (atan (+ (/ C B) (- -1.0 (/ A B)))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.5e-178) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= 1.1e-290) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	} else if (B <= 9e-244) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.5e-178) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= 1.1e-290) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	} else if (B <= 9e-244) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C / B) + (-1.0 - (A / B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.5e-178:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= 1.1e-290:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	elif B <= 9e-244:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C / B) + (-1.0 - (A / B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.5e-178)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= 1.1e-290)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	elseif (B <= 9e-244)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.5e-178)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= 1.1e-290)
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	elseif (B <= 9e-244)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	else
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.5e-178], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.1e-290], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9e-244], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.4999999999999999e-178

   1. Initial program 64.2%

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

   3. Taylor expanded in B around -inf 74.4%

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

      1. associate--l+ 74.4%

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

      2. div-sub 75.5%

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

   5. Simplified 75.5%

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

   if -1.4999999999999999e-178 < B < 1.1e-290

   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. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 31.9%

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

      2. un-div-inv 31.9%

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

      3. associate-*l/ 31.9%

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

      4. *-un-lft-identity 31.9%

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

      5. associate--l- 31.5%

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

      6. unpow2 31.5%

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

      7. unpow2 31.5%

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

      8. hypot-define 56.3%

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

   4. Applied egg-rr 56.3%

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

   5. Taylor expanded in C around inf 55.7%

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

   6. Taylor expanded in A around 0 55.8%

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

      1. associate-*r/ 55.8%

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

      2. associate-*r/ 55.8%

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

      3. distribute-rgt1-in 55.8%

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

      4. metadata-eval 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      5. mul0-lft 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      6. metadata-eval 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      7. div0 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\color{blue}{0} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      8. +-lft-identity 55.8%

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

      9. associate-*r/ 55.8%

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

   8. Simplified 55.8%

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

   if 1.1e-290 < B < 9.0000000000000003e-244

   1. Initial program 59.9%

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

   3. Taylor expanded in A around -inf 67.7%

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

      1. associate-*r/ 67.7%

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

   5. Simplified 67.7%

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

   if 9.0000000000000003e-244 < B

   1. Initial program 60.6%

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

   3. Taylor expanded in B around inf 79.4%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.5 \cdot 10^{-178}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-290}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-244}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.2% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -4 \cdot 10^{-65}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.1 \cdot 10^{-175}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 4.2 \cdot 10^{-153}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{elif}\;B \leq 0.017:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (/ C B)) PI))))
   (if (<= B -4e-65)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -2.1e-175)
       t_0
       (if (<= B 4.2e-153)
         (/ 180.0 (/ PI (atan 0.0)))
         (if (<= B 0.017) t_0 (* 180.0 (/ (atan -1.0) PI))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((C / B)) / ((double) M_PI));
	double tmp;
	if (B <= -4e-65) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2.1e-175) {
		tmp = t_0;
	} else if (B <= 4.2e-153) {
		tmp = 180.0 / (((double) M_PI) / atan(0.0));
	} else if (B <= 0.017) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((C / B)) / Math.PI);
	double tmp;
	if (B <= -4e-65) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2.1e-175) {
		tmp = t_0;
	} else if (B <= 4.2e-153) {
		tmp = 180.0 / (Math.PI / Math.atan(0.0));
	} else if (B <= 0.017) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((C / B)) / math.pi)
	tmp = 0
	if B <= -4e-65:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2.1e-175:
		tmp = t_0
	elif B <= 4.2e-153:
		tmp = 180.0 / (math.pi / math.atan(0.0))
	elif B <= 0.017:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(C / B)) / pi))
	tmp = 0.0
	if (B <= -4e-65)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2.1e-175)
		tmp = t_0;
	elseif (B <= 4.2e-153)
		tmp = Float64(180.0 / Float64(pi / atan(0.0)));
	elseif (B <= 0.017)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((C / B)) / pi);
	tmp = 0.0;
	if (B <= -4e-65)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2.1e-175)
		tmp = t_0;
	elseif (B <= 4.2e-153)
		tmp = 180.0 / (pi / atan(0.0));
	elseif (B <= 0.017)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -4e-65], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.1e-175], t$95$0, If[LessEqual[B, 4.2e-153], N[(180.0 / N[(Pi / N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 0.017], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -3.99999999999999969e-65

   1. Initial program 63.7%

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

   3. Taylor expanded in B around -inf 62.6%

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

   if -3.99999999999999969e-65 < B < -2.1e-175 or 4.20000000000000008e-153 < B < 0.017000000000000001

   1. Initial program 72.6%

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

   3. Taylor expanded in B around inf 68.0%

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

   4. Taylor expanded in C around inf 49.5%

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

   if -2.1e-175 < B < 4.20000000000000008e-153

   1. Initial program 43.6%

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

      1. clear-num 43.6%

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

      2. un-div-inv 43.6%

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

      3. associate-*l/ 43.6%

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

      4. *-un-lft-identity 43.6%

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

      5. associate--l- 41.6%

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

      6. unpow2 41.6%

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

      7. unpow2 41.6%

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

      8. hypot-define 60.6%

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

   4. Applied egg-rr 60.6%

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

   5. Taylor expanded in C around inf 43.0%

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

   6. Taylor expanded in B around 0 45.1%

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

      1. associate-*r/ 45.1%

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

      2. distribute-rgt1-in 45.1%

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

      3. metadata-eval 45.1%

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

      4. mul0-lft 45.1%

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

      5. metadata-eval 45.1%

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

      6. div0 45.1%

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

   8. Simplified 45.1%

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

   if 0.017000000000000001 < B

   1. Initial program 51.0%

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

   3. Taylor expanded in B around inf 69.8%

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

Alternative 13: 61.4% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.5 \cdot 10^{-178}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-292}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{elif}\;B \leq 0.21:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \left(\frac{1}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))
   (if (<= B -1.5e-178)
     t_0
     (if (<= B 3.2e-292)
       (* (/ 180.0 PI) (atan (/ (* B -0.5) C)))
       (if (<= B 0.21)
         t_0
         (* 180.0 (* (/ 1.0 PI) (atan (- -1.0 (/ A B))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double tmp;
	if (B <= -1.5e-178) {
		tmp = t_0;
	} else if (B <= 3.2e-292) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	} else if (B <= 0.21) {
		tmp = t_0;
	} else {
		tmp = 180.0 * ((1.0 / ((double) M_PI)) * atan((-1.0 - (A / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double tmp;
	if (B <= -1.5e-178) {
		tmp = t_0;
	} else if (B <= 3.2e-292) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	} else if (B <= 0.21) {
		tmp = t_0;
	} else {
		tmp = 180.0 * ((1.0 / Math.PI) * Math.atan((-1.0 - (A / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	tmp = 0
	if B <= -1.5e-178:
		tmp = t_0
	elif B <= 3.2e-292:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	elif B <= 0.21:
		tmp = t_0
	else:
		tmp = 180.0 * ((1.0 / math.pi) * math.atan((-1.0 - (A / B))))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	tmp = 0.0
	if (B <= -1.5e-178)
		tmp = t_0;
	elseif (B <= 3.2e-292)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	elseif (B <= 0.21)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(Float64(1.0 / pi) * atan(Float64(-1.0 - Float64(A / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	tmp = 0.0;
	if (B <= -1.5e-178)
		tmp = t_0;
	elseif (B <= 3.2e-292)
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	elseif (B <= 0.21)
		tmp = t_0;
	else
		tmp = 180.0 * ((1.0 / pi) * atan((-1.0 - (A / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -1.5e-178], t$95$0, If[LessEqual[B, 3.2e-292], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 0.21], t$95$0, N[(180.0 * N[(N[(1.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.4999999999999999e-178 or 3.2000000000000002e-292 < B < 0.209999999999999992

   1. Initial program 66.6%

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

   3. Taylor expanded in B around -inf 68.6%

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

      1. associate--l+ 68.6%

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

      2. div-sub 70.6%

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

   5. Simplified 70.6%

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

   if -1.4999999999999999e-178 < B < 3.2000000000000002e-292

   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. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 31.9%

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

      2. un-div-inv 31.9%

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

      3. associate-*l/ 31.9%

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

      4. *-un-lft-identity 31.9%

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

      5. associate--l- 31.5%

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

      6. unpow2 31.5%

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

      7. unpow2 31.5%

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

      8. hypot-define 56.3%

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

   4. Applied egg-rr 56.3%

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

   5. Taylor expanded in C around inf 55.7%

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

   6. Taylor expanded in A around 0 55.8%

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

      1. associate-*r/ 55.8%

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

      2. associate-*r/ 55.8%

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

      3. distribute-rgt1-in 55.8%

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

      4. metadata-eval 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      5. mul0-lft 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      6. metadata-eval 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      7. div0 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\color{blue}{0} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      8. +-lft-identity 55.8%

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

      9. associate-*r/ 55.8%

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

   8. Simplified 55.8%

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

   if 0.209999999999999992 < B

   1. Initial program 51.0%

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

   3. Taylor expanded in B around inf 86.5%

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

      1. clear-num 86.5%

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

      2. associate-/r/ 86.5%

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

      3. associate-*r* 86.5%

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

      4. lft-mult-inverse 86.5%

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

      5. *-un-lft-identity 86.5%

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

   5. Applied egg-rr 86.5%

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

   6. Taylor expanded in C around 0 84.2%

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

      1. distribute-lft-in 84.2%

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

      2. metadata-eval 84.2%

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

      3. mul-1-neg 84.2%

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

      4. unsub-neg 84.2%

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

   8. Simplified 84.2%

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

Alternative 14: 65.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -6.8 \cdot 10^{-181}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B \cdot \left(1 + t\_0\right)\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-292}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 + t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -6.8e-181)
     (* 180.0 (/ (atan (* (/ 1.0 B) (* B (+ 1.0 t_0)))) PI))
     (if (<= B 1.45e-292)
       (* (/ 180.0 PI) (atan (/ (* B -0.5) C)))
       (* (/ 180.0 PI) (atan (+ -1.0 t_0)))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -6.8e-181) {
		tmp = 180.0 * (atan(((1.0 / B) * (B * (1.0 + t_0)))) / ((double) M_PI));
	} else if (B <= 1.45e-292) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 + t_0));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -6.8e-181) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * (B * (1.0 + t_0)))) / Math.PI);
	} else if (B <= 1.45e-292) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 + t_0));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -6.8e-181:
		tmp = 180.0 * (math.atan(((1.0 / B) * (B * (1.0 + t_0)))) / math.pi)
	elif B <= 1.45e-292:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 + t_0))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -6.8e-181)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(B * Float64(1.0 + t_0)))) / pi));
	elseif (B <= 1.45e-292)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 + t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -6.8e-181)
		tmp = 180.0 * (atan(((1.0 / B) * (B * (1.0 + t_0)))) / pi);
	elseif (B <= 1.45e-292)
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	else
		tmp = (180.0 / pi) * atan((-1.0 + t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -6.8e-181], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(B * N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.45e-292], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -6.8000000000000001e-181

   1. Initial program 64.2%

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

   3. Taylor expanded in B around -inf 75.5%

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

   if -6.8000000000000001e-181 < B < 1.44999999999999996e-292

   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. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 31.9%

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

      2. un-div-inv 31.9%

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

      3. associate-*l/ 31.9%

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

      4. *-un-lft-identity 31.9%

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

      5. associate--l- 31.5%

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

      6. unpow2 31.5%

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

      7. unpow2 31.5%

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

      8. hypot-define 56.3%

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

   4. Applied egg-rr 56.3%

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

   5. Taylor expanded in C around inf 55.7%

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

   6. Taylor expanded in A around 0 55.8%

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

      1. associate-*r/ 55.8%

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

      2. associate-*r/ 55.8%

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

      3. distribute-rgt1-in 55.8%

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

      4. metadata-eval 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      5. mul0-lft 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      6. metadata-eval 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      7. div0 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\color{blue}{0} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      8. +-lft-identity 55.8%

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

      9. associate-*r/ 55.8%

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

   8. Simplified 55.8%

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

   if 1.44999999999999996e-292 < B

   1. Initial program 60.5%

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

   3. Taylor expanded in B around -inf 41.6%

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

      1. clear-num 41.6%

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

      2. un-div-inv 41.6%

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

      3. associate-*l/ 41.6%

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

      4. *-un-lft-identity 41.6%

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

   5. Applied egg-rr 76.1%

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

      1. associate-/r/ 76.0%

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

      2. *-rgt-identity 76.0%

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

      3. times-frac 76.0%

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

      4. *-inverses 76.0%

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

      5. /-rgt-identity 76.0%

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

   7. Simplified 76.0%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{-181}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B \cdot \left(1 + \frac{C - A}{B}\right)\right)\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-292}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 + \frac{C - A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.1% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -2.8 \cdot 10^{-181}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-292}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 + t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -2.8e-181)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 1.45e-292)
       (* (/ 180.0 PI) (atan (/ (* B -0.5) C)))
       (* (/ 180.0 PI) (atan (+ -1.0 t_0)))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -2.8e-181) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 1.45e-292) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 + t_0));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -2.8e-181) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 1.45e-292) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 + t_0));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -2.8e-181:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 1.45e-292:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 + t_0))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -2.8e-181)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 1.45e-292)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 + t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -2.8e-181)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 1.45e-292)
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	else
		tmp = (180.0 / pi) * atan((-1.0 + t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -2.8e-181], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.45e-292], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.79999999999999986e-181

   1. Initial program 64.2%

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

   3. Taylor expanded in B around -inf 74.4%

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

      1. associate--l+ 74.4%

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

      2. div-sub 75.5%

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

   5. Simplified 75.5%

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

   if -2.79999999999999986e-181 < B < 1.44999999999999996e-292

   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. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 31.9%

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

      2. un-div-inv 31.9%

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

      3. associate-*l/ 31.9%

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

      4. *-un-lft-identity 31.9%

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

      5. associate--l- 31.5%

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

      6. unpow2 31.5%

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

      7. unpow2 31.5%

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

      8. hypot-define 56.3%

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

   4. Applied egg-rr 56.3%

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

   5. Taylor expanded in C around inf 55.7%

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

   6. Taylor expanded in A around 0 55.8%

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

      1. associate-*r/ 55.8%

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

      2. associate-*r/ 55.8%

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

      3. distribute-rgt1-in 55.8%

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

      4. metadata-eval 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \left(\color{blue}{0} \cdot A\right)}{B} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      5. mul0-lft 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{0}}{B} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      6. metadata-eval 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      7. div0 55.8%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\color{blue}{0} + \frac{-0.5 \cdot B}{C}\right)}{\pi} \]

      8. +-lft-identity 55.8%

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

      9. associate-*r/ 55.8%

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

   8. Simplified 55.8%

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

   if 1.44999999999999996e-292 < B

   1. Initial program 60.5%

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

   3. Taylor expanded in B around -inf 41.6%

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

      1. clear-num 41.6%

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

      2. un-div-inv 41.6%

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

      3. associate-*l/ 41.6%

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

      4. *-un-lft-identity 41.6%

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

   5. Applied egg-rr 76.1%

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

      1. associate-/r/ 76.0%

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

      2. *-rgt-identity 76.0%

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

      3. times-frac 76.0%

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

      4. *-inverses 76.0%

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

      5. /-rgt-identity 76.0%

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

   7. Simplified 76.0%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.8 \cdot 10^{-181}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-292}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 + \frac{C - A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 58.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6 \cdot 10^{-84}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq 2.05 \cdot 10^{-94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \left(\frac{1}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6e-84)
   (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
   (if (<= A 2.05e-94)
     (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
     (* 180.0 (* (/ 1.0 PI) (atan (- -1.0 (/ A B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6e-84) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (A <= 2.05e-94) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * ((1.0 / ((double) M_PI)) * atan((-1.0 - (A / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6e-84) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (A <= 2.05e-94) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * ((1.0 / Math.PI) * Math.atan((-1.0 - (A / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6e-84:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif A <= 2.05e-94:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * ((1.0 / math.pi) * math.atan((-1.0 - (A / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6e-84)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= 2.05e-94)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(Float64(1.0 / pi) * atan(Float64(-1.0 - Float64(A / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6e-84)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (A <= 2.05e-94)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * ((1.0 / pi) * atan((-1.0 - (A / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6e-84], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.05e-94], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[(1.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -6.0000000000000002e-84

   1. Initial program 22.1%

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

      1. clear-num 22.1%

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

      2. un-div-inv 22.1%

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

      3. associate-*l/ 22.1%

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

      4. *-un-lft-identity 22.1%

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

      5. associate--l- 20.3%

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

      6. unpow2 20.3%

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

      7. unpow2 20.3%

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

      8. hypot-define 45.1%

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

   4. Applied egg-rr 45.1%

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

   5. Taylor expanded in A around -inf 65.9%

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

   if -6.0000000000000002e-84 < A < 2.05e-94

   1. Initial program 66.3%

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

   3. Taylor expanded in B around inf 51.8%

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

   4. Taylor expanded in A around 0 50.9%

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

   if 2.05e-94 < A

   1. Initial program 76.5%

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

   3. Taylor expanded in B around inf 76.1%

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

      1. clear-num 76.1%

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

      2. associate-/r/ 76.1%

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

      3. associate-*r* 76.1%

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

      4. lft-mult-inverse 76.1%

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

      5. *-un-lft-identity 76.1%

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

   5. Applied egg-rr 76.1%

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

   6. Taylor expanded in C around 0 78.4%

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

      1. distribute-lft-in 78.4%

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

      2. metadata-eval 78.4%

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

      3. mul-1-neg 78.4%

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

      4. unsub-neg 78.4%

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

   8. Simplified 78.4%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6 \cdot 10^{-84}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq 2.05 \cdot 10^{-94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \left(\frac{1}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6 \cdot 10^{-84}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{-93}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6e-84)
   (/ 180.0 (/ PI (atan (* 0.5 (/ B A)))))
   (if (<= A 7.5e-93)
     (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6e-84) {
		tmp = 180.0 / (((double) M_PI) / atan((0.5 * (B / A))));
	} else if (A <= 7.5e-93) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6e-84) {
		tmp = 180.0 / (Math.PI / Math.atan((0.5 * (B / A))));
	} else if (A <= 7.5e-93) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6e-84:
		tmp = 180.0 / (math.pi / math.atan((0.5 * (B / A))))
	elif A <= 7.5e-93:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6e-84)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(0.5 * Float64(B / A)))));
	elseif (A <= 7.5e-93)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6e-84)
		tmp = 180.0 / (pi / atan((0.5 * (B / A))));
	elseif (A <= 7.5e-93)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6e-84], N[(180.0 / N[(Pi / N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 7.5e-93], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[(C / 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 3 regimes

2. if A < -6.0000000000000002e-84

   1. Initial program 22.1%

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

      1. clear-num 22.1%

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

      2. un-div-inv 22.1%

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

      3. associate-*l/ 22.1%

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

      4. *-un-lft-identity 22.1%

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

      5. associate--l- 20.3%

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

      6. unpow2 20.3%

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

      7. unpow2 20.3%

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

      8. hypot-define 45.1%

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

   4. Applied egg-rr 45.1%

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

   5. Taylor expanded in A around -inf 65.9%

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

   if -6.0000000000000002e-84 < A < 7.50000000000000034e-93

   1. Initial program 66.3%

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

   3. Taylor expanded in B around inf 51.8%

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

   4. Taylor expanded in A around 0 50.9%

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

   if 7.50000000000000034e-93 < A

   1. Initial program 76.5%

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

   3. Taylor expanded in B around inf 76.1%

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

   4. Taylor expanded in C around 0 78.4%

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

      1. distribute-lft-in 78.4%

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

      2. metadata-eval 78.4%

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

      3. neg-mul-1 78.4%

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

      4. unsub-neg 78.4%

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

   6. Simplified 78.4%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6 \cdot 10^{-84}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}}\\ \mathbf{elif}\;A \leq 7.5 \cdot 10^{-93}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 59.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.02 \cdot 10^{-84}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.2 \cdot 10^{-92}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.02e-84)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 3.2e-92)
     (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (- -1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.02e-84) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 3.2e-92) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.02e-84) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 3.2e-92) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.02e-84:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 3.2e-92:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.02e-84)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 3.2e-92)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.02e-84)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 3.2e-92)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.02e-84], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.2e-92], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[(C / 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 3 regimes

2. if A < -1.02000000000000004e-84

   1. Initial program 22.1%

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

   3. Taylor expanded in A around -inf 65.7%

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

      1. associate-*r/ 65.7%

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

   5. Simplified 65.7%

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

   if -1.02000000000000004e-84 < A < 3.1999999999999997e-92

   1. Initial program 66.3%

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

   3. Taylor expanded in B around inf 51.8%

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

   4. Taylor expanded in A around 0 50.9%

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

   if 3.1999999999999997e-92 < A

   1. Initial program 76.5%

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

   3. Taylor expanded in B around inf 76.1%

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

   4. Taylor expanded in C around 0 78.4%

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

      1. distribute-lft-in 78.4%

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

      2. metadata-eval 78.4%

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

      3. neg-mul-1 78.4%

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

      4. unsub-neg 78.4%

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

   6. Simplified 78.4%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.02 \cdot 10^{-84}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.2 \cdot 10^{-92}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 45.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.55 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{-90}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} 0}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.55e-184)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 5.4e-90)
     (/ 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 <= -1.55e-184) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 5.4e-90) {
		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 <= -1.55e-184) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 5.4e-90) {
		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 <= -1.55e-184:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 5.4e-90:
		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 <= -1.55e-184)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 5.4e-90)
		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 <= -1.55e-184)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 5.4e-90)
		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, -1.55e-184], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.4e-90], 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 < -1.5500000000000001e-184

   1. Initial program 62.9%

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

   3. Taylor expanded in B around -inf 49.4%

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

   if -1.5500000000000001e-184 < B < 5.39999999999999993e-90

   1. Initial program 49.2%

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

      1. clear-num 49.2%

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

      2. un-div-inv 49.2%

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

      3. associate-*l/ 49.2%

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

      4. *-un-lft-identity 49.2%

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

      5. associate--l- 47.6%

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

      6. unpow2 47.6%

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

      7. unpow2 47.6%

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

      8. hypot-define 63.5%

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

   4. Applied egg-rr 63.5%

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

   5. Taylor expanded in C around inf 37.3%

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

   6. Taylor expanded in B around 0 38.2%

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

      1. associate-*r/ 38.2%

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

      2. distribute-rgt1-in 38.2%

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

      3. metadata-eval 38.2%

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

      4. mul0-lft 38.2%

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

      5. metadata-eval 38.2%

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

      6. div0 38.2%

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

   8. Simplified 38.2%

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

   if 5.39999999999999993e-90 < B

   1. Initial program 60.6%

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

   3. Taylor expanded in B around inf 59.5%

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

Alternative 20: 41.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8.6 \cdot 10^{-307}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8.6e-307)
   (* 180.0 (/ (atan 1.0) PI))
   (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.6e-307) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.6e-307) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -8.6e-307:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -8.6e-307)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -8.6e-307)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -8.6e-307], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -8.60000000000000021e-307

   1. Initial program 57.5%

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

   3. Taylor expanded in B around -inf 40.7%

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

   if -8.60000000000000021e-307 < B

   1. Initial program 58.4%

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

   3. Taylor expanded in B around inf 40.4%

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

Alternative 21: 21.6% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.9%

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

3. Taylor expanded in B around inf 22.2%

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

Reproduce

herbie shell --seed 2024111 
(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)))