ABCF->ab-angle angle

Percentage Accurate: 53.7% → 81.9%

Time: 6.5s

Alternatives: 15

Speedup: 2.4×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\left(\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)\right) \cdot {B}^{-1}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.2e+113)
   (/ (* 180.0 (atan (* (/ B A) 0.5))) PI)
   (/ (* 180.0 (atan (* (- (- C A) (hypot (- A C) B)) (pow B -1.0)))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.2e+113) {
		tmp = (180.0 * atan(((B / A) * 0.5))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) * pow(B, -1.0)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.2e+113) {
		tmp = (180.0 * Math.atan(((B / A) * 0.5))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan((((C - A) - Math.hypot((A - C), B)) * Math.pow(B, -1.0)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.2e+113:
		tmp = (180.0 * math.atan(((B / A) * 0.5))) / math.pi
	else:
		tmp = (180.0 * math.atan((((C - A) - math.hypot((A - C), B)) * math.pow(B, -1.0)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.2e+113)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) * (B ^ -1.0)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.2e+113)
		tmp = (180.0 * atan(((B / A) * 0.5))) / pi;
	else
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) * (B ^ -1.0)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.2e+113], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] * N[Power[B, -1.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -4.1999999999999998e113

   1. Initial program 15.5%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 53.5%

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

   5. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 77.6

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

   7. Applied rewrites 77.6%

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

   if -4.1999999999999998e113 < A

   1. Initial program 61.3%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 82.8%

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

Alternative 2: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - B\right)\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (*
          180.0
          (/
           (atan
            (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
           PI))))
   (if (<= t_0 -1e-21)
     (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) B))) PI))
     (if (<= t_0 0.0)
       (/ (* 180.0 (atan (* (/ B A) 0.5))) PI)
       (/ (* 180.0 (atan (+ 1.0 (/ (- C A) B)))) PI)))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
	double tmp;
	if (t_0 <= -1e-21) {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / ((double) M_PI));
	} else if (t_0 <= 0.0) {
		tmp = (180.0 * atan(((B / A) * 0.5))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((1.0 + ((C - A) / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
	double tmp;
	if (t_0 <= -1e-21) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - B))) / Math.PI);
	} else if (t_0 <= 0.0) {
		tmp = (180.0 * Math.atan(((B / A) * 0.5))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan((1.0 + ((C - A) / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)
	tmp = 0
	if t_0 <= -1e-21:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C - A) - B))) / math.pi)
	elif t_0 <= 0.0:
		tmp = (180.0 * math.atan(((B / A) * 0.5))) / math.pi
	else:
		tmp = (180.0 * math.atan((1.0 + ((C - A) / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = 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))
	tmp = 0.0
	if (t_0 <= -1e-21)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - B))) / pi));
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(Float64(C - A) / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
	tmp = 0.0;
	if (t_0 <= -1e-21)
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / pi);
	elseif (t_0 <= 0.0)
		tmp = (180.0 * atan(((B / A) * 0.5))) / pi;
	else
		tmp = (180.0 * atan((1.0 + ((C - A) / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, If[LessEqual[t$95$0, -1e-21], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.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))))))) (PI.f64))) < -9.99999999999999908e-22

   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

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

   5. Applied rewrites 76.6%

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

   if -9.99999999999999908e-22 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.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))))))) (PI.f64))) < 0.0

   1. Initial program 18.9%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 20.1%

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

   5. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 53.7

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

   7. Applied rewrites 53.7%

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

   if 0.0 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.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))))))) (PI.f64)))

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 86.4%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 74.9

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

   7. Applied rewrites 74.9%

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

Alternative 3: 61.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-21}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (*
          180.0
          (/
           (atan
            (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
           PI))))
   (if (<= t_0 -1e-21)
     (/ (* 180.0 (atan (- (/ C B) 1.0))) PI)
     (if (<= t_0 0.0)
       (* 180.0 (/ (atan (* (/ B C) -0.5)) PI))
       (/ (* 180.0 (atan (+ 1.0 (/ C B)))) PI)))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
	double tmp;
	if (t_0 <= -1e-21) {
		tmp = (180.0 * atan(((C / B) - 1.0))) / ((double) M_PI);
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan(((B / C) * -0.5)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((1.0 + (C / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
	double tmp;
	if (t_0 <= -1e-21) {
		tmp = (180.0 * Math.atan(((C / B) - 1.0))) / Math.PI;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan(((B / C) * -0.5)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((1.0 + (C / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)
	tmp = 0
	if t_0 <= -1e-21:
		tmp = (180.0 * math.atan(((C / B) - 1.0))) / math.pi
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan(((B / C) * -0.5)) / math.pi)
	else:
		tmp = (180.0 * math.atan((1.0 + (C / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = 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))
	tmp = 0.0
	if (t_0 <= -1e-21)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B) - 1.0))) / pi);
	elseif (t_0 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / C) * -0.5)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(C / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
	tmp = 0.0;
	if (t_0 <= -1e-21)
		tmp = (180.0 * atan(((C / B) - 1.0))) / pi;
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan(((B / C) * -0.5)) / pi);
	else
		tmp = (180.0 * atan((1.0 + (C / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, If[LessEqual[t$95$0, -1e-21], N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.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))))))) (PI.f64))) < -9.99999999999999908e-22

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 87.1%

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

   5. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. pow2 N/A

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

      4. unpow2 N/A

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

      5. lower-hypot.f64 70.9

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

   7. Applied rewrites 70.9%

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

   8. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 63.6

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

   10. Applied rewrites 63.6%

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

   if -9.99999999999999908e-22 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.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))))))) (PI.f64))) < 0.0

   1. Initial program 18.9%

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

   3. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 48.8

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   5. Applied rewrites 48.8%

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

   6. Taylor expanded in A around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 48.8

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

   8. Applied rewrites 48.8%

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

   if 0.0 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.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))))))) (PI.f64)))

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 86.4%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 74.9

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

   7. Applied rewrites 74.9%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 62.5%

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

Alternative 4: 78.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.85 \cdot 10^{+99}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.8 \cdot 10^{-10}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-\frac{\mathsf{hypot}\left(B, A\right) + A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.85e+99)
   (/ (* 180.0 (atan (* (/ B A) 0.5))) PI)
   (if (<= A 7.8e-10)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (/ (* 180.0 (atan (- (/ (+ (hypot B A) A) B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.85e+99) {
		tmp = (180.0 * atan(((B / A) * 0.5))) / ((double) M_PI);
	} else if (A <= 7.8e-10) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(-((hypot(B, A) + A) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.85e+99) {
		tmp = (180.0 * Math.atan(((B / A) * 0.5))) / Math.PI;
	} else if (A <= 7.8e-10) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(-((Math.hypot(B, A) + A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.85e+99:
		tmp = (180.0 * math.atan(((B / A) * 0.5))) / math.pi
	elif A <= 7.8e-10:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan(-((math.hypot(B, A) + A) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.85e+99)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	elseif (A <= 7.8e-10)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-Float64(Float64(hypot(B, A) + A) / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.85e+99)
		tmp = (180.0 * atan(((B / A) * 0.5))) / pi;
	elseif (A <= 7.8e-10)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = (180.0 * atan(-((hypot(B, A) + A) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.85e+99], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 7.8e-10], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[(-N[(N[(N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision] + A), $MachinePrecision] / B), $MachinePrecision])], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.85000000000000005e99

   1. Initial program 16.4%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 53.9%

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

   5. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 76.1

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

   7. Applied rewrites 76.1%

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

   if -1.85000000000000005e99 < A < 7.7999999999999999e-10

   1. Initial program 54.8%

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

   3. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. unpow2 N/A

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

      5. unpow2 N/A

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

      6. lower-hypot.f64 74.9

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

   5. Applied rewrites 74.9%

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

   if 7.7999999999999999e-10 < A

   1. Initial program 76.7%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 94.3%

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

   5. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. pow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 88.3

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

   7. Applied rewrites 88.3%

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

Alternative 5: 76.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.85 \cdot 10^{+99}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{+61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.85e+99)
   (/ (* 180.0 (atan (* (/ B A) 0.5))) PI)
   (if (<= A 8.5e+61)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.85e+99) {
		tmp = (180.0 * atan(((B / A) * 0.5))) / ((double) M_PI);
	} else if (A <= 8.5e+61) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.85e+99) {
		tmp = (180.0 * Math.atan(((B / A) * 0.5))) / Math.PI;
	} else if (A <= 8.5e+61) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.85e+99:
		tmp = (180.0 * math.atan(((B / A) * 0.5))) / math.pi
	elif A <= 8.5e+61:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.85e+99)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	elseif (A <= 8.5e+61)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.85e+99)
		tmp = (180.0 * atan(((B / A) * 0.5))) / pi;
	elseif (A <= 8.5e+61)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.85e+99], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 8.5e+61], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.85000000000000005e99

   1. Initial program 16.4%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 53.9%

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

   5. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 76.1

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

   7. Applied rewrites 76.1%

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

   if -1.85000000000000005e99 < A < 8.50000000000000035e61

   1. Initial program 55.8%

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

   3. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. +-commutative N/A

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

      4. unpow2 N/A

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

      5. unpow2 N/A

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

      6. lower-hypot.f64 74.6

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

   5. Applied rewrites 74.6%

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

   if 8.50000000000000035e61 < A

   1. Initial program 79.9%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 82.9

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

   5. Applied rewrites 82.9%

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

Alternative 6: 58.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq -9 \cdot 10^{-261}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{+61}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.9e-32)
   (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
   (if (<= A -7e-54)
     (* 180.0 (/ (atan (* (/ B C) -0.5)) PI))
     (if (<= A -9e-261)
       (/ (* 180.0 (atan (+ 1.0 (/ C B)))) PI)
       (if (<= A 8.5e+61)
         (/ (* 180.0 (atan (- (/ C B) 1.0))) PI)
         (* 180.0 (/ (atan (* (/ A B) -2.0)) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-32) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((double) M_PI));
	} else if (A <= -7e-54) {
		tmp = 180.0 * (atan(((B / C) * -0.5)) / ((double) M_PI));
	} else if (A <= -9e-261) {
		tmp = (180.0 * atan((1.0 + (C / B)))) / ((double) M_PI);
	} else if (A <= 8.5e+61) {
		tmp = (180.0 * atan(((C / B) - 1.0))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((A / B) * -2.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-32) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else if (A <= -7e-54) {
		tmp = 180.0 * (Math.atan(((B / C) * -0.5)) / Math.PI);
	} else if (A <= -9e-261) {
		tmp = (180.0 * Math.atan((1.0 + (C / B)))) / Math.PI;
	} else if (A <= 8.5e+61) {
		tmp = (180.0 * Math.atan(((C / B) - 1.0))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((A / B) * -2.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.9e-32:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	elif A <= -7e-54:
		tmp = 180.0 * (math.atan(((B / C) * -0.5)) / math.pi)
	elif A <= -9e-261:
		tmp = (180.0 * math.atan((1.0 + (C / B)))) / math.pi
	elif A <= 8.5e+61:
		tmp = (180.0 * math.atan(((C / B) - 1.0))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((A / B) * -2.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.9e-32)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	elseif (A <= -7e-54)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / C) * -0.5)) / pi));
	elseif (A <= -9e-261)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(C / B)))) / pi);
	elseif (A <= 8.5e+61)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B) - 1.0))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B) * -2.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.9e-32)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	elseif (A <= -7e-54)
		tmp = 180.0 * (atan(((B / C) * -0.5)) / pi);
	elseif (A <= -9e-261)
		tmp = (180.0 * atan((1.0 + (C / B)))) / pi;
	elseif (A <= 8.5e+61)
		tmp = (180.0 * atan(((C / B) - 1.0))) / pi;
	else
		tmp = 180.0 * (atan(((A / B) * -2.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.9e-32], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -7e-54], N[(180.0 * N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -9e-261], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 8.5e+61], N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -1.90000000000000004e-32

   1. Initial program 26.0%

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

   3. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 65.0

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

   5. Applied rewrites 65.0%

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

   if -1.90000000000000004e-32 < A < -6.99999999999999964e-54

   1. Initial program 45.2%

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

   3. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 21.8

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   5. Applied rewrites 21.8%

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

   6. Taylor expanded in A around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 21.8

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

   8. Applied rewrites 21.8%

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

   if -6.99999999999999964e-54 < A < -9.0000000000000002e-261

   1. Initial program 54.8%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 77.2%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 47.8

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

   7. Applied rewrites 47.8%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 47.8%

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

   if -9.0000000000000002e-261 < A < 8.50000000000000035e61

   1. Initial program 60.8%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 85.3%

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

   5. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. pow2 N/A

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

      4. unpow2 N/A

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

      5. lower-hypot.f64 78.2

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

   7. Applied rewrites 78.2%

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

   8. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 48.4

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

   10. Applied rewrites 48.4%

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

   if 8.50000000000000035e61 < A

   1. Initial program 79.9%

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

   3. Taylor expanded in A around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 75.5

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

   5. Applied rewrites 75.5%

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

Alternative 7: 50.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-37}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.9 \cdot 10^{-208}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-268}:\\ \;\;\;\;\frac{\tan^{-1} 0 \cdot 180}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-110}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.6e-37)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -2.9e-208)
     (/ (* 180.0 (atan (/ C B))) PI)
     (if (<= B 1.05e-268)
       (/ (* (atan 0.0) 180.0) PI)
       (if (<= B 1.05e-110)
         (/ (* 180.0 (atan (/ (- A) B))) PI)
         (/ (* 180.0 (atan (- (/ C B) 1.0))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.6e-37) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2.9e-208) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else if (B <= 1.05e-268) {
		tmp = (atan(0.0) * 180.0) / ((double) M_PI);
	} else if (B <= 1.05e-110) {
		tmp = (180.0 * atan((-A / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(((C / B) - 1.0))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.6e-37) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2.9e-208) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else if (B <= 1.05e-268) {
		tmp = (Math.atan(0.0) * 180.0) / Math.PI;
	} else if (B <= 1.05e-110) {
		tmp = (180.0 * Math.atan((-A / B))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan(((C / B) - 1.0))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.6e-37:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2.9e-208:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	elif B <= 1.05e-268:
		tmp = (math.atan(0.0) * 180.0) / math.pi
	elif B <= 1.05e-110:
		tmp = (180.0 * math.atan((-A / B))) / math.pi
	else:
		tmp = (180.0 * math.atan(((C / B) - 1.0))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.6e-37)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2.9e-208)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	elseif (B <= 1.05e-268)
		tmp = Float64(Float64(atan(0.0) * 180.0) / pi);
	elseif (B <= 1.05e-110)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-A) / B))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B) - 1.0))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.6e-37)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2.9e-208)
		tmp = (180.0 * atan((C / B))) / pi;
	elseif (B <= 1.05e-268)
		tmp = (atan(0.0) * 180.0) / pi;
	elseif (B <= 1.05e-110)
		tmp = (180.0 * atan((-A / B))) / pi;
	else
		tmp = (180.0 * atan(((C / B) - 1.0))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.6e-37], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.9e-208], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.05e-268], N[(N[(N[ArcTan[0.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.05e-110], N[(N[(180.0 * N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.5999999999999998e-37

   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

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]
   4. Step-by-step derivation

   5. Applied rewrites 59.5%

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

   if -2.5999999999999998e-37 < B < -2.8999999999999999e-208

   1. Initial program 56.2%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 73.5%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 54.7

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

   7. Applied rewrites 54.7%

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

   8. Taylor expanded in C around inf

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

      1. lower-/.f64 29.6

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

   10. Applied rewrites 29.6%

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

   if -2.8999999999999999e-208 < B < 1.04999999999999999e-268

   1. Initial program 62.3%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 84.2%

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

   5. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lift-*.f64 N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. mul0-lft N/A

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

      9. lift-*.f64 N/A

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

      10. lift-/.f64 35.4

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

      11. lift-*.f64 N/A

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

      12. mul0-lft 35.4

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

   7. Applied rewrites 35.4%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 35.4

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

      4. lift-/.f64 N/A

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

      5. div0 35.4

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

   9. Applied rewrites 35.4%

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

   if 1.04999999999999999e-268 < B < 1.05000000000000001e-110

   1. Initial program 57.1%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 77.5%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 48.1

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

   7. Applied rewrites 48.1%

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

   8. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 34.8

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

   10. Applied rewrites 34.8%

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

   if 1.05000000000000001e-110 < B

   1. Initial program 52.8%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 77.5%

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

   5. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. pow2 N/A

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

      4. unpow2 N/A

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

      5. lower-hypot.f64 66.3

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

   7. Applied rewrites 66.3%

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

   8. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 63.8

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

   10. Applied rewrites 63.8%

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

Alternative 8: 46.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-37}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.9 \cdot 10^{-208}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-268}:\\ \;\;\;\;\frac{\tan^{-1} 0 \cdot 180}{\pi}\\ \mathbf{elif}\;B \leq 250000000000:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.6e-37)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -2.9e-208)
     (/ (* 180.0 (atan (/ C B))) PI)
     (if (<= B 1.05e-268)
       (/ (* (atan 0.0) 180.0) PI)
       (if (<= B 250000000000.0)
         (/ (* 180.0 (atan (/ (- A) B))) PI)
         (* 180.0 (/ (atan -1.0) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.6e-37) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2.9e-208) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else if (B <= 1.05e-268) {
		tmp = (atan(0.0) * 180.0) / ((double) M_PI);
	} else if (B <= 250000000000.0) {
		tmp = (180.0 * atan((-A / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.6e-37) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2.9e-208) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else if (B <= 1.05e-268) {
		tmp = (Math.atan(0.0) * 180.0) / Math.PI;
	} else if (B <= 250000000000.0) {
		tmp = (180.0 * Math.atan((-A / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.6e-37:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2.9e-208:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	elif B <= 1.05e-268:
		tmp = (math.atan(0.0) * 180.0) / math.pi
	elif B <= 250000000000.0:
		tmp = (180.0 * math.atan((-A / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.6e-37)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2.9e-208)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	elseif (B <= 1.05e-268)
		tmp = Float64(Float64(atan(0.0) * 180.0) / pi);
	elseif (B <= 250000000000.0)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-A) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.6e-37)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2.9e-208)
		tmp = (180.0 * atan((C / B))) / pi;
	elseif (B <= 1.05e-268)
		tmp = (atan(0.0) * 180.0) / pi;
	elseif (B <= 250000000000.0)
		tmp = (180.0 * atan((-A / B))) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.6e-37], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.9e-208], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.05e-268], N[(N[(N[ArcTan[0.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 250000000000.0], N[(N[(180.0 * N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if B < -2.5999999999999998e-37

   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

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]
   4. Step-by-step derivation

   5. Applied rewrites 59.5%

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

   if -2.5999999999999998e-37 < B < -2.8999999999999999e-208

   1. Initial program 56.2%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 73.5%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 54.7

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

   7. Applied rewrites 54.7%

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

   8. Taylor expanded in C around inf

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

      1. lower-/.f64 29.6

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

   10. Applied rewrites 29.6%

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

   if -2.8999999999999999e-208 < B < 1.04999999999999999e-268

   1. Initial program 62.3%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 84.2%

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

   5. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lift-*.f64 N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. mul0-lft N/A

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

      9. lift-*.f64 N/A

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

      10. lift-/.f64 35.4

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

      11. lift-*.f64 N/A

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

      12. mul0-lft 35.4

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

   7. Applied rewrites 35.4%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 35.4

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

      4. lift-/.f64 N/A

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

      5. div0 35.4

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

   9. Applied rewrites 35.4%

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

   if 1.04999999999999999e-268 < B < 2.5e11

   1. Initial program 59.5%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 74.2%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 45.4

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

   7. Applied rewrites 45.4%

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

   8. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 30.7

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

   10. Applied rewrites 30.7%

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

   if 2.5e11 < B

   1. Initial program 48.7%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
   4. Step-by-step derivation

   5. Applied rewrites 62.2%

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

Alternative 9: 46.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -2.6 \cdot 10^{-37}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -2.9 \cdot 10^{-208}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 3.3 \cdot 10^{-265}:\\ \;\;\;\;\frac{\tan^{-1} 0 \cdot 180}{\pi}\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-19}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ C B))) PI)))
   (if (<= B -2.6e-37)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B -2.9e-208)
       t_0
       (if (<= B 3.3e-265)
         (/ (* (atan 0.0) 180.0) PI)
         (if (<= B 7.8e-19) 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 <= -2.6e-37) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -2.9e-208) {
		tmp = t_0;
	} else if (B <= 3.3e-265) {
		tmp = (atan(0.0) * 180.0) / ((double) M_PI);
	} else if (B <= 7.8e-19) {
		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 <= -2.6e-37) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -2.9e-208) {
		tmp = t_0;
	} else if (B <= 3.3e-265) {
		tmp = (Math.atan(0.0) * 180.0) / Math.PI;
	} else if (B <= 7.8e-19) {
		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 <= -2.6e-37:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -2.9e-208:
		tmp = t_0
	elif B <= 3.3e-265:
		tmp = (math.atan(0.0) * 180.0) / math.pi
	elif B <= 7.8e-19:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(C / B))) / pi)
	tmp = 0.0
	if (B <= -2.6e-37)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -2.9e-208)
		tmp = t_0;
	elseif (B <= 3.3e-265)
		tmp = Float64(Float64(atan(0.0) * 180.0) / pi);
	elseif (B <= 7.8e-19)
		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 <= -2.6e-37)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -2.9e-208)
		tmp = t_0;
	elseif (B <= 3.3e-265)
		tmp = (atan(0.0) * 180.0) / pi;
	elseif (B <= 7.8e-19)
		tmp = t_0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[B, -2.6e-37], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -2.9e-208], t$95$0, If[LessEqual[B, 3.3e-265], N[(N[(N[ArcTan[0.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 7.8e-19], t$95$0, N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.5999999999999998e-37

   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

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]
   4. Step-by-step derivation

   5. Applied rewrites 59.5%

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

   if -2.5999999999999998e-37 < B < -2.8999999999999999e-208 or 3.30000000000000002e-265 < B < 7.7999999999999999e-19

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 74.6%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 49.7

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

   7. Applied rewrites 49.7%

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

   8. Taylor expanded in C around inf

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

      1. lower-/.f64 30.6

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

   10. Applied rewrites 30.6%

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

   if -2.8999999999999999e-208 < B < 3.30000000000000002e-265

   1. Initial program 62.4%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 84.2%

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

   5. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lift-*.f64 N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. mul0-lft N/A

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

      9. lift-*.f64 N/A

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

      10. lift-/.f64 35.1

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

      11. lift-*.f64 N/A

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

      12. mul0-lft 35.1

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

   7. Applied rewrites 35.1%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 35.1

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

      4. lift-/.f64 N/A

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

      5. div0 35.1

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

   9. Applied rewrites 35.1%

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

   if 7.7999999999999999e-19 < B

   1. Initial program 49.9%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
   4. Step-by-step derivation

   5. Applied rewrites 59.5%

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

Alternative 10: 60.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{-32}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.8 \cdot 10^{-178}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-\frac{B + A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.9e-32)
   (/ (* 180.0 (atan (* (/ B A) 0.5))) PI)
   (if (<= A -7e-54)
     (* 180.0 (/ (atan (* (/ B C) -0.5)) PI))
     (if (<= A 5.8e-178)
       (/ (* 180.0 (atan (+ 1.0 (/ C B)))) PI)
       (/ (* 180.0 (atan (- (/ (+ B A) B)))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-32) {
		tmp = (180.0 * atan(((B / A) * 0.5))) / ((double) M_PI);
	} else if (A <= -7e-54) {
		tmp = 180.0 * (atan(((B / C) * -0.5)) / ((double) M_PI));
	} else if (A <= 5.8e-178) {
		tmp = (180.0 * atan((1.0 + (C / B)))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(-((B + A) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-32) {
		tmp = (180.0 * Math.atan(((B / A) * 0.5))) / Math.PI;
	} else if (A <= -7e-54) {
		tmp = 180.0 * (Math.atan(((B / C) * -0.5)) / Math.PI);
	} else if (A <= 5.8e-178) {
		tmp = (180.0 * Math.atan((1.0 + (C / B)))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan(-((B + A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.9e-32:
		tmp = (180.0 * math.atan(((B / A) * 0.5))) / math.pi
	elif A <= -7e-54:
		tmp = 180.0 * (math.atan(((B / C) * -0.5)) / math.pi)
	elif A <= 5.8e-178:
		tmp = (180.0 * math.atan((1.0 + (C / B)))) / math.pi
	else:
		tmp = (180.0 * math.atan(-((B + A) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.9e-32)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	elseif (A <= -7e-54)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / C) * -0.5)) / pi));
	elseif (A <= 5.8e-178)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(C / B)))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-Float64(Float64(B + A) / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.9e-32)
		tmp = (180.0 * atan(((B / A) * 0.5))) / pi;
	elseif (A <= -7e-54)
		tmp = 180.0 * (atan(((B / C) * -0.5)) / pi);
	elseif (A <= 5.8e-178)
		tmp = (180.0 * atan((1.0 + (C / B)))) / pi;
	else
		tmp = (180.0 * atan(-((B + A) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.9e-32], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -7e-54], N[(180.0 * N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.8e-178], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[(-N[(N[(B + A), $MachinePrecision] / B), $MachinePrecision])], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.90000000000000004e-32

   1. Initial program 26.0%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 57.1%

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

   5. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 65.1

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

   7. Applied rewrites 65.1%

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

   if -1.90000000000000004e-32 < A < -6.99999999999999964e-54

   1. Initial program 45.2%

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

   3. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 21.8

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   5. Applied rewrites 21.8%

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

   6. Taylor expanded in A around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 21.8

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

   8. Applied rewrites 21.8%

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

   if -6.99999999999999964e-54 < A < 5.7999999999999995e-178

   1. Initial program 56.0%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 80.1%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 49.1

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

   7. Applied rewrites 49.1%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 48.8%

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

   if 5.7999999999999995e-178 < A

   1. Initial program 71.7%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 91.2%

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

   5. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. pow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 82.3

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

   7. Applied rewrites 82.3%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 66.8%

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

Alternative 11: 60.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.9 \cdot 10^{-32}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq -7 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.8 \cdot 10^{-178}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-\frac{B + A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.9e-32)
   (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
   (if (<= A -7e-54)
     (* 180.0 (/ (atan (* (/ B C) -0.5)) PI))
     (if (<= A 5.8e-178)
       (/ (* 180.0 (atan (+ 1.0 (/ C B)))) PI)
       (/ (* 180.0 (atan (- (/ (+ B A) B)))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-32) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((double) M_PI));
	} else if (A <= -7e-54) {
		tmp = 180.0 * (atan(((B / C) * -0.5)) / ((double) M_PI));
	} else if (A <= 5.8e-178) {
		tmp = (180.0 * atan((1.0 + (C / B)))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(-((B + A) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.9e-32) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else if (A <= -7e-54) {
		tmp = 180.0 * (Math.atan(((B / C) * -0.5)) / Math.PI);
	} else if (A <= 5.8e-178) {
		tmp = (180.0 * Math.atan((1.0 + (C / B)))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan(-((B + A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.9e-32:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	elif A <= -7e-54:
		tmp = 180.0 * (math.atan(((B / C) * -0.5)) / math.pi)
	elif A <= 5.8e-178:
		tmp = (180.0 * math.atan((1.0 + (C / B)))) / math.pi
	else:
		tmp = (180.0 * math.atan(-((B + A) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.9e-32)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	elseif (A <= -7e-54)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / C) * -0.5)) / pi));
	elseif (A <= 5.8e-178)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(C / B)))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-Float64(Float64(B + A) / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.9e-32)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	elseif (A <= -7e-54)
		tmp = 180.0 * (atan(((B / C) * -0.5)) / pi);
	elseif (A <= 5.8e-178)
		tmp = (180.0 * atan((1.0 + (C / B)))) / pi;
	else
		tmp = (180.0 * atan(-((B + A) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.9e-32], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -7e-54], N[(180.0 * N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.8e-178], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[(-N[(N[(B + A), $MachinePrecision] / B), $MachinePrecision])], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.90000000000000004e-32

   1. Initial program 26.0%

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

   3. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 65.0

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

   5. Applied rewrites 65.0%

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

   if -1.90000000000000004e-32 < A < -6.99999999999999964e-54

   1. Initial program 45.2%

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

   3. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 21.8

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   5. Applied rewrites 21.8%

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

   6. Taylor expanded in A around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 21.8

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

   8. Applied rewrites 21.8%

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

   if -6.99999999999999964e-54 < A < 5.7999999999999995e-178

   1. Initial program 56.0%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 80.1%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 49.1

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

   7. Applied rewrites 49.1%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 48.8%

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

   if 5.7999999999999995e-178 < A

   1. Initial program 71.7%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 91.2%

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

   5. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. pow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 82.3

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

   7. Applied rewrites 82.3%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 66.8%

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

Alternative 12: 54.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.25 \cdot 10^{-220}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-268}:\\ \;\;\;\;\frac{\tan^{-1} 0 \cdot 180}{\pi}\\ \mathbf{elif}\;B \leq 1.05 \cdot 10^{-110}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.25e-220)
   (/ (* 180.0 (atan (+ 1.0 (/ C B)))) PI)
   (if (<= B 1.05e-268)
     (/ (* (atan 0.0) 180.0) PI)
     (if (<= B 1.05e-110)
       (/ (* 180.0 (atan (/ (- A) B))) PI)
       (/ (* 180.0 (atan (- (/ C B) 1.0))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.25e-220) {
		tmp = (180.0 * atan((1.0 + (C / B)))) / ((double) M_PI);
	} else if (B <= 1.05e-268) {
		tmp = (atan(0.0) * 180.0) / ((double) M_PI);
	} else if (B <= 1.05e-110) {
		tmp = (180.0 * atan((-A / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(((C / B) - 1.0))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.25e-220) {
		tmp = (180.0 * Math.atan((1.0 + (C / B)))) / Math.PI;
	} else if (B <= 1.05e-268) {
		tmp = (Math.atan(0.0) * 180.0) / Math.PI;
	} else if (B <= 1.05e-110) {
		tmp = (180.0 * Math.atan((-A / B))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan(((C / B) - 1.0))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.25e-220:
		tmp = (180.0 * math.atan((1.0 + (C / B)))) / math.pi
	elif B <= 1.05e-268:
		tmp = (math.atan(0.0) * 180.0) / math.pi
	elif B <= 1.05e-110:
		tmp = (180.0 * math.atan((-A / B))) / math.pi
	else:
		tmp = (180.0 * math.atan(((C / B) - 1.0))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.25e-220)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(C / B)))) / pi);
	elseif (B <= 1.05e-268)
		tmp = Float64(Float64(atan(0.0) * 180.0) / pi);
	elseif (B <= 1.05e-110)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-A) / B))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B) - 1.0))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.25e-220)
		tmp = (180.0 * atan((1.0 + (C / B)))) / pi;
	elseif (B <= 1.05e-268)
		tmp = (atan(0.0) * 180.0) / pi;
	elseif (B <= 1.05e-110)
		tmp = (180.0 * atan((-A / B))) / pi;
	else
		tmp = (180.0 * atan(((C / B) - 1.0))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.25e-220], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.05e-268], N[(N[(N[ArcTan[0.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.05e-110], N[(N[(180.0 * N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.24999999999999984e-220

   1. Initial program 51.2%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 76.7%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 68.4

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

   7. Applied rewrites 68.4%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 58.0%

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

   if -2.24999999999999984e-220 < B < 1.04999999999999999e-268

   1. Initial program 63.4%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lift-*.f64 N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. mul0-lft N/A

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

      9. lift-*.f64 N/A

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

      10. lift-/.f64 35.8

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

      11. lift-*.f64 N/A

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

      12. mul0-lft 35.8

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

   7. Applied rewrites 35.8%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 35.8

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

      4. lift-/.f64 N/A

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

      5. div0 35.8

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

   9. Applied rewrites 35.8%

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

   if 1.04999999999999999e-268 < B < 1.05000000000000001e-110

   1. Initial program 57.1%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 77.5%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 48.1

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

   7. Applied rewrites 48.1%

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

   8. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 34.8

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

   10. Applied rewrites 34.8%

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

   if 1.05000000000000001e-110 < B

   1. Initial program 52.8%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 77.5%

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

   5. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. pow2 N/A

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

      4. unpow2 N/A

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

      5. lower-hypot.f64 66.3

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

   7. Applied rewrites 66.3%

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

   8. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 63.8

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

   10. Applied rewrites 63.8%

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

Alternative 13: 45.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.3 \cdot 10^{-133}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.45 \cdot 10^{-186}:\\ \;\;\;\;\frac{\tan^{-1} 0 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.3e-133)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.45e-186)
     (/ (* (atan 0.0) 180.0) PI)
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.3e-133) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.45e-186) {
		tmp = (atan(0.0) * 180.0) / ((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 <= -3.3e-133) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.45e-186) {
		tmp = (Math.atan(0.0) * 180.0) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.3e-133:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.45e-186:
		tmp = (math.atan(0.0) * 180.0) / 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 <= -3.3e-133)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.45e-186)
		tmp = Float64(Float64(atan(0.0) * 180.0) / 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 <= -3.3e-133)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.45e-186)
		tmp = (atan(0.0) * 180.0) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.3e-133], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.45e-186], N[(N[(N[ArcTan[0.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.30000000000000009e-133

   1. Initial program 50.8%

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

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]
   4. Step-by-step derivation

   5. Applied rewrites 51.1%

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

   if -3.30000000000000009e-133 < B < 2.4499999999999998e-186

   1. Initial program 58.8%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 81.6%

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

   5. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lift-*.f64 N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. mul0-lft N/A

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

      9. lift-*.f64 N/A

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

      10. lift-/.f64 32.4

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

      11. lift-*.f64 N/A

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

      12. mul0-lft 32.4

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

   7. Applied rewrites 32.4%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\pi} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 32.4

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

      4. lift-/.f64 N/A

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

      5. div0 32.4

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

   9. Applied rewrites 32.4%

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

   if 2.4499999999999998e-186 < B

   1. Initial program 53.3%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
   4. Step-by-step derivation

   5. Applied rewrites 47.2%

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

Alternative 14: 40.3% accurate, 2.9× speedup

Math

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

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -9.999999999999969e-311

   1. Initial program 52.6%

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

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]
   4. Step-by-step derivation

   5. Applied rewrites 40.5%

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

   if -9.999999999999969e-311 < B

   1. Initial program 54.8%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
   4. Step-by-step derivation

   5. Applied rewrites 40.2%

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

Alternative 15: 20.9% accurate, 3.1× 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 53.7%

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

3. Taylor expanded in B around inf

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
4. Step-by-step derivation

5. Applied rewrites 20.9%

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

Reproduce

herbie shell --seed 2025089 
(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)))