ABCF->ab-angle angle

Percentage Accurate: 54.0% → 80.4%

Time: 5.5s

Alternatives: 17

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -7.5 \cdot 10^{+176}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\left(\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)\right) \cdot {B}^{-1}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -7.5e+176)
   (* 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 <= -7.5e+176) {
		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 <= -7.5e+176) {
		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 <= -7.5e+176:
		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 <= -7.5e+176)
		tmp = Float64(180.0 * Float64(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 <= -7.5e+176)
		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, -7.5e+176], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $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 < -7.499999999999999e176

   1. Initial program 11.7%

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

   3. Taylor expanded in 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 81.8

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

   5. Applied rewrites 81.8%

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

   if -7.499999999999999e176 < A

   1. Initial program 59.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 80.2%

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

Alternative 2: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ \mathbf{if}\;t\_0 \leq -40:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - B\right)\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

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 -40.0)
     (* 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 <= -40.0) {
		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 <= -40.0) {
		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 <= -40.0:
		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 <= -40.0)
		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(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)
	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 <= -40.0)
		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, -40.0], 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[(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 (*.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))) < -40

   1. Initial program 60.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 77.1%

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

   if -40 < (*.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 16.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 18.1%

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

   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 52.9

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

   7. Applied rewrites 52.9%

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

   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 59.2%

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

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   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 75.8

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

   5. Applied rewrites 75.8%

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

Alternative 3: 67.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ \mathbf{if}\;t\_0 \leq -40:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (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 -40.0)
     (/ (* 180.0 (atan (/ (- C B) 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 <= -40.0) {
		tmp = (180.0 * atan(((C - B) / 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 <= -40.0) {
		tmp = (180.0 * Math.atan(((C - B) / 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 <= -40.0:
		tmp = (180.0 * math.atan(((C - B) / 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 <= -40.0)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi);
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / 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)
	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 <= -40.0)
		tmp = (180.0 * atan(((C - B) / 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, -40.0], N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $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[(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 (*.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))) < -40

   1. Initial program 60.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 87.8%

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

   5. Taylor expanded in 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. pow2 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 72.0

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

   7. Applied rewrites 72.0%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 64.4%

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

   if -40 < (*.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 16.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 18.1%

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

   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 52.9

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

   7. Applied rewrites 52.9%

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

   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 59.2%

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

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   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 75.8

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

   5. Applied rewrites 75.8%

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

Alternative 4: 62.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	elseif (t_0 <= 0.0)
		tmp = (180.0 * atan(((B / A) * 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[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $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[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 60.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 87.8%

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

   5. Taylor expanded in 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. pow2 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 72.0

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

   7. Applied rewrites 72.0%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 64.4%

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

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

   1. Initial program 16.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 18.0%

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

   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 52.9

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

   7. Applied rewrites 52.9%

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

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

   1. Initial program 59.2%

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

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   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 75.8

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

   5. Applied rewrites 75.8%

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

   6. Taylor expanded in A around 0

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

   8. Applied rewrites 62.5%

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

Alternative 5: 62.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan(((B / A) * 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[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 60.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 87.8%

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

   5. Taylor expanded in 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. pow2 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 72.0

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

   7. Applied rewrites 72.0%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 64.4%

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

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

   1. Initial program 16.7%

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

   3. Taylor expanded in 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 52.8

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

   5. Applied rewrites 52.8%

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

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

   1. Initial program 59.2%

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

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   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 75.8

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

   5. Applied rewrites 75.8%

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

   6. Taylor expanded in A around 0

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

   8. Applied rewrites 62.5%

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

Alternative 6: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -0.5:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0.0005:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -0.5)
     (/ (* 180.0 (atan (/ (- C B) B))) PI)
     (if (<= t_0 0.0005)
       (* 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 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	} else if (t_0 <= 0.0005) {
		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 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	} else if (t_0 <= 0.0005) {
		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 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_0 <= -0.5:
		tmp = (180.0 * math.atan(((C - B) / B))) / math.pi
	elif t_0 <= 0.0005:
		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(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi);
	elseif (t_0 <= 0.0005)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / C) * -0.5)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	elseif (t_0 <= 0.0005)
		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[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[t$95$0, 0.0005], N[(180.0 * N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 60.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 87.8%

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

   5. Taylor expanded in 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. pow2 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 72.0

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

   7. Applied rewrites 72.0%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 64.4%

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

   if -0.5 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 5.0000000000000001e-4

   1. Initial program 16.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 48.0

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

   5. Applied rewrites 48.0%

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

   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 48.0

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

   8. Applied rewrites 48.0%

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

   if 5.0000000000000001e-4 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 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. 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 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in A around 0

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

   8. Applied rewrites 62.8%

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

Alternative 7: 75.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.9 \cdot 10^{+128}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{+46}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - B\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.9e+128)
   (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
   (if (<= A 1.9e+46)
     (/ (* 180.0 (atan (/ (- C (hypot B C)) B))) PI)
     (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.9e+128) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((double) M_PI));
	} else if (A <= 1.9e+46) {
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.9e+128) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else if (A <= 1.9e+46) {
		tmp = (180.0 * Math.atan(((C - Math.hypot(B, C)) / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.9e+128:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	elif A <= 1.9e+46:
		tmp = (180.0 * math.atan(((C - math.hypot(B, C)) / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C - A) - B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.9e+128)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	elseif (A <= 1.9e+46)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - hypot(B, C)) / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.9e+128)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	elseif (A <= 1.9e+46)
		tmp = (180.0 * atan(((C - hypot(B, C)) / B))) / pi;
	else
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.9e+128], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.9e+46], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.89999999999999987e128

   1. Initial program 15.6%

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

   3. Taylor expanded in 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 78.3

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

   5. Applied rewrites 78.3%

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

   if -5.89999999999999987e128 < A < 1.9e46

   1. Initial program 54.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 76.9%

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

   5. Taylor expanded in A around 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. pow2 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 72.5

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

   7. Applied rewrites 72.5%

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

   if 1.9e46 < A

   1. Initial program 80.0%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 82.6%

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

Alternative 8: 75.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.9 \cdot 10^{+128}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{+46}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - B\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.9e+128)
   (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
   (if (<= A 1.9e+46)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.9e+128) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((double) M_PI));
	} else if (A <= 1.9e+46) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.9e+128) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else if (A <= 1.9e+46) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.9e+128:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	elif A <= 1.9e+46:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C - A) - B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.9e+128)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	elseif (A <= 1.9e+46)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.9e+128)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	elseif (A <= 1.9e+46)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.9e+128], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.9e+46], 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[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.89999999999999987e128

   1. Initial program 15.6%

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

   3. Taylor expanded in 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 78.3

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

   5. Applied rewrites 78.3%

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

   if -5.89999999999999987e128 < A < 1.9e46

   1. Initial program 54.1%

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

   3. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}}{\pi} \]
   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 72.5

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

   5. Applied rewrites 72.5%

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

   if 1.9e46 < A

   1. Initial program 80.0%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 82.6%

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

Alternative 9: 45.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.35 \cdot 10^{+28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5.8 \cdot 10^{-300}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 2.25 \cdot 10^{-166}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{+26}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ C B))) PI)))
   (if (<= B -1.35e+28)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= B 5.8e-300)
       t_0
       (if (<= B 2.25e-166)
         (/ (* 180.0 (atan (/ 0.0 B))) PI)
         (if (<= B 3.2e+26) 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 <= -1.35e+28) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 5.8e-300) {
		tmp = t_0;
	} else if (B <= 2.25e-166) {
		tmp = (180.0 * atan((0.0 / B))) / ((double) M_PI);
	} else if (B <= 3.2e+26) {
		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 <= -1.35e+28) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 5.8e-300) {
		tmp = t_0;
	} else if (B <= 2.25e-166) {
		tmp = (180.0 * Math.atan((0.0 / B))) / Math.PI;
	} else if (B <= 3.2e+26) {
		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 <= -1.35e+28:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 5.8e-300:
		tmp = t_0
	elif B <= 2.25e-166:
		tmp = (180.0 * math.atan((0.0 / B))) / math.pi
	elif B <= 3.2e+26:
		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 <= -1.35e+28)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 5.8e-300)
		tmp = t_0;
	elseif (B <= 2.25e-166)
		tmp = Float64(Float64(180.0 * atan(Float64(0.0 / B))) / pi);
	elseif (B <= 3.2e+26)
		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 <= -1.35e+28)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 5.8e-300)
		tmp = t_0;
	elseif (B <= 2.25e-166)
		tmp = (180.0 * atan((0.0 / B))) / pi;
	elseif (B <= 3.2e+26)
		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, -1.35e+28], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.8e-300], t$95$0, If[LessEqual[B, 2.25e-166], N[(N[(180.0 * N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 3.2e+26], 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 < -1.3500000000000001e28

   1. Initial program 46.5%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 64.5%

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

   if -1.3500000000000001e28 < B < 5.79999999999999985e-300 or 2.2499999999999999e-166 < B < 3.20000000000000029e26

   1. Initial program 59.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 72.5%

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

   5. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 49.5

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

   7. Applied rewrites 49.5%

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

   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. lift-/.f64 30.2

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

   10. Applied rewrites 30.2%

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

   if 5.79999999999999985e-300 < B < 2.2499999999999999e-166

   1. Initial program 57.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 80.0%

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

   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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt1-in N/A

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

      4. metadata-eval N/A

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

      5. mul0-lft N/A

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

      6. metadata-eval N/A

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

      7. mul0-lft N/A

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

      8. lift-/.f64 N/A

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

      9. mul0-lft 30.7

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

   7. Applied rewrites 30.7%

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

   if 3.20000000000000029e26 < 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 64.5%

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

Alternative 10: 50.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 5.8 \cdot 10^{-300}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.25 \cdot 10^{-166}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 5.8e-300)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= B 2.25e-166)
     (/ (* 180.0 (atan (/ 0.0 B))) PI)
     (if (<= B 3.2e+26)
       (/ (* 180.0 (atan (/ C B))) PI)
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.8e-300) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (B <= 2.25e-166) {
		tmp = (180.0 * atan((0.0 / B))) / ((double) M_PI);
	} else if (B <= 3.2e+26) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.8e-300) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (B <= 2.25e-166) {
		tmp = (180.0 * Math.atan((0.0 / B))) / Math.PI;
	} else if (B <= 3.2e+26) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 5.8e-300:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif B <= 2.25e-166:
		tmp = (180.0 * math.atan((0.0 / B))) / math.pi
	elif B <= 3.2e+26:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 5.8e-300)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (B <= 2.25e-166)
		tmp = Float64(Float64(180.0 * atan(Float64(0.0 / B))) / pi);
	elseif (B <= 3.2e+26)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 5.8e-300)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (B <= 2.25e-166)
		tmp = (180.0 * atan((0.0 / B))) / pi;
	elseif (B <= 3.2e+26)
		tmp = (180.0 * atan((C / B))) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 5.8e-300], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.25e-166], N[(N[(180.0 * N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 3.2e+26], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < 5.79999999999999985e-300

   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

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   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 66.0

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

   5. Applied rewrites 66.0%

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

   6. Taylor expanded in A around 0

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

   8. Applied rewrites 54.6%

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

   if 5.79999999999999985e-300 < B < 2.2499999999999999e-166

   1. Initial program 57.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 80.0%

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

   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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt1-in N/A

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

      4. metadata-eval N/A

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

      5. mul0-lft N/A

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

      6. metadata-eval N/A

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

      7. mul0-lft N/A

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

      8. lift-/.f64 N/A

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

      9. mul0-lft 30.7

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

   7. Applied rewrites 30.7%

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

   if 2.2499999999999999e-166 < B < 3.20000000000000029e26

   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 69.9%

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

   5. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 58.5

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

   7. Applied rewrites 58.5%

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

   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. lift-/.f64 29.7

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

   10. Applied rewrites 29.7%

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

   if 3.20000000000000029e26 < 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 64.5%

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

Alternative 11: 50.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 9.6 \cdot 10^{-299}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.25 \cdot 10^{-166}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 9.6e-299)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (if (<= B 2.25e-166)
     (/ (* 180.0 (atan (/ 0.0 B))) PI)
     (if (<= B 3.2e+26)
       (/ (* 180.0 (atan (/ C B))) PI)
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 9.6e-299) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= 2.25e-166) {
		tmp = (180.0 * atan((0.0 / B))) / ((double) M_PI);
	} else if (B <= 3.2e+26) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 9.6e-299) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= 2.25e-166) {
		tmp = (180.0 * Math.atan((0.0 / B))) / Math.PI;
	} else if (B <= 3.2e+26) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 9.6e-299:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= 2.25e-166:
		tmp = (180.0 * math.atan((0.0 / B))) / math.pi
	elif B <= 3.2e+26:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 9.6e-299)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= 2.25e-166)
		tmp = Float64(Float64(180.0 * atan(Float64(0.0 / B))) / pi);
	elseif (B <= 3.2e+26)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 9.6e-299)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= 2.25e-166)
		tmp = (180.0 * atan((0.0 / B))) / pi;
	elseif (B <= 3.2e+26)
		tmp = (180.0 * atan((C / B))) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 9.6e-299], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.25e-166], N[(N[(180.0 * N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 3.2e+26], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < 9.60000000000000077e-299

   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

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   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 66.0

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

   5. Applied rewrites 66.0%

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

   6. Taylor expanded in C around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 55.6

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

   8. Applied rewrites 55.6%

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

   if 9.60000000000000077e-299 < B < 2.2499999999999999e-166

   1. Initial program 56.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 79.9%

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

   5. Taylor expanded in 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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt1-in N/A

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

      4. metadata-eval N/A

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

      5. mul0-lft N/A

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

      6. metadata-eval N/A

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

      7. mul0-lft N/A

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

      8. lift-/.f64 N/A

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

      9. mul0-lft 30.7

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

   7. Applied rewrites 30.7%

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

   if 2.2499999999999999e-166 < B < 3.20000000000000029e26

   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 69.9%

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

   5. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 58.5

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

   7. Applied rewrites 58.5%

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

   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. lift-/.f64 29.7

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

   10. Applied rewrites 29.7%

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

   if 3.20000000000000029e26 < 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 64.5%

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

Alternative 12: 54.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 5.8 \cdot 10^{-300}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-166}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 5.8e-300)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= B 1.6e-166)
     (/ (* 180.0 (atan (/ 0.0 B))) PI)
     (/ (* 180.0 (atan (/ (- C B) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.8e-300) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (B <= 1.6e-166) {
		tmp = (180.0 * atan((0.0 / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.8e-300) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (B <= 1.6e-166) {
		tmp = (180.0 * Math.atan((0.0 / B))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 5.8e-300:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif B <= 1.6e-166:
		tmp = (180.0 * math.atan((0.0 / B))) / math.pi
	else:
		tmp = (180.0 * math.atan(((C - B) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 5.8e-300)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (B <= 1.6e-166)
		tmp = Float64(Float64(180.0 * atan(Float64(0.0 / B))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 5.8e-300)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (B <= 1.6e-166)
		tmp = (180.0 * atan((0.0 / B))) / pi;
	else
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 5.8e-300], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.6e-166], N[(N[(180.0 * N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 5.79999999999999985e-300

   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

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   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 66.0

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

   5. Applied rewrites 66.0%

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

   6. Taylor expanded in A around 0

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

   8. Applied rewrites 54.6%

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

   if 5.79999999999999985e-300 < B < 1.6e-166

   1. Initial program 57.2%

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

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

      2. *-commutative N/A

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

      3. distribute-rgt1-in N/A

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

      4. metadata-eval N/A

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

      5. mul0-lft N/A

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

      6. metadata-eval N/A

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

      7. mul0-lft N/A

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

      8. lift-/.f64 N/A

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

      9. mul0-lft 30.8

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

   7. Applied rewrites 30.8%

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

   if 1.6e-166 < B

   1. Initial program 53.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 77.4%

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

   5. Taylor expanded in 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. pow2 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 65.4

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

   7. Applied rewrites 65.4%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 61.3%

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

Alternative 13: 54.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 5.8 \cdot 10^{-300}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.1 \cdot 10^{-166}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 5.8e-300)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= B 4.1e-166)
     (/ (* 180.0 (atan (/ 0.0 B))) PI)
     (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.8e-300) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (B <= 4.1e-166) {
		tmp = (180.0 * atan((0.0 / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.8e-300) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (B <= 4.1e-166) {
		tmp = (180.0 * Math.atan((0.0 / B))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 5.8e-300:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif B <= 4.1e-166:
		tmp = (180.0 * math.atan((0.0 / B))) / math.pi
	else:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 5.8e-300)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (B <= 4.1e-166)
		tmp = Float64(Float64(180.0 * atan(Float64(0.0 / B))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 5.8e-300)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (B <= 4.1e-166)
		tmp = (180.0 * atan((0.0 / B))) / pi;
	else
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 5.8e-300], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.1e-166], N[(N[(180.0 * N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 5.79999999999999985e-300

   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

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   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 66.0

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

   5. Applied rewrites 66.0%

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

   6. Taylor expanded in A around 0

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

   8. Applied rewrites 54.6%

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

   if 5.79999999999999985e-300 < B < 4.0999999999999997e-166

   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 79.9%

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

   5. Taylor expanded in 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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt1-in N/A

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

      4. metadata-eval N/A

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

      5. mul0-lft N/A

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

      6. metadata-eval N/A

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

      7. mul0-lft N/A

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

      8. lift-/.f64 N/A

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

      9. mul0-lft 30.6

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

   7. Applied rewrites 30.6%

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

   if 4.0999999999999997e-166 < B

   1. Initial program 53.6%

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

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 71.2

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

   7. Applied rewrites 71.2%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 61.4%

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

Alternative 14: 46.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.35 \cdot 10^{+28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.35e+28)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 3.2e+26)
     (/ (* 180.0 (atan (/ C B))) PI)
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.35e+28) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 3.2e+26) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.35e+28) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 3.2e+26) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.35e+28:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 3.2e+26:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.35e+28)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 3.2e+26)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.35e+28)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 3.2e+26)
		tmp = (180.0 * atan((C / B))) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.35e+28], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.2e+26], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $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 < -1.3500000000000001e28

   1. Initial program 46.5%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 64.5%

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

   if -1.3500000000000001e28 < B < 3.20000000000000029e26

   1. Initial program 59.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 73.9%

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

   5. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 49.3

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

   7. Applied rewrites 49.3%

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

   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. lift-/.f64 31.4

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

   10. Applied rewrites 31.4%

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

   if 3.20000000000000029e26 < 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 64.5%

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

Alternative 15: 46.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.35 \cdot 10^{+28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{+26}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.35e+28)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 3.2e+26)
     (* 180.0 (/ (atan (/ C B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.35e+28) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 3.2e+26) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.35e+28) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 3.2e+26) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.35e+28:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 3.2e+26:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.35e+28)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 3.2e+26)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.35e+28)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 3.2e+26)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.35e+28], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.2e+26], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.3500000000000001e28

   1. Initial program 46.5%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 64.5%

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

   if -1.3500000000000001e28 < B < 3.20000000000000029e26

   1. Initial program 59.3%

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

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\pi} \]
   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 51.5

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

   5. Applied rewrites 51.5%

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

   6. Taylor expanded in C around inf

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

      1. lift-/.f64 31.4

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

   8. Applied rewrites 31.4%

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

   if 3.20000000000000029e26 < 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 64.5%

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

Alternative 16: 39.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2e-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 <= -2e-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 <= -2e-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 <= -2e-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 <= -2e-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 <= -2e-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, -2e-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 < -1.999999999999994e-310

   1. Initial program 53.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 40.1%

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

   if -1.999999999999994e-310 < B

   1. Initial program 54.4%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 39.7%

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

Alternative 17: 20.5% 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 54.0%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
2. 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 20.5%

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

Reproduce

herbie shell --seed 2025088 
(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)))