ABCF->ab-angle angle

Percentage Accurate: 53.6% → 79.9%

Time: 7.3s

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: 53.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 79.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\left(\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)\right) \cdot {B}^{-1}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.5e+24)
   (/ (* 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 <= -8.5e+24) {
		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 <= -8.5e+24) {
		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 <= -8.5e+24:
		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 <= -8.5e+24)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) * (B ^ -1.0)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.5e+24)
		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, -8.5e+24], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] * N[Power[B, -1.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -8.49999999999999959e24

   1. Initial program 13.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 44.8%

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

   5. Taylor expanded in A around -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 74.2

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

   7. Applied rewrites 74.2%

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

   if -8.49999999999999959e24 < A

   1. Initial program 64.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 87.6%

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

Alternative 2: 72.4% accurate, 0.4× speedup

Math

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

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(180.0 * Float64(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[(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[(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 54.9%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 74.3%

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

   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 18.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 50.3

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

   5. Applied rewrites 50.3%

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

   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 62.3%

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

   3. 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 79.5

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

   5. Applied rewrites 79.5%

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

4. Final simplification 73.1%

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

Alternative 3: 67.0% accurate, 0.4× speedup

Math

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

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(180.0 * Float64(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[(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[(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 54.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 86.7%

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

   5. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. pow2 N/A

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

      4. unpow2 N/A

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

      5. lower-hypot.f64 76.3

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

   7. Applied rewrites 76.3%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 65.9%

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

   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 18.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 50.3

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

   5. Applied rewrites 50.3%

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

   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 62.3%

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

   3. 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 79.5

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

   5. Applied rewrites 79.5%

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

4. Final simplification 69.1%

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

Alternative 4: 62.2% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (A B C)
 :precision binary64
 (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 -10.0)
     (/ (* 180.0 (atan (/ (- C B) B))) PI)
     (if (<= t_0 0.0)
       (* 180.0 (/ (atan (* (/ B C) -0.5)) PI))
       (/ (* 180.0 (atan (+ (/ C B) 1.0))) 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 <= -10.0) {
		tmp = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan(((B / C) * -0.5)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((C / B) + 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(((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 <= -10.0) {
		tmp = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan(((B / C) * -0.5)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((C / B) + 1.0))) / 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 <= -10.0:
		tmp = (180.0 * math.atan(((C - B) / B))) / math.pi
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan(((B / C) * -0.5)) / math.pi)
	else:
		tmp = (180.0 * math.atan(((C / B) + 1.0))) / 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 <= -10.0)
		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 / C) * -0.5)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B) + 1.0))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	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 <= -10.0)
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan(((B / C) * -0.5)) / pi);
	else
		tmp = (180.0 * atan(((C / B) + 1.0))) / 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, -10.0], 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[(180.0 * N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -10

   1. Initial program 55.3%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 86.8%

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

   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. unpow2 N/A

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

      5. lower-hypot.f64 75.8

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

   7. Applied rewrites 75.8%

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

   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 65.5%

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

   if -10 < (*.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 16.4%

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

   3. Taylor expanded in 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 49.2

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

   5. Applied rewrites 49.2%

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

   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 49.2

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

   8. Applied rewrites 49.2%

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

   if 0.0 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64)))

   1. Initial program 62.3%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 86.9%

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

   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. unpow2 N/A

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

      5. lower-hypot.f64 72.3

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

   7. Applied rewrites 72.3%

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

   8. Taylor expanded in B around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 67.4

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

   10. Applied rewrites 67.4%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \leq -10:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{elif}\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.22 \cdot 10^{+24}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{+63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\mathsf{hypot}\left(B, A\right) + A}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.22e+24)
   (/ (* 180.0 (atan (* (/ B A) 0.5))) PI)
   (if (<= A 1.35e+63)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (/ (* 180.0 (atan (/ (+ (hypot B A) A) (- B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.22e+24) {
		tmp = (180.0 * atan(((B / A) * 0.5))) / ((double) M_PI);
	} else if (A <= 1.35e+63) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((hypot(B, A) + A) / -B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.22e+24) {
		tmp = (180.0 * Math.atan(((B / A) * 0.5))) / Math.PI;
	} else if (A <= 1.35e+63) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((Math.hypot(B, A) + A) / -B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.22e+24:
		tmp = (180.0 * math.atan(((B / A) * 0.5))) / math.pi
	elif A <= 1.35e+63:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan(((math.hypot(B, A) + A) / -B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.22e+24)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	elseif (A <= 1.35e+63)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(hypot(B, A) + A) / Float64(-B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.22e+24)
		tmp = (180.0 * atan(((B / A) * 0.5))) / pi;
	elseif (A <= 1.35e+63)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = (180.0 * atan(((hypot(B, A) + A) / -B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.22e+24], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.35e+63], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision] + A), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.21999999999999994e24

   1. Initial program 13.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 44.8%

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

   5. Taylor expanded in A around -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 74.2

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

   7. Applied rewrites 74.2%

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

   if -2.21999999999999994e24 < A < 1.35000000000000009e63

   1. Initial program 55.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 80.9

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

   5. Applied rewrites 80.9%

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

   if 1.35000000000000009e63 < A

   1. Initial program 85.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 96.7%

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

   5. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. pow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 90.8

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

   7. Applied rewrites 90.8%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.22 \cdot 10^{+24}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{+63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\mathsf{hypot}\left(B, A\right) + A}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.22 \cdot 10^{+24}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{+63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{hypot}\left(A, B\right) + A}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.22e+24)
   (/ (* 180.0 (atan (* (/ B A) 0.5))) PI)
   (if (<= A 1.35e+63)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (* 180.0 (/ (atan (/ (+ (hypot A B) A) (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.22e+24) {
		tmp = (180.0 * atan(((B / A) * 0.5))) / ((double) M_PI);
	} else if (A <= 1.35e+63) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((hypot(A, B) + A) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.22e+24) {
		tmp = (180.0 * Math.atan(((B / A) * 0.5))) / Math.PI;
	} else if (A <= 1.35e+63) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((Math.hypot(A, B) + A) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.22e+24:
		tmp = (180.0 * math.atan(((B / A) * 0.5))) / math.pi
	elif A <= 1.35e+63:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((math.hypot(A, B) + A) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.22e+24)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	elseif (A <= 1.35e+63)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(hypot(A, B) + A) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.22e+24)
		tmp = (180.0 * atan(((B / A) * 0.5))) / pi;
	elseif (A <= 1.35e+63)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((hypot(A, B) + A) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.22e+24], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.35e+63], 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[(N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision] + A), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.21999999999999994e24

   1. Initial program 13.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 44.8%

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

   5. Taylor expanded in A around -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 74.2

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

   7. Applied rewrites 74.2%

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

   if -2.21999999999999994e24 < A < 1.35000000000000009e63

   1. Initial program 55.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 80.9

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

   5. Applied rewrites 80.9%

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

   if 1.35000000000000009e63 < A

   1. Initial program 85.9%

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

   3. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. unpow2 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 90.8

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

   5. Applied rewrites 90.8%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.22 \cdot 10^{+24}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{+63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{hypot}\left(A, B\right) + A}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.22 \cdot 10^{+24}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.4 \cdot 10^{+58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.22e+24)
   (/ (* 180.0 (atan (* (/ B A) 0.5))) PI)
   (if (<= A 3.4e+58)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (/ (* 180.0 (atan (+ 1.0 (/ (- C A) B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.22e+24) {
		tmp = (180.0 * atan(((B / A) * 0.5))) / ((double) M_PI);
	} else if (A <= 3.4e+58) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((1.0 + ((C - A) / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.22e+24) {
		tmp = (180.0 * Math.atan(((B / A) * 0.5))) / Math.PI;
	} else if (A <= 3.4e+58) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((1.0 + ((C - A) / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.22e+24:
		tmp = (180.0 * math.atan(((B / A) * 0.5))) / math.pi
	elif A <= 3.4e+58:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan((1.0 + ((C - A) / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.22e+24)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	elseif (A <= 3.4e+58)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(Float64(C - A) / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.22e+24)
		tmp = (180.0 * atan(((B / A) * 0.5))) / pi;
	elseif (A <= 3.4e+58)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = (180.0 * atan((1.0 + ((C - A) / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.22e+24], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 3.4e+58], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.21999999999999994e24

   1. Initial program 13.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 44.8%

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

   5. Taylor expanded in A around -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 74.2

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

   7. Applied rewrites 74.2%

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

   if -2.21999999999999994e24 < A < 3.4000000000000001e58

   1. Initial program 55.0%

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

   3. Taylor expanded in A around 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 80.8

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

   5. Applied rewrites 80.8%

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

   if 3.4000000000000001e58 < A

   1. Initial program 86.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 96.8%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 89.7

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

   7. Applied rewrites 89.7%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.22 \cdot 10^{+24}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.4 \cdot 10^{+58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-179}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + A}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.8e+24)
   (/ (* 180.0 (atan (* (/ B A) 0.5))) PI)
   (if (<= A 6e-179)
     (/ (* 180.0 (atan (/ (- C B) B))) PI)
     (/ (* 180.0 (atan (/ (+ B A) (- B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+24) {
		tmp = (180.0 * atan(((B / A) * 0.5))) / ((double) M_PI);
	} else if (A <= 6e-179) {
		tmp = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(((B + A) / -B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+24) {
		tmp = (180.0 * Math.atan(((B / A) * 0.5))) / Math.PI;
	} else if (A <= 6e-179) {
		tmp = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan(((B + A) / -B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.8e+24:
		tmp = (180.0 * math.atan(((B / A) * 0.5))) / math.pi
	elif A <= 6e-179:
		tmp = (180.0 * math.atan(((C - B) / B))) / math.pi
	else:
		tmp = (180.0 * math.atan(((B + A) / -B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.8e+24)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	elseif (A <= 6e-179)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B + A) / Float64(-B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.8e+24)
		tmp = (180.0 * atan(((B / A) * 0.5))) / pi;
	elseif (A <= 6e-179)
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	else
		tmp = (180.0 * atan(((B + A) / -B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.8e+24], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 6e-179], N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B + A), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.79999999999999992e24

   1. Initial program 13.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 44.8%

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

   5. Taylor expanded in A around -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 74.2

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

   7. Applied rewrites 74.2%

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

   if -1.79999999999999992e24 < A < 6.00000000000000012e-179

   1. Initial program 55.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. 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 83.0%

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

   5. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. pow2 N/A

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

      4. unpow2 N/A

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

      5. lower-hypot.f64 82.1

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

   7. Applied rewrites 82.1%

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

   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 57.4%

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

   if 6.00000000000000012e-179 < A

   1. Initial program 72.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 91.7%

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

   5. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. pow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 81.0

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

   7. Applied rewrites 81.0%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 69.1%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-179}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + A}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-179}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + A}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.8e+24)
   (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
   (if (<= A 6e-179)
     (/ (* 180.0 (atan (/ (- C B) B))) PI)
     (/ (* 180.0 (atan (/ (+ B A) (- B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+24) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((double) M_PI));
	} else if (A <= 6e-179) {
		tmp = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(((B + A) / -B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+24) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else if (A <= 6e-179) {
		tmp = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan(((B + A) / -B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.8e+24:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	elif A <= 6e-179:
		tmp = (180.0 * math.atan(((C - B) / B))) / math.pi
	else:
		tmp = (180.0 * math.atan(((B + A) / -B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.8e+24)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	elseif (A <= 6e-179)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / B))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B + A) / Float64(-B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.8e+24)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	elseif (A <= 6e-179)
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	else
		tmp = (180.0 * atan(((B + A) / -B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.8e+24], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6e-179], N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B + A), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.79999999999999992e24

   1. Initial program 13.9%

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

   3. Taylor expanded in A around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}}{\pi} \]
   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 74.1

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

   5. Applied rewrites 74.1%

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

   if -1.79999999999999992e24 < A < 6.00000000000000012e-179

   1. Initial program 55.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing
   3. 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 83.0%

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

   5. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. pow2 N/A

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

      4. unpow2 N/A

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

      5. lower-hypot.f64 82.1

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

   7. Applied rewrites 82.1%

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

   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 57.4%

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

   if 6.00000000000000012e-179 < A

   1. Initial program 72.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 91.7%

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

   5. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. pow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 81.0

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

   7. Applied rewrites 81.0%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 69.1%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 6 \cdot 10^{-179}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B + A}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.4 \cdot 10^{+62}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.8e+24)
   (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
   (if (<= A 5.4e+62)
     (/ (* 180.0 (atan (/ (- C B) B))) PI)
     (/ (* 180.0 (atan (- 1.0 (/ A B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+24) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((double) M_PI));
	} else if (A <= 5.4e+62) {
		tmp = (180.0 * atan(((C - B) / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((1.0 - (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+24) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else if (A <= 5.4e+62) {
		tmp = (180.0 * Math.atan(((C - B) / B))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan((1.0 - (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.8e+24:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	elif A <= 5.4e+62:
		tmp = (180.0 * math.atan(((C - B) / B))) / math.pi
	else:
		tmp = (180.0 * math.atan((1.0 - (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.8e+24)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	elseif (A <= 5.4e+62)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - B) / 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 (A <= -1.8e+24)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	elseif (A <= 5.4e+62)
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	else
		tmp = (180.0 * atan((1.0 - (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.8e+24], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.4e+62], N[(N[(180.0 * N[ArcTan[N[(N[(C - B), $MachinePrecision] / 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 A < -1.79999999999999992e24

   1. Initial program 13.9%

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

   3. Taylor expanded in A around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}}{\pi} \]
   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 74.1

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

   5. Applied rewrites 74.1%

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

   if -1.79999999999999992e24 < A < 5.4e62

   1. Initial program 55.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 83.8%

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

   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. unpow2 N/A

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

      5. lower-hypot.f64 80.9

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

   7. Applied rewrites 80.9%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 54.5%

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

   if 5.4e62 < A

   1. Initial program 85.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 96.7%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 89.5

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

   7. Applied rewrites 89.5%

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

   8. Taylor expanded in C around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 84.8

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

   10. Applied rewrites 84.8%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.4 \cdot 10^{+62}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 3.8 \cdot 10^{-233}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-152}:\\ \;\;\;\;\frac{\tan^{-1} 0 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - B}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 3.8e-233)
   (/ (* 180.0 (atan (+ (/ C B) 1.0))) PI)
   (if (<= B 1.6e-152)
     (/ (* (atan 0.0) 180.0) PI)
     (/ (* 180.0 (atan (/ (- C B) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 3.8e-233) {
		tmp = (180.0 * atan(((C / B) + 1.0))) / ((double) M_PI);
	} else if (B <= 1.6e-152) {
		tmp = (atan(0.0) * 180.0) / ((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 <= 3.8e-233) {
		tmp = (180.0 * Math.atan(((C / B) + 1.0))) / Math.PI;
	} else if (B <= 1.6e-152) {
		tmp = (Math.atan(0.0) * 180.0) / 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 <= 3.8e-233:
		tmp = (180.0 * math.atan(((C / B) + 1.0))) / math.pi
	elif B <= 1.6e-152:
		tmp = (math.atan(0.0) * 180.0) / 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 <= 3.8e-233)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B) + 1.0))) / pi);
	elseif (B <= 1.6e-152)
		tmp = Float64(Float64(atan(0.0) * 180.0) / 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 <= 3.8e-233)
		tmp = (180.0 * atan(((C / B) + 1.0))) / pi;
	elseif (B <= 1.6e-152)
		tmp = (atan(0.0) * 180.0) / pi;
	else
		tmp = (180.0 * atan(((C - B) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 3.8e-233], N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.6e-152], N[(N[(N[ArcTan[0.0], $MachinePrecision] * 180.0), $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 < 3.8e-233

   1. Initial program 58.8%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 80.2%

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

   5. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. pow2 N/A

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

      4. unpow2 N/A

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

      5. lower-hypot.f64 66.3

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

   7. Applied rewrites 66.3%

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

   8. Taylor expanded in B around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 58.8

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

   10. Applied rewrites 58.8%

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

   if 3.8e-233 < B < 1.60000000000000006e-152

   1. Initial program 20.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 74.2%

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

   5. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lift-*.f64 N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. mul0-lft N/A

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

      9. lift-*.f64 N/A

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

      10. lift-/.f64 58.1

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

      11. lift-*.f64 N/A

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

      12. mul0-lft 58.1

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

   7. Applied rewrites 58.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 58.1

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

      4. lift-/.f64 N/A

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

      5. div0 58.1

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

   9. Applied rewrites 58.1%

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

   if 1.60000000000000006e-152 < B

   1. Initial program 50.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 75.5%

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

   5. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. pow2 N/A

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

      4. unpow2 N/A

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

      5. lower-hypot.f64 66.5

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

   7. Applied rewrites 66.5%

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

   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 64.6%

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

Alternative 12: 46.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -0.155:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-233}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-151}:\\ \;\;\;\;\frac{\tan^{-1} 0 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -0.155)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 3.8e-233)
     (/ (* 180.0 (atan (/ C B))) PI)
     (if (<= B 1.3e-151)
       (/ (* (atan 0.0) 180.0) PI)
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -0.155) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 3.8e-233) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else if (B <= 1.3e-151) {
		tmp = (atan(0.0) * 180.0) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -0.155) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 3.8e-233) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else if (B <= 1.3e-151) {
		tmp = (Math.atan(0.0) * 180.0) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -0.155:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 3.8e-233:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	elif B <= 1.3e-151:
		tmp = (math.atan(0.0) * 180.0) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -0.155)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 3.8e-233)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	elseif (B <= 1.3e-151)
		tmp = Float64(Float64(atan(0.0) * 180.0) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -0.155)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 3.8e-233)
		tmp = (180.0 * atan((C / B))) / pi;
	elseif (B <= 1.3e-151)
		tmp = (atan(0.0) * 180.0) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -0.155], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.8e-233], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.3e-151], N[(N[(N[ArcTan[0.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -0.154999999999999999

   1. Initial program 43.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 57.7%

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

   if -0.154999999999999999 < B < 3.8e-233

   1. Initial program 70.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 82.3%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 65.9

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

   7. Applied rewrites 65.9%

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

   8. Taylor expanded in C around inf

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

      1. lift-/.f64 44.7

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

   10. Applied rewrites 44.7%

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

   if 3.8e-233 < B < 1.3e-151

   1. Initial program 20.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 74.2%

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

   5. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lift-*.f64 N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. mul0-lft N/A

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

      9. lift-*.f64 N/A

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

      10. lift-/.f64 58.1

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

      11. lift-*.f64 N/A

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

      12. mul0-lft 58.1

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

   7. Applied rewrites 58.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 58.1

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

      4. lift-/.f64 N/A

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

      5. div0 58.1

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

   9. Applied rewrites 58.1%

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

   if 1.3e-151 < B

   1. Initial program 50.9%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 51.4%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -0.155:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-233}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-151}:\\ \;\;\;\;\frac{\tan^{-1} 0 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 3.8 \cdot 10^{-233}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-151}:\\ \;\;\;\;\frac{\tan^{-1} 0 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 3.8e-233)
   (/ (* 180.0 (atan (+ (/ C B) 1.0))) PI)
   (if (<= B 1.3e-151)
     (/ (* (atan 0.0) 180.0) PI)
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 3.8e-233) {
		tmp = (180.0 * atan(((C / B) + 1.0))) / ((double) M_PI);
	} else if (B <= 1.3e-151) {
		tmp = (atan(0.0) * 180.0) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 3.8e-233) {
		tmp = (180.0 * Math.atan(((C / B) + 1.0))) / Math.PI;
	} else if (B <= 1.3e-151) {
		tmp = (Math.atan(0.0) * 180.0) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 3.8e-233:
		tmp = (180.0 * math.atan(((C / B) + 1.0))) / math.pi
	elif B <= 1.3e-151:
		tmp = (math.atan(0.0) * 180.0) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 3.8e-233)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B) + 1.0))) / pi);
	elseif (B <= 1.3e-151)
		tmp = Float64(Float64(atan(0.0) * 180.0) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 3.8e-233)
		tmp = (180.0 * atan(((C / B) + 1.0))) / pi;
	elseif (B <= 1.3e-151)
		tmp = (atan(0.0) * 180.0) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 3.8e-233], N[(N[(180.0 * N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.3e-151], N[(N[(N[ArcTan[0.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 3.8e-233

   1. Initial program 58.8%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 80.2%

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

   5. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. pow2 N/A

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

      4. unpow2 N/A

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

      5. lower-hypot.f64 66.3

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

   7. Applied rewrites 66.3%

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

   8. Taylor expanded in B around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 58.8

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

   10. Applied rewrites 58.8%

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

   if 3.8e-233 < B < 1.3e-151

   1. Initial program 20.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 74.2%

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

   5. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lift-*.f64 N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. mul0-lft N/A

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

      9. lift-*.f64 N/A

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

      10. lift-/.f64 58.1

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

      11. lift-*.f64 N/A

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

      12. mul0-lft 58.1

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

   7. Applied rewrites 58.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 58.1

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

      4. lift-/.f64 N/A

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

      5. div0 58.1

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

   9. Applied rewrites 58.1%

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

   if 1.3e-151 < B

   1. Initial program 50.9%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 51.4%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 3.8 \cdot 10^{-233}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-151}:\\ \;\;\;\;\frac{\tan^{-1} 0 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.7 \cdot 10^{-233}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-151}:\\ \;\;\;\;\frac{\tan^{-1} 0 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.7e-233)
   (/ (* 180.0 (atan (- 1.0 (/ A B)))) PI)
   (if (<= B 1.3e-151)
     (/ (* (atan 0.0) 180.0) PI)
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.7e-233) {
		tmp = (180.0 * atan((1.0 - (A / B)))) / ((double) M_PI);
	} else if (B <= 1.3e-151) {
		tmp = (atan(0.0) * 180.0) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.7e-233) {
		tmp = (180.0 * Math.atan((1.0 - (A / B)))) / Math.PI;
	} else if (B <= 1.3e-151) {
		tmp = (Math.atan(0.0) * 180.0) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 1.7e-233:
		tmp = (180.0 * math.atan((1.0 - (A / B)))) / math.pi
	elif B <= 1.3e-151:
		tmp = (math.atan(0.0) * 180.0) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 1.7e-233)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 - Float64(A / B)))) / pi);
	elseif (B <= 1.3e-151)
		tmp = Float64(Float64(atan(0.0) * 180.0) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 1.7e-233)
		tmp = (180.0 * atan((1.0 - (A / B)))) / pi;
	elseif (B <= 1.3e-151)
		tmp = (atan(0.0) * 180.0) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 1.7e-233], N[(N[(180.0 * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 1.3e-151], N[(N[(N[ArcTan[0.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 1.7000000000000001e-233

   1. Initial program 58.8%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   4. Applied rewrites 80.2%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 69.3

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

   7. Applied rewrites 69.3%

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

   8. Taylor expanded in C around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 55.6

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

   10. Applied rewrites 55.6%

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

   if 1.7000000000000001e-233 < B < 1.3e-151

   1. Initial program 20.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 74.2%

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

   5. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lift-*.f64 N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. mul0-lft N/A

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

      9. lift-*.f64 N/A

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

      10. lift-/.f64 58.1

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

      11. lift-*.f64 N/A

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

      12. mul0-lft 58.1

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

   7. Applied rewrites 58.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 58.1

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

      4. lift-/.f64 N/A

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

      5. div0 58.1

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

   9. Applied rewrites 58.1%

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

   if 1.3e-151 < B

   1. Initial program 50.9%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 51.4%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.7 \cdot 10^{-233}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-151}:\\ \;\;\;\;\frac{\tan^{-1} 0 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 44.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -8.2 \cdot 10^{-207}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-151}:\\ \;\;\;\;\frac{\tan^{-1} 0 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -8.2e-207)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.3e-151)
     (/ (* (atan 0.0) 180.0) PI)
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.2e-207) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.3e-151) {
		tmp = (atan(0.0) * 180.0) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -8.2e-207) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.3e-151) {
		tmp = (Math.atan(0.0) * 180.0) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -8.2e-207:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.3e-151:
		tmp = (math.atan(0.0) * 180.0) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -8.2e-207)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.3e-151)
		tmp = Float64(Float64(atan(0.0) * 180.0) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -8.2e-207)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.3e-151)
		tmp = (atan(0.0) * 180.0) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -8.2e-207], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.3e-151], N[(N[(N[ArcTan[0.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -8.1999999999999998e-207

   1. Initial program 54.8%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 42.2%

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

   if -8.1999999999999998e-207 < B < 1.3e-151

   1. Initial program 53.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 82.8%

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

   5. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lift-*.f64 N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. mul0-lft N/A

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

      9. lift-*.f64 N/A

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

      10. lift-/.f64 41.3

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

      11. lift-*.f64 N/A

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

      12. mul0-lft 41.3

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

   7. Applied rewrites 41.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 41.3

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

      4. lift-/.f64 N/A

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

      5. div0 41.3

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

   9. Applied rewrites 41.3%

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

   if 1.3e-151 < B

   1. Initial program 50.9%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 51.4%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -8.2 \cdot 10^{-207}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.3 \cdot 10^{-151}:\\ \;\;\;\;\frac{\tan^{-1} 0 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.45 \cdot 10^{-301}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.45e-301)
   (* 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 <= -1.45e-301) {
		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 <= -1.45e-301) {
		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 <= -1.45e-301:
		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 <= -1.45e-301)
		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 <= -1.45e-301)
		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, -1.45e-301], 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 < -1.44999999999999992e-301

   1. Initial program 56.2%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 39.1%

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

   if -1.44999999999999992e-301 < B

   1. Initial program 50.2%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 40.3%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.45 \cdot 10^{-301}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. 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 52.9%

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

3. Taylor expanded in B around inf

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

5. Applied rewrites 23.0%

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

6. Final simplification 23.0%

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

Reproduce

herbie shell --seed 2025064 
(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)))