ABCF->ab-angle angle

Percentage Accurate: 54.0% → 81.9%

Time: 4.7s

Alternatives: 11

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{+133}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5}{A} \cdot B\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)\right)\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.1e+133)
   (* (atan (* (/ 0.5 A) B)) (/ 180.0 PI))
   (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (hypot (- C A) B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.1e+133) {
		tmp = atan(((0.5 / A) * B)) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((C - A), B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.1e+133) {
		tmp = Math.atan(((0.5 / A) * B)) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.hypot((C - A), B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.1e+133:
		tmp = math.atan(((0.5 / A) * B)) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.hypot((C - A), B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.1e+133)
		tmp = Float64(atan(Float64(Float64(0.5 / A) * B)) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - hypot(Float64(C - A), B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.1e+133)
		tmp = atan(((0.5 / A) * B)) * (180.0 / pi);
	else
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((C - A), B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.1e+133], N[(N[ArcTan[N[(N[(0.5 / A), $MachinePrecision] * B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -2.1e133

   1. Initial program 54.0%

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

   2. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 25.6

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

   4. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 25.6

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

   8. Applied rewrites 25.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

         \[\leadsto \tan^{-1} \left(\frac{\frac{1}{2}}{A} \cdot \color{blue}{B}\right) \cdot \mathsf{Rewrite=>}\left(lower-/.f64, \left(\frac{180}{\pi}\right)\right) \]

   10. Applied rewrites 25.6%

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

   if -2.1e133 < A

   1. Initial program 54.0%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. sqr-neg-rev N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lift--.f64 N/A

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-hypot.f64 78.4

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

   3. Applied rewrites 78.4%

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

Alternative 2: 78.7% accurate, 1.2× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{+107}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5}{A} \cdot \left|B\right|\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 8 \cdot 10^{-39}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{\left|B\right|} \cdot \left(C - \mathsf{hypot}\left(C, \left|B\right|\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{\left|B\right|} - 1\right) \cdot 180}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= A -1.15e+107)
    (* (atan (* (/ 0.5 A) (fabs B))) (/ 180.0 PI))
    (if (<= A 8e-39)
      (* 180.0 (/ (atan (* (/ 1.0 (fabs B)) (- C (hypot C (fabs B))))) PI))
      (/ (* (atan (- (/ (- C A) (fabs B)) 1.0)) 180.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+107) {
		tmp = atan(((0.5 / A) * fabs(B))) * (180.0 / ((double) M_PI));
	} else if (A <= 8e-39) {
		tmp = 180.0 * (atan(((1.0 / fabs(B)) * (C - hypot(C, fabs(B))))) / ((double) M_PI));
	} else {
		tmp = (atan((((C - A) / fabs(B)) - 1.0)) * 180.0) / ((double) M_PI);
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+107) {
		tmp = Math.atan(((0.5 / A) * Math.abs(B))) * (180.0 / Math.PI);
	} else if (A <= 8e-39) {
		tmp = 180.0 * (Math.atan(((1.0 / Math.abs(B)) * (C - Math.hypot(C, Math.abs(B))))) / Math.PI);
	} else {
		tmp = (Math.atan((((C - A) / Math.abs(B)) - 1.0)) * 180.0) / Math.PI;
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.15e+107:
		tmp = math.atan(((0.5 / A) * math.fabs(B))) * (180.0 / math.pi)
	elif A <= 8e-39:
		tmp = 180.0 * (math.atan(((1.0 / math.fabs(B)) * (C - math.hypot(C, math.fabs(B))))) / math.pi)
	else:
		tmp = (math.atan((((C - A) / math.fabs(B)) - 1.0)) * 180.0) / math.pi
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.15e+107)
		tmp = Float64(atan(Float64(Float64(0.5 / A) * abs(B))) * Float64(180.0 / pi));
	elseif (A <= 8e-39)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / abs(B)) * Float64(C - hypot(C, abs(B))))) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) / abs(B)) - 1.0)) * 180.0) / pi);
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.15e+107)
		tmp = atan(((0.5 / A) * abs(B))) * (180.0 / pi);
	elseif (A <= 8e-39)
		tmp = 180.0 * (atan(((1.0 / abs(B)) * (C - hypot(C, abs(B))))) / pi);
	else
		tmp = (atan((((C - A) / abs(B)) - 1.0)) * 180.0) / pi;
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[A, -1.15e+107], N[(N[ArcTan[N[(N[(0.5 / A), $MachinePrecision] * N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 8e-39], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / N[Abs[B], $MachinePrecision]), $MachinePrecision] * N[(C - N[Sqrt[C ^ 2 + N[Abs[B], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -1.15e107

   1. Initial program 54.0%

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

   2. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 25.6

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

   4. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 25.6

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

   8. Applied rewrites 25.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

         \[\leadsto \tan^{-1} \left(\frac{\frac{1}{2}}{A} \cdot \color{blue}{B}\right) \cdot \mathsf{Rewrite=>}\left(lower-/.f64, \left(\frac{180}{\pi}\right)\right) \]

   10. Applied rewrites 25.6%

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

   if -1.15e107 < A < 7.99999999999999943e-39

   1. Initial program 54.0%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-pow.f64 N/A

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

      4. unpow2 N/A

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

      5. sqr-neg-rev N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lift--.f64 N/A

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-hypot.f64 78.4

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

   3. Applied rewrites 78.4%

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

   4. Taylor expanded in A around 0

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

   6. Applied rewrites 72.7%

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

   7. Taylor expanded in A around 0

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

   9. Applied rewrites 63.3%

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

   if 7.99999999999999943e-39 < A

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 49.6

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

   4. Applied rewrites 49.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 50.8%

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

Alternative 3: 75.3% accurate, 1.9× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{+107}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5}{A} \cdot \left|B\right|\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{\left|B\right|} - 1\right) \cdot 180}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= A -1.15e+107)
    (* (atan (* (/ 0.5 A) (fabs B))) (/ 180.0 PI))
    (/ (* (atan (- (/ (- C A) (fabs B)) 1.0)) 180.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+107) {
		tmp = atan(((0.5 / A) * fabs(B))) * (180.0 / ((double) M_PI));
	} else {
		tmp = (atan((((C - A) / fabs(B)) - 1.0)) * 180.0) / ((double) M_PI);
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+107) {
		tmp = Math.atan(((0.5 / A) * Math.abs(B))) * (180.0 / Math.PI);
	} else {
		tmp = (Math.atan((((C - A) / Math.abs(B)) - 1.0)) * 180.0) / Math.PI;
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.15e+107:
		tmp = math.atan(((0.5 / A) * math.fabs(B))) * (180.0 / math.pi)
	else:
		tmp = (math.atan((((C - A) / math.fabs(B)) - 1.0)) * 180.0) / math.pi
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.15e+107)
		tmp = Float64(atan(Float64(Float64(0.5 / A) * abs(B))) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) / abs(B)) - 1.0)) * 180.0) / pi);
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.15e+107)
		tmp = atan(((0.5 / A) * abs(B))) * (180.0 / pi);
	else
		tmp = (atan((((C - A) / abs(B)) - 1.0)) * 180.0) / pi;
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[A, -1.15e+107], N[(N[ArcTan[N[(N[(0.5 / A), $MachinePrecision] * N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < -1.15e107

   1. Initial program 54.0%

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

   2. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 25.6

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

   4. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 25.6

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

   8. Applied rewrites 25.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

         \[\leadsto \tan^{-1} \left(\frac{\frac{1}{2}}{A} \cdot \color{blue}{B}\right) \cdot \mathsf{Rewrite=>}\left(lower-/.f64, \left(\frac{180}{\pi}\right)\right) \]

   10. Applied rewrites 25.6%

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

   if -1.15e107 < A

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 49.6

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

   4. Applied rewrites 49.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 50.8%

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

Alternative 4: 75.3% accurate, 1.9× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{+107}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5}{A} \cdot \left|B\right|\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{\left|B\right|} - 1\right)}{\pi} \cdot 180\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= A -1.15e+107)
    (* (atan (* (/ 0.5 A) (fabs B))) (/ 180.0 PI))
    (* (/ (atan (- (/ (- C A) (fabs B)) 1.0)) PI) 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+107) {
		tmp = atan(((0.5 / A) * fabs(B))) * (180.0 / ((double) M_PI));
	} else {
		tmp = (atan((((C - A) / fabs(B)) - 1.0)) / ((double) M_PI)) * 180.0;
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+107) {
		tmp = Math.atan(((0.5 / A) * Math.abs(B))) * (180.0 / Math.PI);
	} else {
		tmp = (Math.atan((((C - A) / Math.abs(B)) - 1.0)) / Math.PI) * 180.0;
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.15e+107:
		tmp = math.atan(((0.5 / A) * math.fabs(B))) * (180.0 / math.pi)
	else:
		tmp = (math.atan((((C - A) / math.fabs(B)) - 1.0)) / math.pi) * 180.0
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.15e+107)
		tmp = Float64(atan(Float64(Float64(0.5 / A) * abs(B))) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) / abs(B)) - 1.0)) / pi) * 180.0);
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.15e+107)
		tmp = atan(((0.5 / A) * abs(B))) * (180.0 / pi);
	else
		tmp = (atan((((C - A) / abs(B)) - 1.0)) / pi) * 180.0;
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[A, -1.15e+107], N[(N[ArcTan[N[(N[(0.5 / A), $MachinePrecision] * N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < -1.15e107

   1. Initial program 54.0%

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

   2. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 25.6

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

   4. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 25.6

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

   8. Applied rewrites 25.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

         \[\leadsto \tan^{-1} \left(\frac{\frac{1}{2}}{A} \cdot \color{blue}{B}\right) \cdot \mathsf{Rewrite=>}\left(lower-/.f64, \left(\frac{180}{\pi}\right)\right) \]

   10. Applied rewrites 25.6%

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

   if -1.15e107 < A

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 49.6

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

   4. Applied rewrites 49.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 49.6

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

   6. Applied rewrites 50.8%

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

Alternative 5: 69.2% accurate, 1.8× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{+107}:\\ \;\;\;\;\tan^{-1} \left(\frac{0.5}{A} \cdot \left|B\right|\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 33500000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{\left|B\right|} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{\left|B\right|}\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= A -1.15e+107)
    (* (atan (* (/ 0.5 A) (fabs B))) (/ 180.0 PI))
    (if (<= A 33500000000.0)
      (* 180.0 (/ (atan (- (/ C (fabs B)) 1.0)) PI))
      (* 180.0 (/ (atan (/ (- C A) (fabs B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+107) {
		tmp = atan(((0.5 / A) * fabs(B))) * (180.0 / ((double) M_PI));
	} else if (A <= 33500000000.0) {
		tmp = 180.0 * (atan(((C / fabs(B)) - 1.0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - A) / fabs(B))) / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+107) {
		tmp = Math.atan(((0.5 / A) * Math.abs(B))) * (180.0 / Math.PI);
	} else if (A <= 33500000000.0) {
		tmp = 180.0 * (Math.atan(((C / Math.abs(B)) - 1.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - A) / Math.abs(B))) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.15e+107:
		tmp = math.atan(((0.5 / A) * math.fabs(B))) * (180.0 / math.pi)
	elif A <= 33500000000.0:
		tmp = 180.0 * (math.atan(((C / math.fabs(B)) - 1.0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - A) / math.fabs(B))) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.15e+107)
		tmp = Float64(atan(Float64(Float64(0.5 / A) * abs(B))) * Float64(180.0 / pi));
	elseif (A <= 33500000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / abs(B)) - 1.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / abs(B))) / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.15e+107)
		tmp = atan(((0.5 / A) * abs(B))) * (180.0 / pi);
	elseif (A <= 33500000000.0)
		tmp = 180.0 * (atan(((C / abs(B)) - 1.0)) / pi);
	else
		tmp = 180.0 * (atan(((C - A) / abs(B))) / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[A, -1.15e+107], N[(N[ArcTan[N[(N[(0.5 / A), $MachinePrecision] * N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 33500000000.0], N[(180.0 * N[(N[ArcTan[N[(N[(C / N[Abs[B], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -1.15e107

   1. Initial program 54.0%

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

   2. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 25.6

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

   4. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 25.6

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

   8. Applied rewrites 25.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

         \[\leadsto \tan^{-1} \left(\frac{\frac{1}{2}}{A} \cdot \color{blue}{B}\right) \cdot \mathsf{Rewrite=>}\left(lower-/.f64, \left(\frac{180}{\pi}\right)\right) \]

   10. Applied rewrites 25.6%

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

   if -1.15e107 < A < 3.35e10

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 49.6

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

   4. Applied rewrites 49.6%

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

   5. Taylor expanded in A around 0

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

   7. Applied rewrites 38.8%

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

   if 3.35e10 < A

   1. Initial program 54.0%

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

   2. Taylor expanded in B around -inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 49.3

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

   4. Applied rewrites 49.3%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 35.4

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

   7. Applied rewrites 35.4%

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

Alternative 6: 69.2% accurate, 1.8× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq -1.15 \cdot 10^{+107}:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{\left|B\right|}{A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 33500000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{\left|B\right|} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{\left|B\right|}\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= A -1.15e+107)
    (* (atan (* 0.5 (/ (fabs B) A))) (/ 180.0 PI))
    (if (<= A 33500000000.0)
      (* 180.0 (/ (atan (- (/ C (fabs B)) 1.0)) PI))
      (* 180.0 (/ (atan (/ (- C A) (fabs B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+107) {
		tmp = atan((0.5 * (fabs(B) / A))) * (180.0 / ((double) M_PI));
	} else if (A <= 33500000000.0) {
		tmp = 180.0 * (atan(((C / fabs(B)) - 1.0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - A) / fabs(B))) / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.15e+107) {
		tmp = Math.atan((0.5 * (Math.abs(B) / A))) * (180.0 / Math.PI);
	} else if (A <= 33500000000.0) {
		tmp = 180.0 * (Math.atan(((C / Math.abs(B)) - 1.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - A) / Math.abs(B))) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.15e+107:
		tmp = math.atan((0.5 * (math.fabs(B) / A))) * (180.0 / math.pi)
	elif A <= 33500000000.0:
		tmp = 180.0 * (math.atan(((C / math.fabs(B)) - 1.0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - A) / math.fabs(B))) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.15e+107)
		tmp = Float64(atan(Float64(0.5 * Float64(abs(B) / A))) * Float64(180.0 / pi));
	elseif (A <= 33500000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / abs(B)) - 1.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / abs(B))) / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.15e+107)
		tmp = atan((0.5 * (abs(B) / A))) * (180.0 / pi);
	elseif (A <= 33500000000.0)
		tmp = 180.0 * (atan(((C / abs(B)) - 1.0)) / pi);
	else
		tmp = 180.0 * (atan(((C - A) / abs(B))) / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[A, -1.15e+107], N[(N[ArcTan[N[(0.5 * N[(N[Abs[B], $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 33500000000.0], N[(180.0 * N[(N[ArcTan[N[(N[(C / N[Abs[B], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -1.15e107

   1. Initial program 54.0%

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

   2. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 25.6

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

   4. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 25.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-/.f64 N/A

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

      7. mult-flip N/A

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

      8. lift-/.f64 N/A

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

      9. associate-*l* N/A

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

      10. lift-*.f64 N/A

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

      11. lift-*.f64 N/A

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

   8. Applied rewrites 25.6%

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

   if -1.15e107 < A < 3.35e10

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 49.6

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

   4. Applied rewrites 49.6%

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

   5. Taylor expanded in A around 0

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

   7. Applied rewrites 38.8%

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

   if 3.35e10 < A

   1. Initial program 54.0%

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

   2. Taylor expanded in B around -inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 49.3

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

   4. Applied rewrites 49.3%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 35.4

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

   7. Applied rewrites 35.4%

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

Alternative 7: 63.1% accurate, 1.8× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq -1.2 \cdot 10^{+216}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;A \leq 33500000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{\left|B\right|} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{\left|B\right|}\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= A -1.2e+216)
    (* 180.0 (/ (atan 0.0) PI))
    (if (<= A 33500000000.0)
      (* 180.0 (/ (atan (- (/ C (fabs B)) 1.0)) PI))
      (* 180.0 (/ (atan (/ (- C A) (fabs B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.2e+216) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (A <= 33500000000.0) {
		tmp = 180.0 * (atan(((C / fabs(B)) - 1.0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - A) / fabs(B))) / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.2e+216) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (A <= 33500000000.0) {
		tmp = 180.0 * (Math.atan(((C / Math.abs(B)) - 1.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - A) / Math.abs(B))) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.2e+216:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif A <= 33500000000.0:
		tmp = 180.0 * (math.atan(((C / math.fabs(B)) - 1.0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - A) / math.fabs(B))) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.2e+216)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (A <= 33500000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / abs(B)) - 1.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / abs(B))) / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.2e+216)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (A <= 33500000000.0)
		tmp = 180.0 * (atan(((C / abs(B)) - 1.0)) / pi);
	else
		tmp = 180.0 * (atan(((C - A) / abs(B))) / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[A, -1.2e+216], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 33500000000.0], N[(180.0 * N[(N[ArcTan[N[(N[(C / N[Abs[B], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -1.2e216

   1. Initial program 54.0%

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

   2. Taylor expanded in C around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 13.2

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

   4. Applied rewrites 13.2%

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

   5. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]
   6. Step-by-step derivation

   7. Applied rewrites 13.2%

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

   if -1.2e216 < A < 3.35e10

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 49.6

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

   4. Applied rewrites 49.6%

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

   5. Taylor expanded in A around 0

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

   7. Applied rewrites 38.8%

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

   if 3.35e10 < A

   1. Initial program 54.0%

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

   2. Taylor expanded in B around -inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 49.3

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

   4. Applied rewrites 49.3%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 35.4

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

   7. Applied rewrites 35.4%

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

Alternative 8: 52.0% accurate, 1.8× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq -3.8 \cdot 10^{+186}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;A \leq 43000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{\left|B\right|}\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= A -3.8e+186)
    (* 180.0 (/ (atan 0.0) PI))
    (if (<= A 43000.0)
      (* 180.0 (/ (atan -1.0) PI))
      (* 180.0 (/ (atan (/ (- C A) (fabs B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.8e+186) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (A <= 43000.0) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - A) / fabs(B))) / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.8e+186) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (A <= 43000.0) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - A) / Math.abs(B))) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.8e+186:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif A <= 43000.0:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - A) / math.fabs(B))) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.8e+186)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (A <= 43000.0)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / abs(B))) / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.8e+186)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (A <= 43000.0)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan(((C - A) / abs(B))) / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[A, -3.8e+186], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 43000.0], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -3.7999999999999998e186

   1. Initial program 54.0%

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

   2. Taylor expanded in C around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 13.2

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

   4. Applied rewrites 13.2%

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

   5. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]
   6. Step-by-step derivation

   7. Applied rewrites 13.2%

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

   if -3.7999999999999998e186 < A < 43000

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.1%

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

   if 43000 < A

   1. Initial program 54.0%

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

   2. Taylor expanded in B around -inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 49.3

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

   4. Applied rewrites 49.3%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 35.4

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

   7. Applied rewrites 35.4%

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

Alternative 9: 51.2% accurate, 1.8× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq -3.8 \cdot 10^{+186}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;A \leq 33500000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{\left|B\right|}\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= A -3.8e+186)
    (* 180.0 (/ (atan 0.0) PI))
    (if (<= A 33500000000.0)
      (* 180.0 (/ (atan -1.0) PI))
      (* 180.0 (/ (atan (- 1.0 (/ A (fabs B)))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.8e+186) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (A <= 33500000000.0) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / fabs(B)))) / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.8e+186) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (A <= 33500000000.0) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / Math.abs(B)))) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.8e+186:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif A <= 33500000000.0:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / math.fabs(B)))) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.8e+186)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (A <= 33500000000.0)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / abs(B)))) / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.8e+186)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (A <= 33500000000.0)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / abs(B)))) / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[A, -3.8e+186], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 33500000000.0], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / N[Abs[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -3.7999999999999998e186

   1. Initial program 54.0%

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

   2. Taylor expanded in C around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 13.2

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

   4. Applied rewrites 13.2%

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

   5. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]
   6. Step-by-step derivation

   7. Applied rewrites 13.2%

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

   if -3.7999999999999998e186 < A < 3.35e10

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.1%

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

   if 3.35e10 < A

   1. Initial program 54.0%

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

   2. Taylor expanded in B around -inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 49.3

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

   4. Applied rewrites 49.3%

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

   5. Taylor expanded in C around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 38.9

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

   7. Applied rewrites 38.9%

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

Alternative 10: 44.9% accurate, 2.4× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;\left|B\right| \leq 8.8 \cdot 10^{-94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= (fabs B) 8.8e-94)
    (* 180.0 (/ (atan 0.0) PI))
    (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (fabs(B) <= 8.8e-94) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (Math.abs(B) <= 8.8e-94) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if math.fabs(B) <= 8.8e-94:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (abs(B) <= 8.8e-94)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (abs(B) <= 8.8e-94)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[B], $MachinePrecision], 8.8e-94], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if B < 8.80000000000000004e-94

   1. Initial program 54.0%

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

   2. Taylor expanded in C around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 13.2

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

   4. Applied rewrites 13.2%

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

   5. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]
   6. Step-by-step derivation

   7. Applied rewrites 13.2%

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

   if 8.80000000000000004e-94 < B

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.1%

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

Alternative 11: 40.0% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 54.0%

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

2. Taylor expanded in B around inf

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

4. Applied rewrites 21.1%

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

Reproduce

herbie shell --seed 2025171 
(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)))