ABCF->ab-angle angle

Percentage Accurate: 53.8% → 88.9%

Time: 18.4s

Alternatives: 20

Speedup: 3.7×

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: 53.8% 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: 88.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ \mathbf{if}\;C \leq 9.5 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - t\_0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-1}{\mathsf{fma}\left(-1, \frac{A - C}{B}, \frac{t\_0}{B}\right)}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (hypot B (- A C))))
   (if (<= C 9.5e-145)
     (* 180.0 (/ (atan (/ (- (- C A) t_0) B)) PI))
     (/ (* 180.0 (atan (/ -1.0 (fma -1.0 (/ (- A C) B) (/ t_0 B))))) PI))))

C

double code(double A, double B, double C) {
	double t_0 = hypot(B, (A - C));
	double tmp;
	if (C <= 9.5e-145) {
		tmp = 180.0 * (atan((((C - A) - t_0) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((-1.0 / fma(-1.0, ((A - C) / B), (t_0 / B))))) / ((double) M_PI);
	}
	return tmp;
}

Julia

function code(A, B, C)
	t_0 = hypot(B, Float64(A - C))
	tmp = 0.0
	if (C <= 9.5e-145)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - t_0) / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 / fma(-1.0, Float64(Float64(A - C) / B), Float64(t_0 / B))))) / pi);
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]}, If[LessEqual[C, 9.5e-145], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - t$95$0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 / N[(-1.0 * N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision] + N[(t$95$0 / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if C < 9.49999999999999981e-145

   1. Initial program 67.9%

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

      1. associate-*l/ 67.9%

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

      2. *-lft-identity 67.9%

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

      3. +-commutative 67.9%

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

      4. unpow2 67.9%

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

      5. unpow2 67.9%

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

      6. hypot-define 91.0%

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

   3. Simplified 91.0%

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

   if 9.49999999999999981e-145 < C

   1. Initial program 33.8%

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

      1. *-commutative 33.8%

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

      2. associate--l- 33.7%

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

      3. +-commutative 33.7%

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

      4. unpow2 33.7%

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

      5. unpow2 33.7%

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

      6. hypot-undefine 59.7%

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

      7. associate--r+ 63.8%

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

      8. div-inv 63.8%

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

      9. div-sub 48.5%

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

      10. flip-- 32.2%

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

   4. Applied egg-rr 32.2%

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

   5. Taylor expanded in C around -inf 49.1%

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

   7. Simplified 90.2%

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

      1. associate-*r/ 90.2%

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

   9. Applied egg-rr 90.2%

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

Alternative 2: 88.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ \mathbf{if}\;C \leq 6.9 \cdot 10^{-147}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - t\_0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\mathsf{fma}\left(-1, \frac{A - C}{B}, \frac{t\_0}{B}\right)}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (hypot B (- A C))))
   (if (<= C 6.9e-147)
     (* 180.0 (/ (atan (/ (- (- C A) t_0) B)) PI))
     (* 180.0 (/ (atan (/ -1.0 (fma -1.0 (/ (- A C) B) (/ t_0 B)))) PI)))))

C

double code(double A, double B, double C) {
	double t_0 = hypot(B, (A - C));
	double tmp;
	if (C <= 6.9e-147) {
		tmp = 180.0 * (atan((((C - A) - t_0) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 / fma(-1.0, ((A - C) / B), (t_0 / B)))) / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	t_0 = hypot(B, Float64(A - C))
	tmp = 0.0
	if (C <= 6.9e-147)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - t_0) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / fma(-1.0, Float64(Float64(A - C) / B), Float64(t_0 / B)))) / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]}, If[LessEqual[C, 6.9e-147], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - t$95$0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(-1.0 * N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision] + N[(t$95$0 / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if C < 6.89999999999999999e-147

   1. Initial program 67.9%

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

      1. associate-*l/ 67.9%

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

      2. *-lft-identity 67.9%

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

      3. +-commutative 67.9%

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

      4. unpow2 67.9%

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

      5. unpow2 67.9%

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

      6. hypot-define 91.0%

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

   3. Simplified 91.0%

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

   if 6.89999999999999999e-147 < C

   1. Initial program 33.8%

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

      1. *-commutative 33.8%

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

      2. associate--l- 33.7%

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

      3. +-commutative 33.7%

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

      4. unpow2 33.7%

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

      5. unpow2 33.7%

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

      6. hypot-undefine 59.7%

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

      7. associate--r+ 63.8%

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

      8. div-inv 63.8%

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

      9. div-sub 48.5%

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

      10. flip-- 32.2%

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

   4. Applied egg-rr 32.2%

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

   5. Taylor expanded in C around -inf 49.1%

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

   7. Simplified 90.2%

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

Alternative 3: 81.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -3.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{elif}\;C \leq 1.7 \cdot 10^{+14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C}{B} + \frac{\mathsf{hypot}\left(C, B\right)}{B}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -3.8e-44)
   (* (/ 180.0 PI) (atan (/ (- C (hypot C B)) B)))
   (if (<= C 1.7e+14)
     (* 180.0 (/ (atan (/ (+ A (hypot A B)) (- B))) PI))
     (* 180.0 (/ (atan (/ -1.0 (+ (/ C B) (/ (hypot C B) B)))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.8e-44) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(C, B)) / B));
	} else if (C <= 1.7e+14) {
		tmp = 180.0 * (atan(((A + hypot(A, B)) / -B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 / ((C / B) + (hypot(C, B) / B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.8e-44) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(C, B)) / B));
	} else if (C <= 1.7e+14) {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(A, B)) / -B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 / ((C / B) + (Math.hypot(C, B) / B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -3.8e-44:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(C, B)) / B))
	elif C <= 1.7e+14:
		tmp = 180.0 * (math.atan(((A + math.hypot(A, B)) / -B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 / ((C / B) + (math.hypot(C, B) / B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -3.8e-44)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(C, B)) / B)));
	elseif (C <= 1.7e+14)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(A, B)) / Float64(-B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(Float64(C / B) + Float64(hypot(C, B) / B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -3.8e-44)
		tmp = (180.0 / pi) * atan(((C - hypot(C, B)) / B));
	elseif (C <= 1.7e+14)
		tmp = 180.0 * (atan(((A + hypot(A, B)) / -B)) / pi);
	else
		tmp = 180.0 * (atan((-1.0 / ((C / B) + (hypot(C, B) / B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -3.8e-44], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.7e+14], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(N[(C / B), $MachinePrecision] + N[(N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -3.8000000000000001e-44

   1. Initial program 79.7%

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

   3. Taylor expanded in B around 0 79.7%

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

   5. Simplified 94.6%

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

   6. Taylor expanded in A around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. unpow2 78.5%

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

      3. unpow2 78.5%

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

      4. hypot-define 93.4%

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

   8. Simplified 93.4%

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

   if -3.8000000000000001e-44 < C < 1.7e14

   1. Initial program 55.7%

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

   3. Taylor expanded in C around 0 53.1%

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

      1. associate-*r/ 53.1%

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

      2. mul-1-neg 53.1%

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

      3. unpow2 53.1%

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

      4. unpow2 53.1%

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

      5. hypot-define 78.9%

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

   5. Simplified 78.9%

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

   if 1.7e14 < C

   1. Initial program 26.6%

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

      1. *-commutative 26.6%

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

      2. associate--l- 26.6%

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

      3. +-commutative 26.6%

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

      4. unpow2 26.6%

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

      5. unpow2 26.6%

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

      6. hypot-undefine 57.8%

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

      7. associate--r+ 60.8%

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

      8. div-inv 60.8%

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

      9. div-sub 41.1%

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

      10. flip-- 24.6%

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

   4. Applied egg-rr 24.6%

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

   5. Taylor expanded in C around -inf 39.8%

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

   7. Simplified 90.6%

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

   8. Taylor expanded in A around 0 38.2%

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

   10. Simplified 80.7%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -3.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{elif}\;C \leq 1.7 \cdot 10^{+14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C}{B} + \frac{\mathsf{hypot}\left(C, B\right)}{B}}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.6 \cdot 10^{+138}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{-2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-22}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.6e+138)
   (* 180.0 (/ (atan (/ -1.0 (* -2.0 (/ A B)))) PI))
   (if (<= A 3e-22)
     (* (/ 180.0 PI) (atan (/ (- C (hypot C B)) B)))
     (* 180.0 (/ (atan (/ (+ A (hypot A B)) (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.6e+138) {
		tmp = 180.0 * (atan((-1.0 / (-2.0 * (A / B)))) / ((double) M_PI));
	} else if (A <= 3e-22) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(C, B)) / B));
	} else {
		tmp = 180.0 * (atan(((A + hypot(A, B)) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.6e+138) {
		tmp = 180.0 * (Math.atan((-1.0 / (-2.0 * (A / B)))) / Math.PI);
	} else if (A <= 3e-22) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(C, B)) / B));
	} else {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(A, B)) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.6e+138:
		tmp = 180.0 * (math.atan((-1.0 / (-2.0 * (A / B)))) / math.pi)
	elif A <= 3e-22:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(C, B)) / B))
	else:
		tmp = 180.0 * (math.atan(((A + math.hypot(A, B)) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.6e+138)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(-2.0 * Float64(A / B)))) / pi));
	elseif (A <= 3e-22)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(C, B)) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(A, B)) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.6e+138)
		tmp = 180.0 * (atan((-1.0 / (-2.0 * (A / B)))) / pi);
	elseif (A <= 3e-22)
		tmp = (180.0 / pi) * atan(((C - hypot(C, B)) / B));
	else
		tmp = 180.0 * (atan(((A + hypot(A, B)) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.6e+138], N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3e-22], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.6000000000000001e138

   1. Initial program 11.4%

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

      1. *-commutative 11.4%

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

      2. associate--l- 11.3%

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

      3. +-commutative 11.3%

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

      4. unpow2 11.3%

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

      5. unpow2 11.3%

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

      6. hypot-undefine 24.3%

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

      7. associate--r+ 57.0%

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

      8. div-inv 57.0%

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

      9. div-sub 17.6%

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

      10. flip-- 10.0%

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

   4. Applied egg-rr 10.0%

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

   5. Taylor expanded in C around -inf 47.8%

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

   7. Simplified 93.6%

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

   8. Taylor expanded in A around -inf 81.0%

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

   if -3.6000000000000001e138 < A < 2.9999999999999999e-22

   1. Initial program 53.5%

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

   3. Taylor expanded in B around 0 52.7%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in A around 0 51.5%

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

      1. +-commutative 51.5%

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

      2. unpow2 51.5%

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

      3. unpow2 51.5%

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

      4. hypot-define 76.4%

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

   8. Simplified 76.4%

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

   if 2.9999999999999999e-22 < A

   1. Initial program 75.0%

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

   3. Taylor expanded in C around 0 75.0%

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

      1. associate-*r/ 75.0%

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

      2. mul-1-neg 75.0%

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

      3. unpow2 75.0%

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

      4. unpow2 75.0%

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

      5. hypot-define 93.3%

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

   5. Simplified 93.3%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.6 \cdot 10^{+138}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{-2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3 \cdot 10^{-22}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.3 \cdot 10^{+147}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{-2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.3e+147)
   (* 180.0 (/ (atan (/ -1.0 (* -2.0 (/ A B)))) PI))
   (if (<= A 3.2e-9)
     (* (/ 180.0 PI) (atan (/ (- C (hypot C B)) B)))
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.3e+147) {
		tmp = 180.0 * (atan((-1.0 / (-2.0 * (A / B)))) / ((double) M_PI));
	} else if (A <= 3.2e-9) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(C, B)) / B));
	} 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 <= -1.3e+147) {
		tmp = 180.0 * (Math.atan((-1.0 / (-2.0 * (A / B)))) / Math.PI);
	} else if (A <= 3.2e-9) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(C, B)) / B));
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.3e+147:
		tmp = 180.0 * (math.atan((-1.0 / (-2.0 * (A / B)))) / math.pi)
	elif A <= 3.2e-9:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(C, B)) / B))
	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 <= -1.3e+147)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(-2.0 * Float64(A / B)))) / pi));
	elseif (A <= 3.2e-9)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(C, B)) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.3e+147)
		tmp = 180.0 * (atan((-1.0 / (-2.0 * (A / B)))) / pi);
	elseif (A <= 3.2e-9)
		tmp = (180.0 / pi) * atan(((C - hypot(C, B)) / B));
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.3e+147], N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.2e-9], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.2999999999999999e147

   1. Initial program 11.4%

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

      1. *-commutative 11.4%

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

      2. associate--l- 11.3%

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

      3. +-commutative 11.3%

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

      4. unpow2 11.3%

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

      5. unpow2 11.3%

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

      6. hypot-undefine 24.3%

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

      7. associate--r+ 57.0%

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

      8. div-inv 57.0%

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

      9. div-sub 17.6%

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

      10. flip-- 10.0%

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

   4. Applied egg-rr 10.0%

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

   5. Taylor expanded in C around -inf 47.8%

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

   7. Simplified 93.6%

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

   8. Taylor expanded in A around -inf 81.0%

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

   if -1.2999999999999999e147 < A < 3.20000000000000012e-9

   1. Initial program 53.7%

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

   3. Taylor expanded in B around 0 52.9%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in A around 0 51.1%

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

      1. +-commutative 51.1%

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

      2. unpow2 51.1%

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

      3. unpow2 51.1%

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

      4. hypot-define 76.4%

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

   8. Simplified 76.4%

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

   if 3.20000000000000012e-9 < A

   1. Initial program 75.8%

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

   3. Taylor expanded in B around -inf 78.8%

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

      1. associate--l+ 78.8%

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

      2. div-sub 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in C around 0 83.0%

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

Alternative 6: 74.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.4 \cdot 10^{+130}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{-2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.2 \cdot 10^{-9}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.4e+130)
   (* 180.0 (/ (atan (/ -1.0 (* -2.0 (/ A B)))) PI))
   (if (<= A 5.2e-9)
     (* 180.0 (/ (atan (/ (- C (hypot 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 <= -4.4e+130) {
		tmp = 180.0 * (atan((-1.0 / (-2.0 * (A / B)))) / ((double) M_PI));
	} else if (A <= 5.2e-9) {
		tmp = 180.0 * (atan(((C - hypot(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 <= -4.4e+130) {
		tmp = 180.0 * (Math.atan((-1.0 / (-2.0 * (A / B)))) / Math.PI);
	} else if (A <= 5.2e-9) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(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 <= -4.4e+130:
		tmp = 180.0 * (math.atan((-1.0 / (-2.0 * (A / B)))) / math.pi)
	elif A <= 5.2e-9:
		tmp = 180.0 * (math.atan(((C - math.hypot(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 <= -4.4e+130)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(-2.0 * Float64(A / B)))) / pi));
	elseif (A <= 5.2e-9)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.4e+130)
		tmp = 180.0 * (atan((-1.0 / (-2.0 * (A / B)))) / pi);
	elseif (A <= 5.2e-9)
		tmp = 180.0 * (atan(((C - hypot(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, -4.4e+130], N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.2e-9], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -4.39999999999999987e130

   1. Initial program 11.4%

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

      1. *-commutative 11.4%

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

      2. associate--l- 11.3%

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

      3. +-commutative 11.3%

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

      4. unpow2 11.3%

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

      5. unpow2 11.3%

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

      6. hypot-undefine 24.3%

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

      7. associate--r+ 57.0%

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

      8. div-inv 57.0%

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

      9. div-sub 17.6%

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

      10. flip-- 10.0%

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

   4. Applied egg-rr 10.0%

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

   5. Taylor expanded in C around -inf 47.8%

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

   7. Simplified 93.6%

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

   8. Taylor expanded in A around -inf 81.0%

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

   if -4.39999999999999987e130 < A < 5.2000000000000002e-9

   1. Initial program 53.7%

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

   3. Taylor expanded in A around 0 51.0%

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

      1. +-commutative 51.0%

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

      2. unpow2 51.0%

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

      3. unpow2 51.0%

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

      4. hypot-define 76.4%

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

   5. Simplified 76.4%

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

   if 5.2000000000000002e-9 < A

   1. Initial program 75.8%

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

   3. Taylor expanded in B around -inf 78.8%

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

      1. associate--l+ 78.8%

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

      2. div-sub 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in C around 0 83.0%

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

Alternative 7: 84.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 1.4 \cdot 10^{+16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{\frac{C}{B} + \frac{\mathsf{hypot}\left(C, B\right)}{B}}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 1.4e+16)
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))
   (* 180.0 (/ (atan (/ -1.0 (+ (/ C B) (/ (hypot C B) B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.4e+16) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 / ((C / B) + (hypot(C, B) / B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.4e+16) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 / ((C / B) + (Math.hypot(C, B) / B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 1.4e+16:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 / ((C / B) + (math.hypot(C, B) / B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 1.4e+16)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(Float64(C / B) + Float64(hypot(C, B) / B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 1.4e+16)
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	else
		tmp = 180.0 * (atan((-1.0 / ((C / B) + (hypot(C, B) / B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 1.4e+16], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(N[(C / B), $MachinePrecision] + N[(N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 1.4e16

   1. Initial program 64.7%

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

      1. associate-*l/ 64.7%

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

      2. *-lft-identity 64.7%

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

      3. +-commutative 64.7%

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

      4. unpow2 64.7%

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

      5. unpow2 64.7%

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

      6. hypot-define 87.5%

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

   3. Simplified 87.5%

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

   if 1.4e16 < C

   1. Initial program 26.6%

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

      1. *-commutative 26.6%

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

      2. associate--l- 26.6%

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

      3. +-commutative 26.6%

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

      4. unpow2 26.6%

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

      5. unpow2 26.6%

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

      6. hypot-undefine 57.8%

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

      7. associate--r+ 60.8%

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

      8. div-inv 60.8%

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

      9. div-sub 41.1%

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

      10. flip-- 24.6%

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

   4. Applied egg-rr 24.6%

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

   5. Taylor expanded in C around -inf 39.8%

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

   7. Simplified 90.6%

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

   8. Taylor expanded in A around 0 38.2%

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

   10. Simplified 80.7%

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

Alternative 8: 80.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.8 \cdot 10^{+129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{-2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.8e+129)
   (* 180.0 (/ (atan (/ -1.0 (* -2.0 (/ A B)))) PI))
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.8e+129) {
		tmp = 180.0 * (atan((-1.0 / (-2.0 * (A / B)))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.8e+129) {
		tmp = 180.0 * (Math.atan((-1.0 / (-2.0 * (A / B)))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.8e+129:
		tmp = 180.0 * (math.atan((-1.0 / (-2.0 * (A / B)))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.8e+129)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(-2.0 * Float64(A / B)))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.8e+129)
		tmp = 180.0 * (atan((-1.0 / (-2.0 * (A / B)))) / pi);
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.8e+129], N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -8.7999999999999997e129

   1. Initial program 11.4%

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

      1. *-commutative 11.4%

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

      2. associate--l- 11.3%

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

      3. +-commutative 11.3%

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

      4. unpow2 11.3%

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

      5. unpow2 11.3%

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

      6. hypot-undefine 24.3%

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

      7. associate--r+ 57.0%

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

      8. div-inv 57.0%

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

      9. div-sub 17.6%

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

      10. flip-- 10.0%

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

   4. Applied egg-rr 10.0%

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

   5. Taylor expanded in C around -inf 47.8%

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

   7. Simplified 93.6%

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

   8. Taylor expanded in A around -inf 81.0%

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

   if -8.7999999999999997e129 < A

   1. Initial program 61.3%

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

   3. Simplified 83.6%

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

Alternative 9: 66.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.65 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-45}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{C \cdot \left(-2 \cdot \frac{A}{C \cdot B} + 2 \cdot \frac{1}{B}\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.65e-95)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= B 4.4e-45)
     (*
      180.0
      (/
       (atan (/ -1.0 (* C (+ (* -2.0 (/ A (* C B))) (* 2.0 (/ 1.0 B))))))
       PI))
     (* 180.0 (/ (atan (+ (/ C B) (- -1.0 (/ A B)))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.65e-95) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= 4.4e-45) {
		tmp = 180.0 * (atan((-1.0 / (C * ((-2.0 * (A / (C * B))) + (2.0 * (1.0 / B)))))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.65e-95) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= 4.4e-45) {
		tmp = 180.0 * (Math.atan((-1.0 / (C * ((-2.0 * (A / (C * B))) + (2.0 * (1.0 / B)))))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C / B) + (-1.0 - (A / B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 1.65e-95:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= 4.4e-45:
		tmp = 180.0 * (math.atan((-1.0 / (C * ((-2.0 * (A / (C * B))) + (2.0 * (1.0 / B)))))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C / B) + (-1.0 - (A / B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 1.65e-95)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= 4.4e-45)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 / Float64(C * Float64(Float64(-2.0 * Float64(A / Float64(C * B))) + Float64(2.0 * Float64(1.0 / B)))))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 1.65e-95)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= 4.4e-45)
		tmp = 180.0 * (atan((-1.0 / (C * ((-2.0 * (A / (C * B))) + (2.0 * (1.0 / B)))))) / pi);
	else
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 1.65e-95], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.4e-45], N[(180.0 * N[(N[ArcTan[N[(-1.0 / N[(C * N[(N[(-2.0 * N[(A / N[(C * B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(1.0 / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 1.65e-95

   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 B around -inf 60.5%

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

      1. associate--l+ 60.5%

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

      2. div-sub 65.2%

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

   5. Simplified 65.2%

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

   if 1.65e-95 < B < 4.39999999999999987e-45

   1. Initial program 30.8%

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

      1. *-commutative 30.8%

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

      2. associate--l- 30.6%

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

      3. +-commutative 30.6%

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

      4. unpow2 30.6%

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

      5. unpow2 30.6%

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

      6. hypot-undefine 39.1%

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

      7. associate--r+ 63.4%

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

      8. div-inv 63.4%

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

      9. div-sub 29.8%

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

      10. flip-- 3.5%

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

   4. Applied egg-rr 3.5%

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

   5. Taylor expanded in C around -inf 67.7%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in C around inf 65.9%

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

   if 4.39999999999999987e-45 < B

   1. Initial program 57.8%

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

   3. Taylor expanded in B around inf 84.2%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.65 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-45}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-1}{C \cdot \left(-2 \cdot \frac{A}{C \cdot B} + 2 \cdot \frac{1}{B}\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.7 \cdot 10^{+124}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.7 \cdot 10^{-33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.7e+124)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 3.7e-33)
     (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.7e+124) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 3.7e-33) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.7e+124) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 3.7e-33) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.7e+124:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 3.7e-33:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.7e+124)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 3.7e-33)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.7e+124)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 3.7e-33)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.7e+124], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.7e-33], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.69999999999999978e124

   1. Initial program 11.4%

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

   3. Taylor expanded in A around -inf 81.0%

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

      1. associate-*r/ 81.0%

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

   5. Simplified 81.0%

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

   if -2.69999999999999978e124 < A < 3.70000000000000014e-33

   1. Initial program 53.5%

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

      1. unpow2 53.5%

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

      2. unpow2 53.5%

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

      3. hypot-define 78.8%

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

   4. Applied egg-rr 78.8%

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

   5. Taylor expanded in A around 0 51.5%

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

      1. +-commutative 51.5%

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

      2. unpow2 51.5%

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

      3. unpow2 51.5%

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

      4. hypot-define 76.7%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in B around inf 53.1%

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

   if 3.70000000000000014e-33 < A

   1. Initial program 74.4%

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

   3. Taylor expanded in B around -inf 75.6%

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

      1. associate--l+ 75.6%

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

      2. div-sub 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in C around 0 79.5%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.7 \cdot 10^{+124}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.7 \cdot 10^{-33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1 \cdot 10^{-160}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 10^{+63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1e-160)
   (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
   (if (<= C 1e+63)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1e-160) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else if (C <= 1e+63) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1e-160) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else if (C <= 1e+63) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1e-160:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	elif C <= 1e+63:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1e-160)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	elseif (C <= 1e+63)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1e-160)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	elseif (C <= 1e+63)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1e-160], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1e+63], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -9.9999999999999999e-161

   1. Initial program 79.4%

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

      1. unpow2 79.4%

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

      2. unpow2 79.4%

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

      3. hypot-define 95.8%

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

   4. Applied egg-rr 95.8%

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

   5. Taylor expanded in A around 0 74.5%

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

      1. +-commutative 74.5%

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

      2. unpow2 74.5%

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

      3. unpow2 74.5%

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

      4. hypot-define 88.8%

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

   7. Simplified 88.8%

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

   8. Taylor expanded in B around inf 79.5%

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

   if -9.9999999999999999e-161 < C < 1.00000000000000006e63

   1. Initial program 49.9%

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

   3. Taylor expanded in B around -inf 51.0%

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

      1. associate--l+ 51.0%

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

      2. div-sub 51.0%

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

   5. Simplified 51.0%

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

   6. Taylor expanded in C around 0 49.8%

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

   if 1.00000000000000006e63 < C

   1. Initial program 25.6%

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

      1. *-commutative 25.6%

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

      2. associate--l- 25.5%

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

      3. +-commutative 25.5%

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

      4. unpow2 25.5%

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

      5. unpow2 25.5%

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

      6. hypot-undefine 56.8%

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

      7. associate--r+ 60.2%

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

      8. div-inv 60.2%

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

      9. div-sub 37.8%

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

      10. flip-- 22.9%

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

   4. Applied egg-rr 22.9%

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

   5. Taylor expanded in C around inf 66.4%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1 \cdot 10^{-160}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 10^{+63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -8 \cdot 10^{-58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.3 \cdot 10^{+62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -8e-58)
   (* 180.0 (/ (atan (+ (/ C B) 1.0)) PI))
   (if (<= C 6.3e+62)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -8e-58) {
		tmp = 180.0 * (atan(((C / B) + 1.0)) / ((double) M_PI));
	} else if (C <= 6.3e+62) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -8e-58) {
		tmp = 180.0 * (Math.atan(((C / B) + 1.0)) / Math.PI);
	} else if (C <= 6.3e+62) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -8e-58:
		tmp = 180.0 * (math.atan(((C / B) + 1.0)) / math.pi)
	elif C <= 6.3e+62:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -8e-58)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + 1.0)) / pi));
	elseif (C <= 6.3e+62)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -8e-58)
		tmp = 180.0 * (atan(((C / B) + 1.0)) / pi);
	elseif (C <= 6.3e+62)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -8e-58], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.3e+62], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -8.0000000000000002e-58

   1. Initial program 78.6%

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

   3. Taylor expanded in B around -inf 69.0%

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

      1. associate--l+ 69.0%

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

      2. div-sub 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in A around 0 74.6%

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

   if -8.0000000000000002e-58 < C < 6.29999999999999998e62

   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 51.3%

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

      1. associate--l+ 51.3%

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

      2. div-sub 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in C around 0 49.5%

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

   if 6.29999999999999998e62 < C

   1. Initial program 25.6%

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

      1. *-commutative 25.6%

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

      2. associate--l- 25.5%

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

      3. +-commutative 25.5%

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

      4. unpow2 25.5%

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

      5. unpow2 25.5%

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

      6. hypot-undefine 56.8%

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

      7. associate--r+ 60.2%

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

      8. div-inv 60.2%

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

      9. div-sub 37.8%

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

      10. flip-- 22.9%

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

   4. Applied egg-rr 22.9%

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

   5. Taylor expanded in C around inf 66.4%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -8 \cdot 10^{-58}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.3 \cdot 10^{+62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.08 \cdot 10^{-58}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -5 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.08e-58)
   (/ (* 180.0 (atan (/ C B))) PI)
   (if (<= C -5e-310)
     (* 180.0 (/ (atan (/ (- A) B)) PI))
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.08e-58) {
		tmp = (180.0 * atan((C / B))) / ((double) M_PI);
	} else if (C <= -5e-310) {
		tmp = 180.0 * (atan((-A / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.08e-58) {
		tmp = (180.0 * Math.atan((C / B))) / Math.PI;
	} else if (C <= -5e-310) {
		tmp = 180.0 * (Math.atan((-A / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.08e-58:
		tmp = (180.0 * math.atan((C / B))) / math.pi
	elif C <= -5e-310:
		tmp = 180.0 * (math.atan((-A / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.08e-58)
		tmp = Float64(Float64(180.0 * atan(Float64(C / B))) / pi);
	elseif (C <= -5e-310)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.08e-58)
		tmp = (180.0 * atan((C / B))) / pi;
	elseif (C <= -5e-310)
		tmp = 180.0 * (atan((-A / B)) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.08e-58], N[(N[(180.0 * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, -5e-310], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.08e-58

   1. Initial program 77.8%

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

   3. Taylor expanded in B around -inf 69.4%

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

      1. associate--l+ 69.4%

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

      2. div-sub 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in C around inf 69.4%

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

      1. associate-*r/ 69.4%

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

   8. Applied egg-rr 69.4%

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

   if -1.08e-58 < C < -4.999999999999985e-310

   1. Initial program 66.5%

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

   3. Taylor expanded in B around -inf 56.7%

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

      1. associate--l+ 56.7%

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

      2. div-sub 56.7%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in A around inf 36.2%

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

      1. associate-*r/ 36.2%

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

      2. mul-1-neg 36.2%

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

   8. Simplified 36.2%

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

   if -4.999999999999985e-310 < C

   1. Initial program 37.9%

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

      1. *-commutative 37.9%

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

      2. associate--l- 37.8%

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

      3. +-commutative 37.8%

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

      4. unpow2 37.8%

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

      5. unpow2 37.8%

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

      6. hypot-undefine 64.5%

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

      7. associate--r+ 70.5%

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

      8. div-inv 70.5%

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

      9. div-sub 56.1%

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

      10. flip-- 36.5%

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

   4. Applied egg-rr 36.5%

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

   5. Taylor expanded in C around inf 49.6%

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

Alternative 14: 66.7% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 4 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 4e-95)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (* 180.0 (/ (atan (+ (/ C B) (- -1.0 (/ A B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 4e-95) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 4e-95) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C / B) + (-1.0 - (A / B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 4e-95:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C / B) + (-1.0 - (A / B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 4e-95)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 4e-95)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	else
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 4e-95], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 3.99999999999999996e-95

   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 B around -inf 60.2%

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

      1. associate--l+ 60.2%

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

      2. div-sub 64.8%

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

   5. Simplified 64.8%

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

   if 3.99999999999999996e-95 < B

   1. Initial program 54.6%

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

   3. Taylor expanded in B around inf 77.0%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 4 \cdot 10^{-95}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -185:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -185.0)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.2e-72)
     (* 180.0 (/ (atan (/ C B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -185.0) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.2e-72) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -185.0) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.2e-72) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -185.0:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.2e-72:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -185.0)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.2e-72)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -185.0)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.2e-72)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -185.0], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.2e-72], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -185

   1. Initial program 40.6%

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

   3. Taylor expanded in B around -inf 55.1%

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

   if -185 < B < 2.20000000000000002e-72

   1. Initial program 63.0%

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

   3. Taylor expanded in B around -inf 52.8%

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

      1. associate--l+ 52.8%

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

      2. div-sub 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in C around inf 37.9%

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

   if 2.20000000000000002e-72 < B

   1. Initial program 54.7%

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

   3. Taylor expanded in B around inf 60.7%

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

Alternative 16: 44.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7 \cdot 10^{-237}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.4 \cdot 10^{-45}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7e-237)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.4e-45)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7e-237) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.4e-45) {
		tmp = 180.0 * (atan((0.0 / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -7e-237) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.4e-45) {
		tmp = 180.0 * (Math.atan((0.0 / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7e-237:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.4e-45:
		tmp = 180.0 * (math.atan((0.0 / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -7e-237)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.4e-45)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -7e-237)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.4e-45)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7e-237], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.4e-45], N[(180.0 * N[(N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -6.99999999999999966e-237

   1. Initial program 52.3%

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

   3. Taylor expanded in B around -inf 40.0%

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

   if -6.99999999999999966e-237 < B < 4.39999999999999987e-45

   1. Initial program 56.0%

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

   3. Taylor expanded in C around inf 28.2%

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

      1. associate-*r/ 28.2%

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

      2. mul-1-neg 28.2%

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

      3. distribute-rgt1-in 28.2%

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

      4. metadata-eval 28.2%

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

      5. mul0-lft 28.2%

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

      6. metadata-eval 28.2%

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

   5. Simplified 28.2%

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

   if 4.39999999999999987e-45 < B

   1. Initial program 57.8%

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

   3. Taylor expanded in B around inf 64.5%

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

Alternative 17: 63.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 2.8 \cdot 10^{-72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 2.8e-72)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 2.8e-72) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 2.8e-72) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 2.8e-72:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 2.8e-72)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 2.8e-72)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 2.8e-72], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 2.7999999999999998e-72

   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 59.9%

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

      1. associate--l+ 59.9%

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

      2. div-sub 64.4%

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

   5. Simplified 64.4%

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

   if 2.7999999999999998e-72 < B

   1. Initial program 54.7%

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

      1. unpow2 54.7%

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

      2. unpow2 54.7%

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

      3. hypot-define 87.6%

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

   4. Applied egg-rr 87.6%

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

   5. Taylor expanded in A around 0 49.5%

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

      1. +-commutative 49.5%

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

      2. unpow2 49.5%

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

      3. unpow2 49.5%

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

      4. hypot-define 76.7%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in B around inf 70.6%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 2.8 \cdot 10^{-72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 53.8% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 10^{-305}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 1e-305)
   (* 180.0 (/ (atan (+ (/ C B) 1.0)) PI))
   (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 1e-305) {
		tmp = 180.0 * (atan(((C / B) + 1.0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 1e-305) {
		tmp = 180.0 * (Math.atan(((C / B) + 1.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 1e-305:
		tmp = 180.0 * (math.atan(((C / B) + 1.0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 1e-305)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + 1.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 1e-305)
		tmp = 180.0 * (atan(((C / B) + 1.0)) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 1e-305], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 9.99999999999999996e-306

   1. Initial program 72.2%

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

   3. Taylor expanded in B around -inf 63.3%

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

      1. associate--l+ 63.3%

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

      2. div-sub 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in A around 0 58.9%

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

   if 9.99999999999999996e-306 < C

   1. Initial program 38.4%

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

      1. *-commutative 38.4%

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

      2. associate--l- 38.3%

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

      3. +-commutative 38.3%

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

      4. unpow2 38.3%

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

      5. unpow2 38.3%

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

      6. hypot-undefine 65.4%

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

      7. associate--r+ 70.7%

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

      8. div-inv 70.7%

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

      9. div-sub 57.0%

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

      10. flip-- 37.1%

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

   4. Applied egg-rr 37.1%

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

   5. Taylor expanded in C around inf 50.3%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 10^{-305}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 40.9% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if B < -9.999999999999969e-311

   1. Initial program 53.7%

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

   3. Taylor expanded in B around -inf 36.0%

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

   if -9.999999999999969e-311 < B

   1. Initial program 56.0%

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

   3. Taylor expanded in B around inf 42.9%

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

Alternative 20: 21.5% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 22.0%

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

Reproduce

herbie shell --seed 2024137 
(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)))