ABCF->ab-angle angle

Percentage Accurate: 53.4% → 88.5%

Time: 13.2s

Alternatives: 16

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.4% 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: 88.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)\right)\right)}{\pi}\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-39}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{1}{\pi} \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (hypot (- C A) B)))) PI)))
        (t_1
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_1 -5e-39)
     t_0
     (if (<= t_1 0.0)
       (* (/ 1.0 PI) (/ (atan (/ (* B 0.5) (- A C))) 0.005555555555555556))
       t_0))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((C - A), B)))) / ((double) M_PI));
	double t_1 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_1 <= -5e-39) {
		tmp = t_0;
	} else if (t_1 <= 0.0) {
		tmp = (1.0 / ((double) M_PI)) * (atan(((B * 0.5) / (A - C))) / 0.005555555555555556);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.hypot((C - A), B)))) / Math.PI);
	double t_1 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_1 <= -5e-39) {
		tmp = t_0;
	} else if (t_1 <= 0.0) {
		tmp = (1.0 / Math.PI) * (Math.atan(((B * 0.5) / (A - C))) / 0.005555555555555556);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.hypot((C - A), B)))) / math.pi)
	t_1 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_1 <= -5e-39:
		tmp = t_0
	elif t_1 <= 0.0:
		tmp = (1.0 / math.pi) * (math.atan(((B * 0.5) / (A - C))) / 0.005555555555555556)
	else:
		tmp = t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - hypot(Float64(C - A), B)))) / pi))
	t_1 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_1 <= -5e-39)
		tmp = t_0;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(1.0 / pi) * Float64(atan(Float64(Float64(B * 0.5) / Float64(A - C))) / 0.005555555555555556));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((C - A), B)))) / pi);
	t_1 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_1 <= -5e-39)
		tmp = t_0;
	elseif (t_1 <= 0.0)
		tmp = (1.0 / pi) * (atan(((B * 0.5) / (A - C))) / 0.005555555555555556);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-39], t$95$0, If[LessEqual[t$95$1, 0.0], N[(N[(1.0 / Pi), $MachinePrecision] * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / N[(A - C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / 0.005555555555555556), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -4.9999999999999998e-39 or -0.0 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 62.2%

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

   4. Applied egg-rr 83.4%

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

   if -4.9999999999999998e-39 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -0.0

   1. Initial program 19.6%

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

   4. Applied egg-rr 19.6%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-lft-in N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. /-lowering-/.f64 N/A

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

      21. mul-1-neg N/A

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

      22. unsub-neg N/A

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

      23. --lowering--.f64 99.4

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

   7. Simplified 99.4%

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

      1. associate-*r/ N/A

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

      2. *-rgt-identity N/A

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

      3. times-frac N/A

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

      4. /-rgt-identity N/A

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

      5. *-lowering-*.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. PI-lowering-PI.f64 N/A

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

      8. atan-lowering-atan.f64 N/A

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

      9. clear-num N/A

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

      10. un-div-inv N/A

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

      11. /-lowering-/.f64 N/A

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

      12. div-inv N/A

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 N/A

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

      15. --lowering--.f64 99.4

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

   9. Applied egg-rr 99.4%

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

       1. clear-num N/A

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

       2. associate-*l/ N/A

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

       3. div-inv N/A

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

       4. times-frac N/A

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

       5. *-lowering-*.f64 N/A

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

       6. /-lowering-/.f64 N/A

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

       7. PI-lowering-PI.f64 N/A

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

       8. /-lowering-/.f64 N/A

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

       9. atan-lowering-atan.f64 N/A

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

       10. associate-/l/ N/A

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

       11. /-lowering-/.f64 N/A

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

       12. div-inv N/A

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

       13. metadata-eval N/A

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

       14. *-lowering-*.f64 N/A

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

       15. --lowering--.f64 N/A

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

       16. metadata-eval 99.6

           \[\leadsto \frac{1}{\pi} \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\color{blue}{0.005555555555555556}} \]

   11. Applied egg-rr 99.6%

       \[\leadsto \color{blue}{\frac{1}{\pi} \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{0.005555555555555556}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 69.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq -0.5:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{1}{\pi} \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))
        (t_1
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_1 -2e+33)
     t_0
     (if (<= t_1 -0.5)
       (* 180.0 (/ (atan -1.0) PI))
       (if (<= t_1 0.0)
         (* (/ 1.0 PI) (/ (atan (/ (* B 0.5) (- A C))) 0.005555555555555556))
         t_0)))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double t_1 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_1 <= -2e+33) {
		tmp = t_0;
	} else if (t_1 <= -0.5) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (t_1 <= 0.0) {
		tmp = (1.0 / ((double) M_PI)) * (atan(((B * 0.5) / (A - C))) / 0.005555555555555556);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double t_1 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_1 <= -2e+33) {
		tmp = t_0;
	} else if (t_1 <= -0.5) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (t_1 <= 0.0) {
		tmp = (1.0 / Math.PI) * (Math.atan(((B * 0.5) / (A - C))) / 0.005555555555555556);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	t_1 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_1 <= -2e+33:
		tmp = t_0
	elif t_1 <= -0.5:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif t_1 <= 0.0:
		tmp = (1.0 / math.pi) * (math.atan(((B * 0.5) / (A - C))) / 0.005555555555555556)
	else:
		tmp = t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	t_1 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_1 <= -2e+33)
		tmp = t_0;
	elseif (t_1 <= -0.5)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(1.0 / pi) * Float64(atan(Float64(Float64(B * 0.5) / Float64(A - C))) / 0.005555555555555556));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	t_1 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_1 <= -2e+33)
		tmp = t_0;
	elseif (t_1 <= -0.5)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (t_1 <= 0.0)
		tmp = (1.0 / pi) * (atan(((B * 0.5) / (A - C))) / 0.005555555555555556);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+33], t$95$0, If[LessEqual[t$95$1, -0.5], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(1.0 / Pi), $MachinePrecision] * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / N[(A - C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / 0.005555555555555556), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -1.9999999999999999e33 or -0.0 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 60.5%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 64.2

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

   5. Simplified 64.2%

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

   if -1.9999999999999999e33 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in B around inf

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

   5. Simplified 100.0%

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

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

   1. Initial program 19.2%

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

   4. Applied egg-rr 21.6%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-lft-in N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. /-lowering-/.f64 N/A

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

      21. mul-1-neg N/A

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

      22. unsub-neg N/A

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

      23. --lowering--.f64 97.5

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

   7. Simplified 97.5%

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

      1. associate-*r/ N/A

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

      2. *-rgt-identity N/A

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

      3. times-frac N/A

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

      4. /-rgt-identity N/A

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

      5. *-lowering-*.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. PI-lowering-PI.f64 N/A

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

      8. atan-lowering-atan.f64 N/A

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

      9. clear-num N/A

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

      10. un-div-inv N/A

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

      11. /-lowering-/.f64 N/A

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

      12. div-inv N/A

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 N/A

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

      15. --lowering--.f64 97.4

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

   9. Applied egg-rr 97.4%

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

       1. clear-num N/A

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

       2. associate-*l/ N/A

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

       3. div-inv N/A

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

       4. times-frac N/A

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

       5. *-lowering-*.f64 N/A

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

       6. /-lowering-/.f64 N/A

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

       7. PI-lowering-PI.f64 N/A

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

       8. /-lowering-/.f64 N/A

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

       9. atan-lowering-atan.f64 N/A

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

       10. associate-/l/ N/A

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

       11. /-lowering-/.f64 N/A

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

       12. div-inv N/A

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

       13. metadata-eval N/A

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

       14. *-lowering-*.f64 N/A

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

       15. --lowering--.f64 N/A

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

       16. metadata-eval 97.7

           \[\leadsto \frac{1}{\pi} \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\color{blue}{0.005555555555555556}} \]

   11. Applied egg-rr 97.7%

       \[\leadsto \color{blue}{\frac{1}{\pi} \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{0.005555555555555556}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 69.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq -0.5:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))
        (t_1
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_1 -2e+33)
     t_0
     (if (<= t_1 -0.5)
       (* 180.0 (/ (atan -1.0) PI))
       (if (<= t_1 0.0) (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI)) t_0)))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	double t_1 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_1 <= -2e+33) {
		tmp = t_0;
	} else if (t_1 <= -0.5) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else if (t_1 <= 0.0) {
		tmp = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	double t_1 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_1 <= -2e+33) {
		tmp = t_0;
	} else if (t_1 <= -0.5) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else if (t_1 <= 0.0) {
		tmp = 180.0 * (Math.atan((B * (0.5 / (A - C)))) / Math.PI);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	t_1 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_1 <= -2e+33:
		tmp = t_0
	elif t_1 <= -0.5:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	elif t_1 <= 0.0:
		tmp = 180.0 * (math.atan((B * (0.5 / (A - C)))) / math.pi)
	else:
		tmp = t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi))
	t_1 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_1 <= -2e+33)
		tmp = t_0;
	elseif (t_1 <= -0.5)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	elseif (t_1 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	t_1 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_1 <= -2e+33)
		tmp = t_0;
	elseif (t_1 <= -0.5)
		tmp = 180.0 * (atan(-1.0) / pi);
	elseif (t_1 <= 0.0)
		tmp = 180.0 * (atan((B * (0.5 / (A - C)))) / pi);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+33], t$95$0, If[LessEqual[t$95$1, -0.5], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -1.9999999999999999e33 or -0.0 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 60.5%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 64.2

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

   5. Simplified 64.2%

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

   if -1.9999999999999999e33 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in B around inf

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

   5. Simplified 100.0%

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

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

   1. Initial program 19.2%

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

   4. Applied egg-rr 21.6%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-lft-in N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. /-lowering-/.f64 N/A

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

      21. mul-1-neg N/A

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

      22. unsub-neg N/A

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

      23. --lowering--.f64 97.5

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

   7. Simplified 97.5%

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

Alternative 4: 75.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+79}:\\ \;\;\;\;\frac{1}{\pi} \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{0.005555555555555556}\\ \mathbf{elif}\;A \leq 3.7 \cdot 10^{-29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.2e+79)
   (* (/ 1.0 PI) (/ (atan (/ (* B 0.5) (- A C))) 0.005555555555555556))
   (if (<= A 3.7e-29)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.2e+79) {
		tmp = (1.0 / ((double) M_PI)) * (atan(((B * 0.5) / (A - C))) / 0.005555555555555556);
	} else if (A <= 3.7e-29) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.2e+79) {
		tmp = (1.0 / Math.PI) * (Math.atan(((B * 0.5) / (A - C))) / 0.005555555555555556);
	} else if (A <= 3.7e-29) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.2e+79:
		tmp = (1.0 / math.pi) * (math.atan(((B * 0.5) / (A - C))) / 0.005555555555555556)
	elif A <= 3.7e-29:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.2e+79)
		tmp = Float64(Float64(1.0 / pi) * Float64(atan(Float64(Float64(B * 0.5) / Float64(A - C))) / 0.005555555555555556));
	elseif (A <= 3.7e-29)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.2e+79)
		tmp = (1.0 / pi) * (atan(((B * 0.5) / (A - C))) / 0.005555555555555556);
	elseif (A <= 3.7e-29)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.2e+79], N[(N[(1.0 / Pi), $MachinePrecision] * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / N[(A - C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.7e-29], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -5.20000000000000029e79

   1. Initial program 19.3%

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

   4. Applied egg-rr 49.5%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-lft-in N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. /-lowering-/.f64 N/A

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

      21. mul-1-neg N/A

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

      22. unsub-neg N/A

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

      23. --lowering--.f64 81.8

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

   7. Simplified 81.8%

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

      1. associate-*r/ N/A

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

      2. *-rgt-identity N/A

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

      3. times-frac N/A

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

      4. /-rgt-identity N/A

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

      5. *-lowering-*.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. PI-lowering-PI.f64 N/A

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

      8. atan-lowering-atan.f64 N/A

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

      9. clear-num N/A

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

      10. un-div-inv N/A

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

      11. /-lowering-/.f64 N/A

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

      12. div-inv N/A

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 N/A

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

      15. --lowering--.f64 82.0

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

   9. Applied egg-rr 82.0%

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

       1. clear-num N/A

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

       2. associate-*l/ N/A

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

       3. div-inv N/A

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

       4. times-frac N/A

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

       5. *-lowering-*.f64 N/A

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

       6. /-lowering-/.f64 N/A

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

       7. PI-lowering-PI.f64 N/A

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

       8. /-lowering-/.f64 N/A

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

       9. atan-lowering-atan.f64 N/A

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

       10. associate-/l/ N/A

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

       11. /-lowering-/.f64 N/A

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

       12. div-inv N/A

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

       13. metadata-eval N/A

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

       14. *-lowering-*.f64 N/A

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

       15. --lowering--.f64 N/A

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

       16. metadata-eval 82.1

           \[\leadsto \frac{1}{\pi} \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{\color{blue}{0.005555555555555556}} \]

   11. Applied egg-rr 82.1%

       \[\leadsto \color{blue}{\frac{1}{\pi} \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A - C}\right)}{0.005555555555555556}} \]

   if -5.20000000000000029e79 < A < 3.6999999999999997e-29

   1. Initial program 53.2%

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

   3. Taylor expanded in A around 0

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. sqrt-lowering-sqrt.f64 N/A

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

      4. unpow2 N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. unpow2 N/A

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

      7. *-lowering-*.f64 52.2

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

   5. Simplified 52.2%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-hypot.f64 69.6

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

   7. Applied egg-rr 69.6%

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

   if 3.6999999999999997e-29 < A

   1. Initial program 79.2%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 78.0

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

   5. Simplified 78.0%

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

Alternative 5: 56.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.2 \cdot 10^{+78}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{A \cdot 2}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 4100000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.2e+78)
   (/ (atan (/ B (* A 2.0))) (* PI 0.005555555555555556))
   (if (<= A 4100000000.0)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.2e+78) {
		tmp = atan((B / (A * 2.0))) / (((double) M_PI) * 0.005555555555555556);
	} else if (A <= 4100000000.0) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.2e+78) {
		tmp = Math.atan((B / (A * 2.0))) / (Math.PI * 0.005555555555555556);
	} else if (A <= 4100000000.0) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.2e+78:
		tmp = math.atan((B / (A * 2.0))) / (math.pi * 0.005555555555555556)
	elif A <= 4100000000.0:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.2e+78)
		tmp = Float64(atan(Float64(B / Float64(A * 2.0))) / Float64(pi * 0.005555555555555556));
	elseif (A <= 4100000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.2e+78)
		tmp = atan((B / (A * 2.0))) / (pi * 0.005555555555555556);
	elseif (A <= 4100000000.0)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.2e+78], N[(N[ArcTan[N[(B / N[(A * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4100000000.0], 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[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -6.2e78

   1. Initial program 19.3%

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

   4. Applied egg-rr 49.5%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-lft-in N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. /-lowering-/.f64 N/A

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

      21. mul-1-neg N/A

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

      22. unsub-neg N/A

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

      23. --lowering--.f64 81.8

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

   7. Simplified 81.8%

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

   8. Taylor expanded in A around inf

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

      1. /-lowering-/.f64 77.4

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

   10. Simplified 77.4%

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

       1. *-commutative N/A

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

       2. div-inv N/A

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

       3. associate-*l* N/A

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

       4. associate-/r/ N/A

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

       5. un-div-inv N/A

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

       6. /-lowering-/.f64 N/A

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

       7. atan-lowering-atan.f64 N/A

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

       8. clear-num N/A

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

       9. un-div-inv N/A

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

       10. /-lowering-/.f64 N/A

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

       11. div-inv N/A

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

       12. metadata-eval N/A

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

       13. *-lowering-*.f64 N/A

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

       14. div-inv N/A

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

       15. *-lowering-*.f64 N/A

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

       16. PI-lowering-PI.f64 N/A

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

       17. metadata-eval 77.6

           \[\leadsto \frac{\tan^{-1} \left(\frac{B}{A \cdot 2}\right)}{\pi \cdot \color{blue}{0.005555555555555556}} \]

   12. Applied egg-rr 77.6%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{A \cdot 2}\right)}{\pi \cdot 0.005555555555555556}} \]

   if -6.2e78 < A < 4.1e9

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 50.6

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

   5. Simplified 50.6%

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

   6. Taylor expanded in A around 0

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

      1. +-lowering-+.f64 N/A

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

      2. /-lowering-/.f64 48.8

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

   8. Simplified 48.8%

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

   if 4.1e9 < A

   1. Initial program 77.0%

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

   3. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 71.7

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

   5. Simplified 71.7%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.2 \cdot 10^{+78}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{A \cdot 2}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{elif}\;A \leq 4100000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.95 \cdot 10^{+80}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{A \cdot 2}\right)\\ \mathbf{elif}\;A \leq 1250000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.95e+80)
   (* (/ 180.0 PI) (atan (/ B (* A 2.0))))
   (if (<= A 1250000000.0)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.95e+80) {
		tmp = (180.0 / ((double) M_PI)) * atan((B / (A * 2.0)));
	} else if (A <= 1250000000.0) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.95e+80) {
		tmp = (180.0 / Math.PI) * Math.atan((B / (A * 2.0)));
	} else if (A <= 1250000000.0) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.95e+80:
		tmp = (180.0 / math.pi) * math.atan((B / (A * 2.0)))
	elif A <= 1250000000.0:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.95e+80)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B / Float64(A * 2.0))));
	elseif (A <= 1250000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.95e+80)
		tmp = (180.0 / pi) * atan((B / (A * 2.0)));
	elseif (A <= 1250000000.0)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.95e+80], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B / N[(A * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1250000000.0], 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[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.94999999999999999e80

   1. Initial program 19.3%

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

   4. Applied egg-rr 49.5%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-lft-in N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. /-lowering-/.f64 N/A

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

      21. mul-1-neg N/A

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

      22. unsub-neg N/A

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

      23. --lowering--.f64 81.8

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

   7. Simplified 81.8%

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

   8. Taylor expanded in A around inf

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

      1. /-lowering-/.f64 77.4

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

   10. Simplified 77.4%

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

       1. clear-num N/A

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

       2. un-div-inv N/A

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

       3. associate-/r/ N/A

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

       4. *-lowering-*.f64 N/A

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

       5. /-lowering-/.f64 N/A

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

       6. PI-lowering-PI.f64 N/A

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

       7. atan-lowering-atan.f64 N/A

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

       8. clear-num N/A

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

       9. un-div-inv N/A

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

       10. /-lowering-/.f64 N/A

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

       11. div-inv N/A

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

       12. metadata-eval N/A

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

       13. *-lowering-*.f64 77.6

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

   12. Applied egg-rr 77.6%

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

   if -1.94999999999999999e80 < A < 1.25e9

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 50.6

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

   5. Simplified 50.6%

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

   6. Taylor expanded in A around 0

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

      1. +-lowering-+.f64 N/A

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

      2. /-lowering-/.f64 48.8

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

   8. Simplified 48.8%

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

   if 1.25e9 < A

   1. Initial program 77.0%

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

   3. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 71.7

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

   5. Simplified 71.7%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.95 \cdot 10^{+80}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{A \cdot 2}\right)\\ \mathbf{elif}\;A \leq 1250000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.04 \cdot 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2300000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.04e+80)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 2300000000.0)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.04e+80) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 2300000000.0) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.04e+80) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 2300000000.0) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.04e+80:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 2300000000.0:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.04e+80)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 2300000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.04e+80)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 2300000000.0)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.04e+80], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2300000000.0], 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[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.04000000000000006e80

   1. Initial program 19.3%

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

   3. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 77.5

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

   5. Simplified 77.5%

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

   if -1.04000000000000006e80 < A < 2.3e9

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 50.6

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

   5. Simplified 50.6%

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

   6. Taylor expanded in A around 0

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

      1. +-lowering-+.f64 N/A

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

      2. /-lowering-/.f64 48.8

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

   8. Simplified 48.8%

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

   if 2.3e9 < A

   1. Initial program 77.0%

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

   3. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 71.7

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

   5. Simplified 71.7%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.04 \cdot 10^{+80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2300000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.35 \cdot 10^{+79}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2400000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.35e+79)
   (* 180.0 (/ (atan (* B (/ 0.5 A))) PI))
   (if (<= A 2400000000.0)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.35e+79) {
		tmp = 180.0 * (atan((B * (0.5 / A))) / ((double) M_PI));
	} else if (A <= 2400000000.0) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.35e+79) {
		tmp = 180.0 * (Math.atan((B * (0.5 / A))) / Math.PI);
	} else if (A <= 2400000000.0) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.35e+79:
		tmp = 180.0 * (math.atan((B * (0.5 / A))) / math.pi)
	elif A <= 2400000000.0:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.35e+79)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / A))) / pi));
	elseif (A <= 2400000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.35e+79)
		tmp = 180.0 * (atan((B * (0.5 / A))) / pi);
	elseif (A <= 2400000000.0)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.35e+79], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2400000000.0], 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[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.35000000000000011e79

   1. Initial program 19.3%

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

   4. Applied egg-rr 49.5%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-lft-in N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. /-lowering-/.f64 N/A

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

      21. mul-1-neg N/A

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

      22. unsub-neg N/A

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

      23. --lowering--.f64 81.8

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

   7. Simplified 81.8%

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

   8. Taylor expanded in A around inf

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

      1. /-lowering-/.f64 77.4

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

   10. Simplified 77.4%

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

   if -2.35000000000000011e79 < A < 2.4e9

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 50.6

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

   5. Simplified 50.6%

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

   6. Taylor expanded in A around 0

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

      1. +-lowering-+.f64 N/A

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

      2. /-lowering-/.f64 48.8

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

   8. Simplified 48.8%

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

   if 2.4e9 < A

   1. Initial program 77.0%

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

   3. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 71.7

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

   5. Simplified 71.7%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.35 \cdot 10^{+79}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2400000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.8 \cdot 10^{+82}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4200000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.8e+82)
   (* 180.0 (/ (atan (* B (/ 0.5 A))) PI))
   (if (<= A 4200000000.0)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* -180.0 (/ (atan (/ A B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+82) {
		tmp = 180.0 * (atan((B * (0.5 / A))) / ((double) M_PI));
	} else if (A <= 4200000000.0) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = -180.0 * (atan((A / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.8e+82) {
		tmp = 180.0 * (Math.atan((B * (0.5 / A))) / Math.PI);
	} else if (A <= 4200000000.0) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = -180.0 * (Math.atan((A / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.8e+82:
		tmp = 180.0 * (math.atan((B * (0.5 / A))) / math.pi)
	elif A <= 4200000000.0:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = -180.0 * (math.atan((A / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.8e+82)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / A))) / pi));
	elseif (A <= 4200000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(-180.0 * Float64(atan(Float64(A / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.8e+82)
		tmp = 180.0 * (atan((B * (0.5 / A))) / pi);
	elseif (A <= 4200000000.0)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = -180.0 * (atan((A / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.8e+82], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4200000000.0], 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[(A / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.80000000000000007e82

   1. Initial program 19.3%

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

   4. Applied egg-rr 49.5%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. *-lowering-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-lft-in N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. /-lowering-/.f64 N/A

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

      21. mul-1-neg N/A

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

      22. unsub-neg N/A

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

      23. --lowering--.f64 81.8

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

   7. Simplified 81.8%

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

   8. Taylor expanded in A around inf

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

      1. /-lowering-/.f64 77.4

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

   10. Simplified 77.4%

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

   if -1.80000000000000007e82 < A < 4.2e9

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 50.6

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

   5. Simplified 50.6%

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

   6. Taylor expanded in A around 0

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

      1. +-lowering-+.f64 N/A

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

      2. /-lowering-/.f64 48.8

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

   8. Simplified 48.8%

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

   if 4.2e9 < A

   1. Initial program 77.0%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 75.8

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

   5. Simplified 75.8%

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

   6. Taylor expanded in A around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. neg-lowering-neg.f64 70.9

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

   8. Simplified 70.9%

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

      1. frac-2neg N/A

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

      2. associate-*r/ N/A

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

      3. neg-mul-1 N/A

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

      4. times-frac N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. *-lowering-*.f64 N/A

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

      8. metadata-eval N/A

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

      9. /-lowering-/.f64 N/A

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

      10. distribute-frac-neg2 N/A

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

      11. atan-neg N/A

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

      12. remove-double-neg N/A

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

      13. atan-lowering-atan.f64 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. PI-lowering-PI.f64 70.9

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

   10. Applied egg-rr 70.9%

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

Alternative 10: 49.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9.8 \cdot 10^{+156}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;A \leq 10600000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9.8e+156)
   (* 180.0 (/ (atan 0.0) PI))
   (if (<= A 10600000.0)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* -180.0 (/ (atan (/ A B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.8e+156) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (A <= 10600000.0) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = -180.0 * (atan((A / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.8e+156) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (A <= 10600000.0) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = -180.0 * (Math.atan((A / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -9.8e+156:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif A <= 10600000.0:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = -180.0 * (math.atan((A / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -9.8e+156)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (A <= 10600000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(-180.0 * Float64(atan(Float64(A / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -9.8e+156)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (A <= 10600000.0)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = -180.0 * (atan((A / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -9.8e+156], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 10600000.0], 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[(A / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -9.79999999999999938e156

   1. Initial program 8.0%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 38.0

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

   5. Simplified 38.0%

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

   if -9.79999999999999938e156 < A < 1.06e7

   1. Initial program 54.9%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 50.0

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

   5. Simplified 50.0%

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

   6. Taylor expanded in A around 0

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

      1. +-lowering-+.f64 N/A

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

      2. /-lowering-/.f64 48.4

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

   8. Simplified 48.4%

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

   if 1.06e7 < A

   1. Initial program 77.3%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 74.7

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

   5. Simplified 74.7%

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

   6. Taylor expanded in A around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. neg-lowering-neg.f64 69.9

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

   8. Simplified 69.9%

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

      1. frac-2neg N/A

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

      2. associate-*r/ N/A

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

      3. neg-mul-1 N/A

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

      4. times-frac N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. *-lowering-*.f64 N/A

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

      8. metadata-eval N/A

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

      9. /-lowering-/.f64 N/A

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

      10. distribute-frac-neg2 N/A

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

      11. atan-neg N/A

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

      12. remove-double-neg N/A

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

      13. atan-lowering-atan.f64 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. PI-lowering-PI.f64 69.9

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

   10. Applied egg-rr 69.9%

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

Alternative 11: 37.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -9.8 \cdot 10^{-116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -2.1 \cdot 10^{-272}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.45 \cdot 10^{+105}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -9.8e-116)
   (* 180.0 (/ (atan (/ C B)) PI))
   (if (<= C -2.1e-272)
     (* -180.0 (/ (atan (/ A B)) PI))
     (if (<= C 1.45e+105)
       (* 180.0 (/ (atan 1.0) PI))
       (* 180.0 (/ (atan 0.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -9.8e-116) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (C <= -2.1e-272) {
		tmp = -180.0 * (atan((A / B)) / ((double) M_PI));
	} else if (C <= 1.45e+105) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -9.8e-116) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (C <= -2.1e-272) {
		tmp = -180.0 * (Math.atan((A / B)) / Math.PI);
	} else if (C <= 1.45e+105) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -9.8e-116:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif C <= -2.1e-272:
		tmp = -180.0 * (math.atan((A / B)) / math.pi)
	elif C <= 1.45e+105:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -9.8e-116)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (C <= -2.1e-272)
		tmp = Float64(-180.0 * Float64(atan(Float64(A / B)) / pi));
	elseif (C <= 1.45e+105)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -9.8e-116)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (C <= -2.1e-272)
		tmp = -180.0 * (atan((A / B)) / pi);
	elseif (C <= 1.45e+105)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(0.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -9.8e-116], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -2.1e-272], N[(-180.0 * N[(N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.45e+105], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -9.79999999999999955e-116

   1. Initial program 73.4%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 70.3

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

   5. Simplified 70.3%

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

   6. Taylor expanded in C around inf

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

      1. /-lowering-/.f64 60.1

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

   8. Simplified 60.1%

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

   if -9.79999999999999955e-116 < C < -2.09999999999999987e-272

   1. Initial program 77.2%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 68.8

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

   5. Simplified 68.8%

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

   6. Taylor expanded in A around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. neg-lowering-neg.f64 54.5

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

   8. Simplified 54.5%

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

      1. frac-2neg N/A

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

      2. associate-*r/ N/A

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

      3. neg-mul-1 N/A

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

      4. times-frac N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. *-lowering-*.f64 N/A

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

      8. metadata-eval N/A

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

      9. /-lowering-/.f64 N/A

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

      10. distribute-frac-neg2 N/A

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

      11. atan-neg N/A

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

      12. remove-double-neg N/A

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

      13. atan-lowering-atan.f64 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. PI-lowering-PI.f64 54.5

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

   10. Applied egg-rr 54.5%

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

   if -2.09999999999999987e-272 < C < 1.45000000000000005e105

   1. Initial program 46.6%

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

   3. Taylor expanded in B around -inf

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

   5. Simplified 31.6%

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

   if 1.45000000000000005e105 < C

   1. Initial program 24.4%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 33.7

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

   5. Simplified 33.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 12: 46.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.15 \cdot 10^{-19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5.2 \cdot 10^{+49}:\\ \;\;\;\;-180 \cdot \frac{\tan^{-1} \left(\frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.15e-19)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 5.2e+49)
     (* -180.0 (/ (atan (/ A B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.15e-19) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 5.2e+49) {
		tmp = -180.0 * (atan((A / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.15e-19) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 5.2e+49) {
		tmp = -180.0 * (Math.atan((A / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.15e-19:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 5.2e+49:
		tmp = -180.0 * (math.atan((A / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.15e-19)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 5.2e+49)
		tmp = Float64(-180.0 * Float64(atan(Float64(A / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.15e-19)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 5.2e+49)
		tmp = -180.0 * (atan((A / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.15e-19], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.2e+49], N[(-180.0 * N[(N[ArcTan[N[(A / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.1499999999999999e-19

   1. Initial program 52.8%

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

   3. Taylor expanded in B around -inf

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

   5. Simplified 49.1%

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

   if -1.1499999999999999e-19 < B < 5.19999999999999977e49

   1. Initial program 59.4%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 52.7

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

   5. Simplified 52.7%

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

   6. Taylor expanded in A around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. neg-lowering-neg.f64 32.8

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

   8. Simplified 32.8%

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

      1. frac-2neg N/A

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

      2. associate-*r/ N/A

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

      3. neg-mul-1 N/A

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

      4. times-frac N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. *-lowering-*.f64 N/A

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

      8. metadata-eval N/A

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

      9. /-lowering-/.f64 N/A

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

      10. distribute-frac-neg2 N/A

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

      11. atan-neg N/A

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

      12. remove-double-neg N/A

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

      13. atan-lowering-atan.f64 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. PI-lowering-PI.f64 32.8

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

   10. Applied egg-rr 32.8%

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

   if 5.19999999999999977e49 < B

   1. Initial program 49.2%

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

   3. Taylor expanded in B around inf

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

   5. Simplified 62.1%

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

Alternative 13: 60.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 1.3 \cdot 10^{+56}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B}{C \cdot -2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 1.3e+56)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (* (/ 180.0 PI) (atan (/ B (* C -2.0))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.3e+56) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((B / (C * -2.0)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.3e+56) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((B / (C * -2.0)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 1.3e+56:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((B / (C * -2.0)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 1.3e+56)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B / Float64(C * -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 1.3e+56)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	else
		tmp = (180.0 / pi) * atan((B / (C * -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 1.3e+56], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B / N[(C * -2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 1.30000000000000005e56

   1. Initial program 64.6%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-lowering-+.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 62.1

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

   5. Simplified 62.1%

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

   if 1.30000000000000005e56 < C

   1. Initial program 25.5%

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

   3. Taylor expanded in A around 0

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 N/A

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

      3. sqrt-lowering-sqrt.f64 N/A

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

      4. unpow2 N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. unpow2 N/A

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

      7. *-lowering-*.f64 23.8

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

   5. Simplified 23.8%

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

   6. Taylor expanded in C around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 80.9

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

   8. Simplified 80.9%

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

      1. associate-*r/ N/A

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

      2. *-rgt-identity N/A

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

      3. times-frac N/A

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

      4. /-rgt-identity N/A

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

      5. *-lowering-*.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. PI-lowering-PI.f64 N/A

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

      8. atan-lowering-atan.f64 N/A

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

      9. associate-/l* N/A

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

      10. clear-num N/A

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

      11. un-div-inv N/A

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

      12. /-lowering-/.f64 N/A

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

      13. div-inv N/A

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

      14. metadata-eval N/A

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

      15. metadata-eval N/A

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

      16. *-lowering-*.f64 N/A

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

      17. metadata-eval 81.1

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

   10. Applied egg-rr 81.1%

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

Alternative 14: 44.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.8 \cdot 10^{-102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-122}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.8e-102)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 3.8e-122)
     (* 180.0 (/ (atan 0.0) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.8e-102) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 3.8e-122) {
		tmp = 180.0 * (atan(0.0) / ((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 <= -2.8e-102) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 3.8e-122) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.8e-102:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 3.8e-122:
		tmp = 180.0 * (math.atan(0.0) / 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 <= -2.8e-102)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 3.8e-122)
		tmp = Float64(180.0 * Float64(atan(0.0) / 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 <= -2.8e-102)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 3.8e-122)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.8e-102], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.8e-122], N[(180.0 * N[(N[ArcTan[0.0], $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 < -2.80000000000000013e-102

   1. Initial program 58.5%

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

   3. Taylor expanded in B around -inf

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

   5. Simplified 44.9%

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

   if -2.80000000000000013e-102 < B < 3.8000000000000001e-122

   1. Initial program 54.5%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 31.4

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

   5. Simplified 31.4%

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

   if 3.8000000000000001e-122 < B

   1. Initial program 53.2%

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

   3. Taylor expanded in B around inf

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

   5. Simplified 42.8%

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

Alternative 15: 28.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 3 \cdot 10^{-119}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 3e-119) (* 180.0 (/ (atan 0.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 3e-119) {
		tmp = 180.0 * (atan(0.0) / ((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 <= 3e-119) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 3e-119:
		tmp = 180.0 * (math.atan(0.0) / 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 <= 3e-119)
		tmp = Float64(180.0 * Float64(atan(0.0) / 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 <= 3e-119)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 3e-119], N[(180.0 * N[(N[ArcTan[0.0], $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 < 3.0000000000000002e-119

   1. Initial program 56.8%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 15.7

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

   5. Simplified 15.7%

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

   if 3.0000000000000002e-119 < B

   1. Initial program 53.2%

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

   3. Taylor expanded in B around inf

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

   5. Simplified 42.8%

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

Alternative 16: 20.8% accurate, 3.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 55.6%

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

3. Taylor expanded in B around inf

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

5. Simplified 17.0%

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

Reproduce

herbie shell --seed 2024199 
(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)))