ABCF->ab-angle angle

Percentage Accurate: 54.5% → 85.4%

Time: 17.9s

Alternatives: 18

Speedup: 3.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.5% 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: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_1 \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \left(\frac{\frac{B \cdot \left(B \cdot 0.125\right)}{C - A}}{\left(C - A\right) \cdot \left(C - A\right)} + \frac{-0.5}{C - A}\right)\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (atan (/ (- C (+ A (hypot B (- C A)))) B)) (/ 180.0 PI)))
        (t_1
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_1 -0.5)
     t_0
     (if (<= t_1 0.0)
       (/
        (atan
         (*
          B
          (+
           (/ (/ (* B (* B 0.125)) (- C A)) (* (- C A) (- C A)))
           (/ -0.5 (- C A)))))
        (/ PI 180.0))
       t_0))))

C

double code(double A, double B, double C) {
	double t_0 = atan(((C - (A + hypot(B, (C - A)))) / B)) * (180.0 / ((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 <= -0.5) {
		tmp = t_0;
	} else if (t_1 <= 0.0) {
		tmp = atan((B * ((((B * (B * 0.125)) / (C - A)) / ((C - A) * (C - A))) + (-0.5 / (C - A))))) / (((double) M_PI) / 180.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = Math.atan(((C - (A + Math.hypot(B, (C - A)))) / B)) * (180.0 / 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 <= -0.5) {
		tmp = t_0;
	} else if (t_1 <= 0.0) {
		tmp = Math.atan((B * ((((B * (B * 0.125)) / (C - A)) / ((C - A) * (C - A))) + (-0.5 / (C - A))))) / (Math.PI / 180.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = math.atan(((C - (A + math.hypot(B, (C - A)))) / B)) * (180.0 / 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 <= -0.5:
		tmp = t_0
	elif t_1 <= 0.0:
		tmp = math.atan((B * ((((B * (B * 0.125)) / (C - A)) / ((C - A) * (C - A))) + (-0.5 / (C - A))))) / (math.pi / 180.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(C - A)))) / B)) * Float64(180.0 / 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 <= -0.5)
		tmp = t_0;
	elseif (t_1 <= 0.0)
		tmp = Float64(atan(Float64(B * Float64(Float64(Float64(Float64(B * Float64(B * 0.125)) / Float64(C - A)) / Float64(Float64(C - A) * Float64(C - A))) + Float64(-0.5 / Float64(C - A))))) / Float64(pi / 180.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = atan(((C - (A + hypot(B, (C - A)))) / B)) * (180.0 / pi);
	t_1 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_1 <= -0.5)
		tmp = t_0;
	elseif (t_1 <= 0.0)
		tmp = atan((B * ((((B * (B * 0.125)) / (C - A)) / ((C - A) * (C - A))) + (-0.5 / (C - A))))) / (pi / 180.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / 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, -0.5], t$95$0, If[LessEqual[t$95$1, 0.0], N[(N[ArcTan[N[(B * N[(N[(N[(N[(B * N[(B * 0.125), $MachinePrecision]), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision] / N[(N[(C - A), $MachinePrecision] * N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.5 / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $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)))))) < -0.5 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 65.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 87.8%

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

   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 15.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 10.8%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left({B}^{2} \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} - \frac{1}{2} \cdot \frac{1}{C - A}\right)\right)}, B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8} \cdot {B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8}}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8} \cdot 1}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({B}^{2}\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(B \cdot B\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(B, B\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(B, B\right), \mathsf{+.f64}\left(\left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2}\right), \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 76.5%

      \[\leadsto \tan^{-1} \left(\frac{\color{blue}{\left(B \cdot B\right) \cdot \left(\frac{0.125 \cdot \left(B \cdot B\right)}{\left(C - A\right) \cdot \left(\left(C - A\right) \cdot \left(C - A\right)\right)} + \frac{-0.5}{C - A}\right)}}{B}\right) \cdot \frac{180}{\pi} \]
   8. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \tan^{-1} \left(\frac{\left(B \cdot B\right) \cdot \left(\frac{\frac{1}{8} \cdot \left(B \cdot B\right)}{\left(C - A\right) \cdot \left(\left(C - A\right) \cdot \left(C - A\right)\right)} + \frac{\frac{-1}{2}}{C - A}\right)}{B}\right) \cdot \frac{1}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

      2. un-div-inv N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{\left(B \cdot B\right) \cdot \left(\frac{\frac{1}{8} \cdot \left(B \cdot B\right)}{\left(C - A\right) \cdot \left(\left(C - A\right) \cdot \left(C - A\right)\right)} + \frac{\frac{-1}{2}}{C - A}\right)}{B}\right)}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{\left(B \cdot B\right) \cdot \left(\frac{\frac{1}{8} \cdot \left(B \cdot B\right)}{\left(C - A\right) \cdot \left(\left(C - A\right) \cdot \left(C - A\right)\right)} + \frac{\frac{-1}{2}}{C - A}\right)}{B}\right), \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{180}\right)}\right) \]

   9. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(B \cdot \left(\frac{\frac{B \cdot \left(B \cdot 0.125\right)}{C - A}}{\left(C - A\right) \cdot \left(C - A\right)} + \frac{-0.5}{C - A}\right)\right)}{\frac{\pi}{180}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 79.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -7.6 \cdot 10^{+122}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-114}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -7.6e+122)
   (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
   (if (<= A 2.1e-114)
     (* (/ 180.0 PI) (atan (/ (- C (hypot C B)) B)))
     (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot A B))) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -7.6e+122) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else if (A <= 2.1e-114) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(C, B)) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(A, B))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -7.6e+122) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else if (A <= 2.1e-114) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(C, B)) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(A, B))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -7.6e+122:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	elif A <= 2.1e-114:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(C, B)) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(A, B))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -7.6e+122)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	elseif (A <= 2.1e-114)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(C, B)) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(A, B))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -7.6e+122)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	elseif (A <= 2.1e-114)
		tmp = (180.0 / pi) * atan(((C - hypot(C, B)) / B));
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(A, B))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -7.6e+122], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.1e-114], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -7.5999999999999996e122

   1. Initial program 11.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 22.4%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left({B}^{2} \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} - \frac{1}{2} \cdot \frac{1}{C - A}\right)\right)}, B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8} \cdot {B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8}}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8} \cdot 1}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({B}^{2}\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(B \cdot B\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(B, B\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(B, B\right), \mathsf{+.f64}\left(\left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2}\right), \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 68.6%

      \[\leadsto \tan^{-1} \left(\frac{\color{blue}{\left(B \cdot B\right) \cdot \left(\frac{0.125 \cdot \left(B \cdot B\right)}{\left(C - A\right) \cdot \left(\left(C - A\right) \cdot \left(C - A\right)\right)} + \frac{-0.5}{C - A}\right)}}{B}\right) \cdot \frac{180}{\pi} \]

   8. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), \left(C - A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), \left(C - A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), \left(C - A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 84.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), \mathsf{\_.f64}\left(C, A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 84.1%

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

   if -7.5999999999999996e122 < A < 2.09999999999999993e-114

   1. Initial program 57.5%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 80.2%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(C - \sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{{B}^{2} + {C}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{{C}^{2} + {B}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{C \cdot C + {B}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{C \cdot C + B \cdot B}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. hypot-define N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\mathsf{hypot}\left(C, B\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. hypot-lowering-hypot.f64 79.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \mathsf{hypot.f64}\left(C, B\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 79.2%

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

   if 2.09999999999999993e-114 < A

   1. Initial program 73.9%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 91.5%

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

   5. Taylor expanded in C around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \color{blue}{\left(A + \sqrt{{A}^{2} + {B}^{2}}\right)}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \mathsf{+.f64}\left(A, \left(\sqrt{{A}^{2} + {B}^{2}}\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \mathsf{+.f64}\left(A, \left(\sqrt{A \cdot A + {B}^{2}}\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \mathsf{+.f64}\left(A, \left(\sqrt{A \cdot A + B \cdot B}\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. hypot-define N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \mathsf{+.f64}\left(A, \left(\mathsf{hypot}\left(A, B\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. hypot-lowering-hypot.f64 87.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \mathsf{+.f64}\left(A, \mathsf{hypot.f64}\left(A, B\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 87.3%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7.6 \cdot 10^{+122}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-114}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1 \cdot 10^{+123}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq 8.4 \cdot 10^{-55}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1e+123)
   (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
   (if (<= A 8.4e-55)
     (* (/ 180.0 PI) (atan (/ (- C (hypot C B)) B)))
     (* (/ 180.0 PI) (atan (+ 1.0 (/ (- C A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1e+123) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else if (A <= 8.4e-55) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(C, B)) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1e+123) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else if (A <= 8.4e-55) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(C, B)) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1e+123:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	elif A <= 8.4e-55:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(C, B)) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 + ((C - A) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1e+123)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	elseif (A <= 8.4e-55)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(C, B)) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(Float64(C - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1e+123)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	elseif (A <= 8.4e-55)
		tmp = (180.0 / pi) * atan(((C - hypot(C, B)) / B));
	else
		tmp = (180.0 / pi) * atan((1.0 + ((C - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1e+123], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 8.4e-55], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -9.99999999999999978e122

   1. Initial program 11.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 22.4%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left({B}^{2} \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} - \frac{1}{2} \cdot \frac{1}{C - A}\right)\right)}, B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8} \cdot {B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8}}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8} \cdot 1}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({B}^{2}\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(B \cdot B\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(B, B\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(B, B\right), \mathsf{+.f64}\left(\left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2}\right), \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 68.6%

      \[\leadsto \tan^{-1} \left(\frac{\color{blue}{\left(B \cdot B\right) \cdot \left(\frac{0.125 \cdot \left(B \cdot B\right)}{\left(C - A\right) \cdot \left(\left(C - A\right) \cdot \left(C - A\right)\right)} + \frac{-0.5}{C - A}\right)}}{B}\right) \cdot \frac{180}{\pi} \]

   8. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), \left(C - A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), \left(C - A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), \left(C - A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 84.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), \mathsf{\_.f64}\left(C, A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 84.1%

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

   if -9.99999999999999978e122 < A < 8.4000000000000006e-55

   1. Initial program 57.9%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 80.8%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C - \sqrt{{B}^{2} + {C}^{2}}}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(C - \sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{{B}^{2} + {C}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{{C}^{2} + {B}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{C \cdot C + {B}^{2}}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{C \cdot C + B \cdot B}\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. hypot-define N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\mathsf{hypot}\left(C, B\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. hypot-lowering-hypot.f64 78.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \mathsf{hypot.f64}\left(C, B\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 78.7%

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

   if 8.4000000000000006e-55 < A

   1. Initial program 75.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 92.3%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \frac{C - A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C - A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 82.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 82.2%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1 \cdot 10^{+123}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq 8.4 \cdot 10^{-55}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 9 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-97}:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \left(\frac{\frac{B \cdot \left(B \cdot 0.125\right)}{C - A}}{\left(C - A\right) \cdot \left(C - A\right)} + \frac{-0.5}{C - A}\right)\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C \cdot \left(1 + \frac{C \cdot -0.5}{B}\right) - B}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 9e-189)
   (* (/ 180.0 PI) (atan (+ 1.0 (/ (- C A) B))))
   (if (<= B 1.25e-97)
     (/
      (atan
       (*
        B
        (+
         (/ (/ (* B (* B 0.125)) (- C A)) (* (- C A) (- C A)))
         (/ -0.5 (- C A)))))
      (/ PI 180.0))
     (/ 180.0 (/ PI (atan (/ (- (* C (+ 1.0 (/ (* C -0.5) B))) B) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 9e-189) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + ((C - A) / B)));
	} else if (B <= 1.25e-97) {
		tmp = atan((B * ((((B * (B * 0.125)) / (C - A)) / ((C - A) * (C - A))) + (-0.5 / (C - A))))) / (((double) M_PI) / 180.0);
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((C * (1.0 + ((C * -0.5) / B))) - B) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 9e-189) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + ((C - A) / B)));
	} else if (B <= 1.25e-97) {
		tmp = Math.atan((B * ((((B * (B * 0.125)) / (C - A)) / ((C - A) * (C - A))) + (-0.5 / (C - A))))) / (Math.PI / 180.0);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((C * (1.0 + ((C * -0.5) / B))) - B) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 9e-189:
		tmp = (180.0 / math.pi) * math.atan((1.0 + ((C - A) / B)))
	elif B <= 1.25e-97:
		tmp = math.atan((B * ((((B * (B * 0.125)) / (C - A)) / ((C - A) * (C - A))) + (-0.5 / (C - A))))) / (math.pi / 180.0)
	else:
		tmp = 180.0 / (math.pi / math.atan((((C * (1.0 + ((C * -0.5) / B))) - B) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 9e-189)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(Float64(C - A) / B))));
	elseif (B <= 1.25e-97)
		tmp = Float64(atan(Float64(B * Float64(Float64(Float64(Float64(B * Float64(B * 0.125)) / Float64(C - A)) / Float64(Float64(C - A) * Float64(C - A))) + Float64(-0.5 / Float64(C - A))))) / Float64(pi / 180.0));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C * Float64(1.0 + Float64(Float64(C * -0.5) / B))) - B) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 9e-189)
		tmp = (180.0 / pi) * atan((1.0 + ((C - A) / B)));
	elseif (B <= 1.25e-97)
		tmp = atan((B * ((((B * (B * 0.125)) / (C - A)) / ((C - A) * (C - A))) + (-0.5 / (C - A))))) / (pi / 180.0);
	else
		tmp = 180.0 / (pi / atan((((C * (1.0 + ((C * -0.5) / B))) - B) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 9e-189], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.25e-97], N[(N[ArcTan[N[(B * N[(N[(N[(N[(B * N[(B * 0.125), $MachinePrecision]), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision] / N[(N[(C - A), $MachinePrecision] * N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.5 / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C * N[(1.0 + N[(N[(C * -0.5), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 8.9999999999999992e-189

   1. Initial program 62.9%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 79.4%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \frac{C - A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C - A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 72.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 72.7%

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

   if 8.9999999999999992e-189 < B < 1.2499999999999999e-97

   1. Initial program 37.5%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 59.5%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left({B}^{2} \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} - \frac{1}{2} \cdot \frac{1}{C - A}\right)\right)}, B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8} \cdot {B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8}}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8} \cdot 1}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({B}^{2}\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(B \cdot B\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(B, B\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(B, B\right), \mathsf{+.f64}\left(\left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2}\right), \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 55.4%

      \[\leadsto \tan^{-1} \left(\frac{\color{blue}{\left(B \cdot B\right) \cdot \left(\frac{0.125 \cdot \left(B \cdot B\right)}{\left(C - A\right) \cdot \left(\left(C - A\right) \cdot \left(C - A\right)\right)} + \frac{-0.5}{C - A}\right)}}{B}\right) \cdot \frac{180}{\pi} \]
   8. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \tan^{-1} \left(\frac{\left(B \cdot B\right) \cdot \left(\frac{\frac{1}{8} \cdot \left(B \cdot B\right)}{\left(C - A\right) \cdot \left(\left(C - A\right) \cdot \left(C - A\right)\right)} + \frac{\frac{-1}{2}}{C - A}\right)}{B}\right) \cdot \frac{1}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

      2. un-div-inv N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{\left(B \cdot B\right) \cdot \left(\frac{\frac{1}{8} \cdot \left(B \cdot B\right)}{\left(C - A\right) \cdot \left(\left(C - A\right) \cdot \left(C - A\right)\right)} + \frac{\frac{-1}{2}}{C - A}\right)}{B}\right)}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

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

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{\left(B \cdot B\right) \cdot \left(\frac{\frac{1}{8} \cdot \left(B \cdot B\right)}{\left(C - A\right) \cdot \left(\left(C - A\right) \cdot \left(C - A\right)\right)} + \frac{\frac{-1}{2}}{C - A}\right)}{B}\right), \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{180}\right)}\right) \]

   9. Applied egg-rr 67.2%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(B \cdot \left(\frac{\frac{B \cdot \left(B \cdot 0.125\right)}{C - A}}{\left(C - A\right) \cdot \left(C - A\right)} + \frac{-0.5}{C - A}\right)\right)}{\frac{\pi}{180}}} \]

   if 1.2499999999999999e-97 < B

   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. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(\left(C - A\right) + \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. fma-define N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\mathsf{fma}\left(\frac{1}{B}, C - A, \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\left(\frac{1}{B}\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\left(\frac{1}{B}\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(0 - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. pow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \left(A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. --lowering--.f64 81.4%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   4. Applied egg-rr 81.4%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right) + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + -1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + \left(\mathsf{neg}\left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C}{B}\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1 \cdot \sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{\sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + C \cdot C}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\mathsf{hypot}\left(B, C\right)\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. hypot-lowering-hypot.f64 61.0%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\mathsf{hypot.f64}\left(B, C\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 61.0%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(180, \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{\tan^{-1} \left(\frac{C}{B} - \frac{\sqrt{B \cdot B + C \cdot C}}{B}\right)}\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI}\left(\right), \color{blue}{\tan^{-1} \left(\frac{C}{B} - \frac{\sqrt{B \cdot B + C \cdot C}}{B}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \tan^{-1} \color{blue}{\left(\frac{C}{B} - \frac{\sqrt{B \cdot B + C \cdot C}}{B}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\left(\frac{C}{B} - \frac{\sqrt{B \cdot B + C \cdot C}}{B}\right)\right)\right)\right) \]

      7. sub-div N/A

         \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\left(\frac{C - \sqrt{B \cdot B + C \cdot C}}{B}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(C - \sqrt{B \cdot B + C \cdot C}\right), B\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{B \cdot B + C \cdot C}\right)\right), B\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{C \cdot C + B \cdot B}\right)\right), B\right)\right)\right)\right) \]

      11. hypot-define N/A

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\mathsf{hypot}\left(C, B\right)\right)\right), B\right)\right)\right)\right) \]

      12. hypot-lowering-hypot.f64 61.0%

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \mathsf{hypot.f64}\left(C, B\right)\right), B\right)\right)\right)\right) \]

   9. Applied egg-rr 61.0%

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

   10. Taylor expanded in C around 0

       \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(C \cdot \left(1 + \frac{-1}{2} \cdot \frac{C}{B}\right) - B\right)}, B\right)\right)\right)\right) \]
   11. Step-by-step derivation

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

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(C \cdot \left(1 + \frac{-1}{2} \cdot \frac{C}{B}\right)\right), B\right), B\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(C, \left(1 + \frac{-1}{2} \cdot \frac{C}{B}\right)\right), B\right), B\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(C, \mathsf{+.f64}\left(1, \left(\frac{-1}{2} \cdot \frac{C}{B}\right)\right)\right), B\right), B\right)\right)\right)\right) \]

       4. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(C, \mathsf{+.f64}\left(1, \left(\frac{\frac{-1}{2} \cdot C}{B}\right)\right)\right), B\right), B\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(C, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot C\right), B\right)\right)\right), B\right), B\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(C, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C \cdot \frac{-1}{2}\right), B\right)\right)\right), B\right), B\right)\right)\right)\right) \]

       7. *-lowering-*.f64 67.3%

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(C, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(C, \frac{-1}{2}\right), B\right)\right)\right), B\right), B\right)\right)\right)\right) \]

   12. Simplified 67.3%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 9 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-97}:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \left(\frac{\frac{B \cdot \left(B \cdot 0.125\right)}{C - A}}{\left(C - A\right) \cdot \left(C - A\right)} + \frac{-0.5}{C - A}\right)\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C \cdot \left(1 + \frac{C \cdot -0.5}{B}\right) - B}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.9% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 9.5 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \mathbf{elif}\;B \leq 1.16 \cdot 10^{-98}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C \cdot \left(1 + \frac{C \cdot -0.5}{B}\right) - B}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 9.5e-189)
   (* (/ 180.0 PI) (atan (+ 1.0 (/ (- C A) B))))
   (if (<= B 1.16e-98)
     (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
     (/ 180.0 (/ PI (atan (/ (- (* C (+ 1.0 (/ (* C -0.5) B))) B) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 9.5e-189) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + ((C - A) / B)));
	} else if (B <= 1.16e-98) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((C * (1.0 + ((C * -0.5) / B))) - B) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 9.5e-189) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + ((C - A) / B)));
	} else if (B <= 1.16e-98) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((C * (1.0 + ((C * -0.5) / B))) - B) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 9.5e-189:
		tmp = (180.0 / math.pi) * math.atan((1.0 + ((C - A) / B)))
	elif B <= 1.16e-98:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	else:
		tmp = 180.0 / (math.pi / math.atan((((C * (1.0 + ((C * -0.5) / B))) - B) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 9.5e-189)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(Float64(C - A) / B))));
	elseif (B <= 1.16e-98)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C * Float64(1.0 + Float64(Float64(C * -0.5) / B))) - B) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 9.5e-189)
		tmp = (180.0 / pi) * atan((1.0 + ((C - A) / B)));
	elseif (B <= 1.16e-98)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	else
		tmp = 180.0 / (pi / atan((((C * (1.0 + ((C * -0.5) / B))) - B) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 9.5e-189], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.16e-98], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C * N[(1.0 + N[(N[(C * -0.5), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 9.499999999999999e-189

   1. Initial program 62.9%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 79.4%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \frac{C - A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C - A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 72.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 72.7%

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

   if 9.499999999999999e-189 < B < 1.15999999999999994e-98

   1. Initial program 37.5%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 59.5%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left({B}^{2} \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} - \frac{1}{2} \cdot \frac{1}{C - A}\right)\right)}, B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8} \cdot {B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8}}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8} \cdot 1}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({B}^{2}\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(B \cdot B\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(B, B\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(B, B\right), \mathsf{+.f64}\left(\left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2}\right), \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 55.4%

      \[\leadsto \tan^{-1} \left(\frac{\color{blue}{\left(B \cdot B\right) \cdot \left(\frac{0.125 \cdot \left(B \cdot B\right)}{\left(C - A\right) \cdot \left(\left(C - A\right) \cdot \left(C - A\right)\right)} + \frac{-0.5}{C - A}\right)}}{B}\right) \cdot \frac{180}{\pi} \]

   8. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), \left(C - A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), \left(C - A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), \left(C - A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 67.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), \mathsf{\_.f64}\left(C, A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 67.1%

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

   if 1.15999999999999994e-98 < B

   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. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(\left(C - A\right) + \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. fma-define N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\mathsf{fma}\left(\frac{1}{B}, C - A, \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\left(\frac{1}{B}\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\left(\frac{1}{B}\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(0 - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. pow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \left(A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. --lowering--.f64 81.4%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   4. Applied egg-rr 81.4%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right) + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + -1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + \left(\mathsf{neg}\left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C}{B}\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1 \cdot \sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{\sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + C \cdot C}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\mathsf{hypot}\left(B, C\right)\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. hypot-lowering-hypot.f64 61.0%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\mathsf{hypot.f64}\left(B, C\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 61.0%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(180, \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{\tan^{-1} \left(\frac{C}{B} - \frac{\sqrt{B \cdot B + C \cdot C}}{B}\right)}\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI}\left(\right), \color{blue}{\tan^{-1} \left(\frac{C}{B} - \frac{\sqrt{B \cdot B + C \cdot C}}{B}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \tan^{-1} \color{blue}{\left(\frac{C}{B} - \frac{\sqrt{B \cdot B + C \cdot C}}{B}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\left(\frac{C}{B} - \frac{\sqrt{B \cdot B + C \cdot C}}{B}\right)\right)\right)\right) \]

      7. sub-div N/A

         \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\left(\frac{C - \sqrt{B \cdot B + C \cdot C}}{B}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(C - \sqrt{B \cdot B + C \cdot C}\right), B\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{B \cdot B + C \cdot C}\right)\right), B\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\sqrt{C \cdot C + B \cdot B}\right)\right), B\right)\right)\right)\right) \]

      11. hypot-define N/A

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \left(\mathsf{hypot}\left(C, B\right)\right)\right), B\right)\right)\right)\right) \]

      12. hypot-lowering-hypot.f64 61.0%

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \mathsf{hypot.f64}\left(C, B\right)\right), B\right)\right)\right)\right) \]

   9. Applied egg-rr 61.0%

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

   10. Taylor expanded in C around 0

       \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(C \cdot \left(1 + \frac{-1}{2} \cdot \frac{C}{B}\right) - B\right)}, B\right)\right)\right)\right) \]
   11. Step-by-step derivation

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

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(C \cdot \left(1 + \frac{-1}{2} \cdot \frac{C}{B}\right)\right), B\right), B\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(C, \left(1 + \frac{-1}{2} \cdot \frac{C}{B}\right)\right), B\right), B\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(C, \mathsf{+.f64}\left(1, \left(\frac{-1}{2} \cdot \frac{C}{B}\right)\right)\right), B\right), B\right)\right)\right)\right) \]

       4. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(C, \mathsf{+.f64}\left(1, \left(\frac{\frac{-1}{2} \cdot C}{B}\right)\right)\right), B\right), B\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(C, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot C\right), B\right)\right)\right), B\right), B\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(C, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C \cdot \frac{-1}{2}\right), B\right)\right)\right), B\right), B\right)\right)\right)\right) \]

       7. *-lowering-*.f64 67.3%

          \[\leadsto \mathsf{/.f64}\left(180, \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(C, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(C, \frac{-1}{2}\right), B\right)\right)\right), B\right), B\right)\right)\right)\right) \]

   12. Simplified 67.3%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 9.5 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \mathbf{elif}\;B \leq 1.16 \cdot 10^{-98}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C \cdot \left(1 + \frac{C \cdot -0.5}{B}\right) - B}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.0% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{-261}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.5e-27)
   (* (/ 180.0 PI) (atan (/ (* B -0.5) (- C A))))
   (if (<= A -2.8e-168)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (if (<= A 1.05e-261)
       (* (/ 180.0 PI) (atan (/ (- C B) B)))
       (* (/ 180.0 PI) (atan (+ 1.0 (/ (- C A) B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.5e-27) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / (C - A)));
	} else if (A <= -2.8e-168) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (A <= 1.05e-261) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.5e-27) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / (C - A)));
	} else if (A <= -2.8e-168) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (A <= 1.05e-261) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.5e-27:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / (C - A)))
	elif A <= -2.8e-168:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif A <= 1.05e-261:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 + ((C - A) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.5e-27)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / Float64(C - A))));
	elseif (A <= -2.8e-168)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (A <= 1.05e-261)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(Float64(C - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.5e-27)
		tmp = (180.0 / pi) * atan(((B * -0.5) / (C - A)));
	elseif (A <= -2.8e-168)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (A <= 1.05e-261)
		tmp = (180.0 / pi) * atan(((C - B) / B));
	else
		tmp = (180.0 / pi) * atan((1.0 + ((C - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.5e-27], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.8e-168], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.05e-261], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -4.5000000000000002e-27

   1. Initial program 25.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 43.7%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left({B}^{2} \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} - \frac{1}{2} \cdot \frac{1}{C - A}\right)\right)}, B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8} \cdot {B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8}}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8} \cdot 1}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({B}^{2}\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(B \cdot B\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(B, B\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(B, B\right), \mathsf{+.f64}\left(\left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2}\right), \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 51.0%

      \[\leadsto \tan^{-1} \left(\frac{\color{blue}{\left(B \cdot B\right) \cdot \left(\frac{0.125 \cdot \left(B \cdot B\right)}{\left(C - A\right) \cdot \left(\left(C - A\right) \cdot \left(C - A\right)\right)} + \frac{-0.5}{C - A}\right)}}{B}\right) \cdot \frac{180}{\pi} \]

   8. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), \left(C - A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), \left(C - A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), \left(C - A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 65.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), \mathsf{\_.f64}\left(C, A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 65.8%

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

   if -4.5000000000000002e-27 < A < -2.8000000000000002e-168

   1. Initial program 77.4%

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

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(\left(C - A\right) + \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. fma-define N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\mathsf{fma}\left(\frac{1}{B}, C - A, \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\left(\frac{1}{B}\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\left(\frac{1}{B}\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(0 - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. pow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \left(A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. --lowering--.f64 85.8%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   4. Applied egg-rr 85.8%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right) + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + -1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + \left(\mathsf{neg}\left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C}{B}\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1 \cdot \sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{\sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + C \cdot C}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\mathsf{hypot}\left(B, C\right)\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. hypot-lowering-hypot.f64 85.6%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\mathsf{hypot.f64}\left(B, C\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 85.6%

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

   8. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{C}{B}\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. /-lowering-/.f64 78.5%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(C, B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 78.5%

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

   if -2.8000000000000002e-168 < A < 1.04999999999999998e-261

   1. Initial program 52.3%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 88.2%

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

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \color{blue}{B}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 61.0%

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

   if 1.04999999999999998e-261 < A

   1. Initial program 74.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 90.9%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \frac{C - A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C - A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 76.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 76.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.05 \cdot 10^{-261}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.0% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.1 \cdot 10^{-27}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-172}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{-261}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.1e-27)
   (* (/ 180.0 PI) (atan (* -0.5 (/ B (- C A)))))
   (if (<= A -2e-172)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (if (<= A 1e-261)
       (* (/ 180.0 PI) (atan (/ (- C B) B)))
       (* (/ 180.0 PI) (atan (+ 1.0 (/ (- C A) B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.1e-27) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / (C - A))));
	} else if (A <= -2e-172) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (A <= 1e-261) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.1e-27) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / (C - A))));
	} else if (A <= -2e-172) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (A <= 1e-261) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + ((C - A) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.1e-27:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / (C - A))))
	elif A <= -2e-172:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif A <= 1e-261:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 + ((C - A) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.1e-27)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / Float64(C - A)))));
	elseif (A <= -2e-172)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (A <= 1e-261)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(Float64(C - A) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.1e-27)
		tmp = (180.0 / pi) * atan((-0.5 * (B / (C - A))));
	elseif (A <= -2e-172)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (A <= 1e-261)
		tmp = (180.0 / pi) * atan(((C - B) / B));
	else
		tmp = (180.0 / pi) * atan((1.0 + ((C - A) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.1e-27], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2e-172], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1e-261], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.09999999999999993e-27

   1. Initial program 25.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 43.7%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \left(\frac{B}{C - A}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{/.f64}\left(B, \left(C - A\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. --lowering--.f64 65.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{/.f64}\left(B, \mathsf{\_.f64}\left(C, A\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 65.8%

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

   if -1.09999999999999993e-27 < A < -2.0000000000000001e-172

   1. Initial program 77.4%

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

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(\left(C - A\right) + \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. fma-define N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\mathsf{fma}\left(\frac{1}{B}, C - A, \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\left(\frac{1}{B}\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\left(\frac{1}{B}\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(0 - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. pow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \left(A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. --lowering--.f64 85.8%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   4. Applied egg-rr 85.8%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right) + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + -1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + \left(\mathsf{neg}\left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C}{B}\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1 \cdot \sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{\sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + C \cdot C}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\mathsf{hypot}\left(B, C\right)\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. hypot-lowering-hypot.f64 85.6%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\mathsf{hypot.f64}\left(B, C\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 85.6%

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

   8. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{C}{B}\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. /-lowering-/.f64 78.5%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(C, B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 78.5%

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

   if -2.0000000000000001e-172 < A < 9.99999999999999984e-262

   1. Initial program 52.3%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 88.2%

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

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \color{blue}{B}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 61.0%

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

   if 9.99999999999999984e-262 < A

   1. Initial program 74.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 90.9%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \frac{C - A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C - A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 76.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 76.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.1 \cdot 10^{-27}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq -2 \cdot 10^{-172}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 10^{-261}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.6% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6 \cdot 10^{-28}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.65 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6e-28)
   (* (/ 180.0 PI) (atan (* -0.5 (/ B (- C A)))))
   (if (<= A -2.8e-183)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (if (<= A 1.65e-189)
       (* (/ 180.0 PI) (atan (/ (- C B) B)))
       (* (/ 180.0 PI) (atan (- 1.0 (/ A B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6e-28) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / (C - A))));
	} else if (A <= -2.8e-183) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (A <= 1.65e-189) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6e-28) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / (C - A))));
	} else if (A <= -2.8e-183) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (A <= 1.65e-189) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6e-28:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / (C - A))))
	elif A <= -2.8e-183:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif A <= 1.65e-189:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6e-28)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / Float64(C - A)))));
	elseif (A <= -2.8e-183)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (A <= 1.65e-189)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6e-28)
		tmp = (180.0 / pi) * atan((-0.5 * (B / (C - A))));
	elseif (A <= -2.8e-183)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (A <= 1.65e-189)
		tmp = (180.0 / pi) * atan(((C - B) / B));
	else
		tmp = (180.0 / pi) * atan((1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6e-28], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.8e-183], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.65e-189], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -6.00000000000000005e-28

   1. Initial program 25.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 43.7%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C - A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \left(\frac{B}{C - A}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{/.f64}\left(B, \left(C - A\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. --lowering--.f64 65.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{/.f64}\left(B, \mathsf{\_.f64}\left(C, A\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 65.8%

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

   if -6.00000000000000005e-28 < A < -2.79999999999999985e-183

   1. Initial program 77.4%

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

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(\left(C - A\right) + \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. fma-define N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\mathsf{fma}\left(\frac{1}{B}, C - A, \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\left(\frac{1}{B}\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\left(\frac{1}{B}\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(0 - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. pow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \left(A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. --lowering--.f64 85.8%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   4. Applied egg-rr 85.8%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right) + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + -1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + \left(\mathsf{neg}\left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C}{B}\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1 \cdot \sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{\sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + C \cdot C}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\mathsf{hypot}\left(B, C\right)\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. hypot-lowering-hypot.f64 85.6%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\mathsf{hypot.f64}\left(B, C\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 85.6%

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

   8. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{C}{B}\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. /-lowering-/.f64 78.5%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(C, B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 78.5%

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

   if -2.79999999999999985e-183 < A < 1.65e-189

   1. Initial program 61.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 89.7%

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

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \color{blue}{B}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 60.5%

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

   if 1.65e-189 < A

   1. Initial program 72.9%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 90.5%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + -1 \cdot \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\mathsf{neg}\left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 - \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 41.7%

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

   8. Taylor expanded in C around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{A + \frac{-1}{2} \cdot \frac{{A}^{2}}{B}}{B}\right)}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(A + \frac{-1}{2} \cdot \frac{{A}^{2}}{B}\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \left(\frac{-1}{2} \cdot \frac{{A}^{2}}{B}\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \left(\frac{\frac{-1}{2} \cdot {A}^{2}}{B}\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot {A}^{2}\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \left({A}^{2}\right)\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \left(A \cdot A\right)\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lowering-*.f64 39.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(A, A\right)\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 39.7%

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

   11. Taylor expanded in A around 0

       \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + -1 \cdot \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\mathsf{neg}\left(\frac{A}{B}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 - \frac{A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

       4. /-lowering-/.f64 72.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(A, B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   13. Simplified 72.5%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6 \cdot 10^{-28}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.65 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3300000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-164}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.95 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3300000.0)
   (* (/ 180.0 PI) (atan (/ (* B 0.5) A)))
   (if (<= A -2.8e-164)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (if (<= A 1.95e-189)
       (* (/ 180.0 PI) (atan (/ (- C B) B)))
       (* (/ 180.0 PI) (atan (- 1.0 (/ A B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3300000.0) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * 0.5) / A));
	} else if (A <= -2.8e-164) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (A <= 1.95e-189) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3300000.0) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * 0.5) / A));
	} else if (A <= -2.8e-164) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (A <= 1.95e-189) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3300000.0:
		tmp = (180.0 / math.pi) * math.atan(((B * 0.5) / A))
	elif A <= -2.8e-164:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif A <= 1.95e-189:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3300000.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * 0.5) / A)));
	elseif (A <= -2.8e-164)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (A <= 1.95e-189)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3300000.0)
		tmp = (180.0 / pi) * atan(((B * 0.5) / A));
	elseif (A <= -2.8e-164)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (A <= 1.95e-189)
		tmp = (180.0 / pi) * atan(((C - B) / B));
	else
		tmp = (180.0 / pi) * atan((1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3300000.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -2.8e-164], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.95e-189], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -3.3e6

   1. Initial program 23.3%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 43.7%

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

   5. Taylor expanded in A around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{1}{2} \cdot B}{A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot B\right), A\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-lowering-*.f64 63.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, B\right), A\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 63.2%

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

   if -3.3e6 < A < -2.8000000000000001e-164

   1. Initial program 70.8%

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

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(\left(C - A\right) + \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. fma-define N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\mathsf{fma}\left(\frac{1}{B}, C - A, \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\left(\frac{1}{B}\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\left(\frac{1}{B}\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(0 - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. pow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \left(A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. --lowering--.f64 76.9%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   4. Applied egg-rr 76.9%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right) + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + -1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + \left(\mathsf{neg}\left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C}{B}\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1 \cdot \sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{\sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + C \cdot C}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\mathsf{hypot}\left(B, C\right)\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. hypot-lowering-hypot.f64 77.3%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\mathsf{hypot.f64}\left(B, C\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 77.3%

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

   8. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{C}{B}\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. /-lowering-/.f64 71.2%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(C, B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 71.2%

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

   if -2.8000000000000001e-164 < A < 1.95000000000000012e-189

   1. Initial program 61.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 89.7%

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

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \color{blue}{B}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 60.5%

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

   if 1.95000000000000012e-189 < A

   1. Initial program 72.9%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 90.5%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + -1 \cdot \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\mathsf{neg}\left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 - \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 41.7%

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

   8. Taylor expanded in C around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{A + \frac{-1}{2} \cdot \frac{{A}^{2}}{B}}{B}\right)}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(A + \frac{-1}{2} \cdot \frac{{A}^{2}}{B}\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \left(\frac{-1}{2} \cdot \frac{{A}^{2}}{B}\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \left(\frac{\frac{-1}{2} \cdot {A}^{2}}{B}\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot {A}^{2}\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \left({A}^{2}\right)\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \left(A \cdot A\right)\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lowering-*.f64 39.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(A, A\right)\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 39.7%

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

   11. Taylor expanded in A around 0

       \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + -1 \cdot \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\mathsf{neg}\left(\frac{A}{B}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 - \frac{A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

       4. /-lowering-/.f64 72.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(A, B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   13. Simplified 72.5%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3300000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq -2.8 \cdot 10^{-164}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.95 \cdot 10^{-189}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -9 \cdot 10^{+40}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 7.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -9e+40)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= C 7.2e+55)
     (* (/ 180.0 PI) (atan (- 1.0 (/ A B))))
     (* (/ 180.0 PI) (atan (/ (* B -0.5) C))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -9e+40) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (C <= 7.2e+55) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 - (A / B)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -9e+40) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (C <= 7.2e+55) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 - (A / B)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -9e+40:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif C <= 7.2e+55:
		tmp = (180.0 / math.pi) * math.atan((1.0 - (A / B)))
	else:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -9e+40)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (C <= 7.2e+55)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - Float64(A / B))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -9e+40)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (C <= 7.2e+55)
		tmp = (180.0 / pi) * atan((1.0 - (A / B)));
	else
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -9e+40], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 7.2e+55], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -9.00000000000000064e40

   1. Initial program 80.9%

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

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(\left(C - A\right) + \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. fma-define N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\mathsf{fma}\left(\frac{1}{B}, C - A, \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\left(\frac{1}{B}\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\left(\frac{1}{B}\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(0 - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. pow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \left(A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. --lowering--.f64 94.1%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   4. Applied egg-rr 94.1%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right) + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + -1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + \left(\mathsf{neg}\left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C}{B}\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1 \cdot \sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{\sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + C \cdot C}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\mathsf{hypot}\left(B, C\right)\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. hypot-lowering-hypot.f64 94.2%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\mathsf{hypot.f64}\left(B, C\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 94.2%

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

   8. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{C}{B}\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. /-lowering-/.f64 90.1%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(C, B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 90.1%

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

   if -9.00000000000000064e40 < C < 7.19999999999999975e55

   1. Initial program 62.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 79.9%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + -1 \cdot \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\mathsf{neg}\left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 - \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 39.6%

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

   8. Taylor expanded in C around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{A + \frac{-1}{2} \cdot \frac{{A}^{2}}{B}}{B}\right)}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(A + \frac{-1}{2} \cdot \frac{{A}^{2}}{B}\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \left(\frac{-1}{2} \cdot \frac{{A}^{2}}{B}\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \left(\frac{\frac{-1}{2} \cdot {A}^{2}}{B}\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot {A}^{2}\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \left({A}^{2}\right)\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \left(A \cdot A\right)\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lowering-*.f64 37.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(A, A\right)\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 37.3%

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

   11. Taylor expanded in A around 0

       \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + -1 \cdot \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\mathsf{neg}\left(\frac{A}{B}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 - \frac{A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

       4. /-lowering-/.f64 56.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(A, B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   13. Simplified 56.1%

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

   if 7.19999999999999975e55 < C

   1. Initial program 23.3%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 57.1%

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

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left({B}^{2} \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} - \frac{1}{2} \cdot \frac{1}{C - A}\right)\right)}, B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8} \cdot {B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8}}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\frac{\frac{1}{8} \cdot 1}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left({B}^{2} \cdot \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left({B}^{2}\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(B \cdot B\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(B, B\right), \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(B, B\right), \mathsf{+.f64}\left(\left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2}\right), \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 62.4%

      \[\leadsto \tan^{-1} \left(\frac{\color{blue}{\left(B \cdot B\right) \cdot \left(\frac{0.125 \cdot \left(B \cdot B\right)}{\left(C - A\right) \cdot \left(\left(C - A\right) \cdot \left(C - A\right)\right)} + \frac{-0.5}{C - A}\right)}}{B}\right) \cdot \frac{180}{\pi} \]

   8. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), C\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), C\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. *-lowering-*.f64 74.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 74.5%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -9 \cdot 10^{+40}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 7.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -780000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -780000000.0)
   (* (/ 180.0 PI) (atan (/ (* B 0.5) A)))
   (if (<= A 6.8e-109)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* (/ 180.0 PI) (atan (- 1.0 (/ A B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -780000000.0) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * 0.5) / A));
	} else if (A <= 6.8e-109) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -780000000.0) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * 0.5) / A));
	} else if (A <= 6.8e-109) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -780000000.0:
		tmp = (180.0 / math.pi) * math.atan(((B * 0.5) / A))
	elif A <= 6.8e-109:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -780000000.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * 0.5) / A)));
	elseif (A <= 6.8e-109)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -780000000.0)
		tmp = (180.0 / pi) * atan(((B * 0.5) / A));
	elseif (A <= 6.8e-109)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = (180.0 / pi) * atan((1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -780000000.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6.8e-109], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -7.8e8

   1. Initial program 23.3%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 43.7%

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

   5. Taylor expanded in A around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{1}{2} \cdot B}{A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot B\right), A\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-lowering-*.f64 63.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, B\right), A\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 63.2%

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

   if -7.8e8 < A < 6.80000000000000023e-109

   1. Initial program 65.6%

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

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(\left(C - A\right) + \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. fma-define N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\mathsf{fma}\left(\frac{1}{B}, C - A, \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\left(\frac{1}{B}\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\left(\frac{1}{B}\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(0 - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. pow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \left(A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. --lowering--.f64 80.1%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   4. Applied egg-rr 80.1%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right) + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + -1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + \left(\mathsf{neg}\left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C}{B}\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1 \cdot \sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{\sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + C \cdot C}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\mathsf{hypot}\left(B, C\right)\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. hypot-lowering-hypot.f64 78.7%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\mathsf{hypot.f64}\left(B, C\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 78.7%

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

   8. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{C}{B}\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. /-lowering-/.f64 56.4%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(C, B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 56.4%

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

   if 6.80000000000000023e-109 < A

   1. Initial program 73.3%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 91.3%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + -1 \cdot \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\mathsf{neg}\left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 - \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 40.4%

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

   8. Taylor expanded in C around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{A + \frac{-1}{2} \cdot \frac{{A}^{2}}{B}}{B}\right)}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(A + \frac{-1}{2} \cdot \frac{{A}^{2}}{B}\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \left(\frac{-1}{2} \cdot \frac{{A}^{2}}{B}\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \left(\frac{\frac{-1}{2} \cdot {A}^{2}}{B}\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot {A}^{2}\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \left({A}^{2}\right)\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \left(A \cdot A\right)\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lowering-*.f64 38.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(A, A\right)\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 38.7%

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

   11. Taylor expanded in A around 0

       \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + -1 \cdot \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\mathsf{neg}\left(\frac{A}{B}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 - \frac{A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

       4. /-lowering-/.f64 77.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(A, B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   13. Simplified 77.0%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -780000000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 6.8 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -225000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9.2 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -225000000.0)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 9.2e-109)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* (/ 180.0 PI) (atan (- 1.0 (/ A B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -225000000.0) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 9.2e-109) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -225000000.0) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 9.2e-109) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -225000000.0:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 9.2e-109:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -225000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 9.2e-109)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -225000000.0)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 9.2e-109)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = (180.0 / pi) * atan((1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -225000000.0], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9.2e-109], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.25e8

   1. Initial program 23.3%

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

   3. Taylor expanded in A around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{1}{2} \cdot B}{A}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot B\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-lowering-*.f64 63.2%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, B\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 63.2%

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

   if -2.25e8 < A < 9.2000000000000006e-109

   1. Initial program 65.6%

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

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(\left(C - A\right) + \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. fma-define N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\mathsf{fma}\left(\frac{1}{B}, C - A, \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\left(\frac{1}{B}\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\left(\frac{1}{B}\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(0 - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. pow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \left(A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. --lowering--.f64 80.1%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   4. Applied egg-rr 80.1%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right) + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + -1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + \left(\mathsf{neg}\left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C}{B}\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1 \cdot \sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{\sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + C \cdot C}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\mathsf{hypot}\left(B, C\right)\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. hypot-lowering-hypot.f64 78.7%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\mathsf{hypot.f64}\left(B, C\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 78.7%

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

   8. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{C}{B}\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. /-lowering-/.f64 56.4%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(C, B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 56.4%

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

   if 9.2000000000000006e-109 < A

   1. Initial program 73.3%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 91.3%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + -1 \cdot \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\mathsf{neg}\left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 - \frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot \left(C - A\right) + \frac{-1}{2} \cdot \frac{{\left(C - A\right)}^{2}}{B}\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 40.4%

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

   8. Taylor expanded in C around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{A + \frac{-1}{2} \cdot \frac{{A}^{2}}{B}}{B}\right)}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(A + \frac{-1}{2} \cdot \frac{{A}^{2}}{B}\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \left(\frac{-1}{2} \cdot \frac{{A}^{2}}{B}\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \left(\frac{\frac{-1}{2} \cdot {A}^{2}}{B}\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot {A}^{2}\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \left({A}^{2}\right)\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \left(A \cdot A\right)\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lowering-*.f64 38.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(A, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{*.f64}\left(A, A\right)\right), B\right)\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 38.7%

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

   11. Taylor expanded in A around 0

       \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + -1 \cdot \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\mathsf{neg}\left(\frac{A}{B}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(1 - \frac{A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \left(\frac{A}{B}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

       4. /-lowering-/.f64 77.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(A, B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   13. Simplified 77.0%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -225000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 9.2 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 3.1 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 3.1e-168)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= B 7e+19)
     (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 3.1e-168) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (B <= 7e+19) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 3.1e-168) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (B <= 7e+19) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 3.1e-168:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif B <= 7e+19:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 3.1e-168)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (B <= 7e+19)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 3.1e-168)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (B <= 7e+19)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 3.1e-168], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7e+19], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 3.1e-168

   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

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(\left(C - A\right) + \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. fma-define N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\mathsf{fma}\left(\frac{1}{B}, C - A, \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\left(\frac{1}{B}\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\left(\frac{1}{B}\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(0 - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. pow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \left(A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. --lowering--.f64 74.3%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   4. Applied egg-rr 74.3%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right) + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + -1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + \left(\mathsf{neg}\left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C}{B}\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1 \cdot \sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{\sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + C \cdot C}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\mathsf{hypot}\left(B, C\right)\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. hypot-lowering-hypot.f64 62.4%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\mathsf{hypot.f64}\left(B, C\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 62.4%

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

   8. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{C}{B}\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. /-lowering-/.f64 58.9%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(C, B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 58.9%

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

   if 3.1e-168 < B < 7e19

   1. Initial program 53.3%

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

   3. Taylor expanded in A around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{1}{2} \cdot B}{A}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot B\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-lowering-*.f64 36.2%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, B\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 36.2%

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

   if 7e19 < B

   1. Initial program 53.6%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 88.2%

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

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{-1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 62.1%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 3.1 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{+19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.7% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.8 \cdot 10^{-85}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 5.3 \cdot 10^{-108}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.8e-85)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 5.3e-108)
     (* (/ 180.0 PI) (atan (/ C B)))
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.8e-85) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 5.3e-108) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.8e-85) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 5.3e-108) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5.8e-85:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 5.3e-108:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5.8e-85)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 5.3e-108)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5.8e-85)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 5.3e-108)
		tmp = (180.0 / pi) * atan((C / B));
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5.8e-85], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.3e-108], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -5.8000000000000004e-85

   1. Initial program 56.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 80.7%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 60.7%

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

   if -5.8000000000000004e-85 < B < 5.29999999999999989e-108

   1. Initial program 66.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 75.7%

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

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \color{blue}{B}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 43.5%

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

   8. Taylor expanded in C around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 41.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(C, B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 41.6%

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

   if 5.29999999999999989e-108 < B

   1. Initial program 54.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 79.3%

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

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{-1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 50.4%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.8 \cdot 10^{-85}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 5.3 \cdot 10^{-108}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 44.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.1 \cdot 10^{-175}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-98}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.1e-175)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 1.35e-98)
     (* 180.0 (/ (atan 0.0) PI))
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.1e-175) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 1.35e-98) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.1e-175) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 1.35e-98) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.1e-175:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 1.35e-98:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.1e-175)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 1.35e-98)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.1e-175)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 1.35e-98)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.1e-175], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.35e-98], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.1e-175

   1. Initial program 58.7%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 78.5%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 52.6%

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

   if -1.1e-175 < B < 1.3499999999999999e-98

   1. Initial program 61.7%

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

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(\left(C - A\right) + \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. fma-define N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\mathsf{fma}\left(\frac{1}{B}, C - A, \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\left(\frac{1}{B}\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\left(\frac{1}{B}\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(0 - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. pow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \left(A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. --lowering--.f64 59.8%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   4. Applied egg-rr 59.8%

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

   5. Taylor expanded in A around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \frac{C}{B} + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. distribute-lft1-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\left(-1 + 1\right) \cdot \frac{C}{B}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(0 \cdot \frac{C}{B}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. mul0-lft 29.5%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(0\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 29.5%

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

   if 1.3499999999999999e-98 < B

   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. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 81.8%

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

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{-1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 52.7%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.1 \cdot 10^{-175}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-98}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 52.3% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.9 \cdot 10^{-105}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.9e-105)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (* (/ 180.0 PI) (atan -1.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.9e-105) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.9e-105) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 1.9e-105:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 1.9e-105)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 1.9e-105)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 1.9e-105], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 1.8999999999999999e-105

   1. Initial program 61.2%

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

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(\left(C - A\right) + \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. fma-define N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\mathsf{fma}\left(\frac{1}{B}, C - A, \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\left(\frac{1}{B}\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\left(\frac{1}{B}\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(0 - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. pow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \left(A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. --lowering--.f64 72.3%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   4. Applied egg-rr 72.3%

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

   5. Taylor expanded in A around 0

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right) + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + -1 \cdot \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + \left(\mathsf{neg}\left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C}{B}\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1}{B} \cdot \sqrt{{B}^{2} + {C}^{2}}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{1 \cdot \sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \left(\frac{\sqrt{{B}^{2} + {C}^{2}}}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{{B}^{2} + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + {C}^{2}}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\sqrt{B \cdot B + C \cdot C}\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\left(\mathsf{hypot}\left(B, C\right)\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. hypot-lowering-hypot.f64 60.4%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(C, B\right), \mathsf{/.f64}\left(\mathsf{hypot.f64}\left(B, C\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 60.4%

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

   8. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(1 + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} + 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{C}{B}\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. /-lowering-/.f64 56.3%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(C, B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 56.3%

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

   if 1.8999999999999999e-105 < B

   1. Initial program 54.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 79.3%

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

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{-1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 50.4%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.9 \cdot 10^{-105}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 6.3 \cdot 10^{-99}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 6.3e-99) (* 180.0 (/ (atan 0.0) PI)) (* (/ 180.0 PI) (atan -1.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 6.3e-99) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 6.3e-99) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 6.3e-99:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 6.3e-99)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 6.3e-99)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 6.3e-99], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 6.29999999999999992e-99

   1. Initial program 59.9%

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

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(\left(C - A\right) + \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. fma-define N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\mathsf{fma}\left(\frac{1}{B}, C - A, \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\left(\frac{1}{B}\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\left(\frac{1}{B}\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(0 - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. pow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. hypot-define N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \left(A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. --lowering--.f64 70.8%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   4. Applied egg-rr 70.8%

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

   5. Taylor expanded in A around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \frac{C}{B} + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. distribute-lft1-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\left(-1 + 1\right) \cdot \frac{C}{B}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(0 \cdot \frac{C}{B}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. mul0-lft 15.6%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(0\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 15.6%

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

   if 6.29999999999999992e-99 < B

   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. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 81.8%

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

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{-1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 52.7%

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

4. Final simplification 26.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 6.3 \cdot 10^{-99}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 12.9% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ 180 \cdot \frac{\tan^{-1} 0}{\pi} \end{array} \]

FPCore

(FPCore (A B C) :precision binary64 (* 180.0 (/ (atan 0.0) PI)))

C

double code(double A, double B, double C) {
	return 180.0 * (atan(0.0) / ((double) M_PI));
}

Java

public static double code(double A, double B, double C) {
	return 180.0 * (Math.atan(0.0) / Math.PI);
}

Python

def code(A, B, C):
	return 180.0 * (math.atan(0.0) / math.pi)

Julia

function code(A, B, C)
	return Float64(180.0 * Float64(atan(0.0) / pi))
end

MATLAB

function tmp = code(A, B, C)
	tmp = 180.0 * (atan(0.0) / pi);
end

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 59.0%

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

   1. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(\left(C - A\right) + \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   2. distribute-lft-in N/A

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{1}{B} \cdot \left(C - A\right) + \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   3. fma-define N/A

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\mathsf{fma}\left(\frac{1}{B}, C - A, \frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\left(\frac{1}{B}\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(C - A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \left(\frac{1}{B} \cdot \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\left(\frac{1}{B}\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(\mathsf{neg}\left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   9. neg-sub0 N/A

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \left(0 - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   11. pow2 N/A

       \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   12. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + {\left(A - C\right)}^{2}}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   13. unpow2 N/A

       \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   14. hypot-define N/A

       \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \left(\mathsf{hypot}\left(B, A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

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

       \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \left(A - C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   16. --lowering--.f64 74.1%

       \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(C, A\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, B\right), \mathsf{\_.f64}\left(0, \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

4. Applied egg-rr 74.1%

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

5. Taylor expanded in A around -inf

   \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \frac{C}{B} + \frac{C}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
6. Step-by-step derivation

   1. distribute-lft1-in N/A

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\left(-1 + 1\right) \cdot \frac{C}{B}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   2. metadata-eval N/A

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(0 \cdot \frac{C}{B}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   3. mul0-lft 11.9%

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(0\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

7. Simplified 11.9%

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

Reproduce

herbie shell --seed 2024139 
(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)))