ABCF->ab-angle angle

Percentage Accurate: 54.3% → 88.7%

Time: 17.4s

Alternatives: 20

Speedup: 3.6×

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: 54.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 51.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 79.2%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. associate-*l/ N/A

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

      4. div-inv N/A

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

      5. times-frac N/A

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

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

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

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

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

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

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

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

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

   6. Applied egg-rr 84.9%

      \[\leadsto \color{blue}{\frac{1}{\pi} \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{0.005555555555555556}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. un-div-inv N/A

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

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

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

   8. Applied egg-rr 84.9%

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

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

   1. Initial program 22.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 15.3%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 22.2%

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

   6. Applied egg-rr 22.2%

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

   7. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. --lowering--.f64 99.2%

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

   9. Simplified 99.2%

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

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

   1. Initial program 60.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 83.1%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 89.3%

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

   6. Applied egg-rr 89.3%

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

Alternative 2: 79.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -2.1 \cdot 10^{-14}:\\ \;\;\;\;\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq 5 \cdot 10^{+30}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{0 - B}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -2.1e-14)
   (* (atan (/ (- C (+ A (hypot B (- C A)))) B)) (/ 180.0 PI))
   (if (<= C 5e+30)
     (/ (atan (/ (+ A (hypot A B)) (- 0.0 B))) (/ PI 180.0))
     (/ (atan (/ (* B -0.5) (- C A))) (/ PI 180.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.1e-14) {
		tmp = atan(((C - (A + hypot(B, (C - A)))) / B)) * (180.0 / ((double) M_PI));
	} else if (C <= 5e+30) {
		tmp = atan(((A + hypot(A, B)) / (0.0 - B))) / (((double) M_PI) / 180.0);
	} else {
		tmp = atan(((B * -0.5) / (C - A))) / (((double) M_PI) / 180.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.1e-14) {
		tmp = Math.atan(((C - (A + Math.hypot(B, (C - A)))) / B)) * (180.0 / Math.PI);
	} else if (C <= 5e+30) {
		tmp = Math.atan(((A + Math.hypot(A, B)) / (0.0 - B))) / (Math.PI / 180.0);
	} else {
		tmp = Math.atan(((B * -0.5) / (C - A))) / (Math.PI / 180.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -2.1e-14:
		tmp = math.atan(((C - (A + math.hypot(B, (C - A)))) / B)) * (180.0 / math.pi)
	elif C <= 5e+30:
		tmp = math.atan(((A + math.hypot(A, B)) / (0.0 - B))) / (math.pi / 180.0)
	else:
		tmp = math.atan(((B * -0.5) / (C - A))) / (math.pi / 180.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -2.1e-14)
		tmp = Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(C - A)))) / B)) * Float64(180.0 / pi));
	elseif (C <= 5e+30)
		tmp = Float64(atan(Float64(Float64(A + hypot(A, B)) / Float64(0.0 - B))) / Float64(pi / 180.0));
	else
		tmp = Float64(atan(Float64(Float64(B * -0.5) / Float64(C - A))) / Float64(pi / 180.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -2.1e-14)
		tmp = atan(((C - (A + hypot(B, (C - A)))) / B)) * (180.0 / pi);
	elseif (C <= 5e+30)
		tmp = atan(((A + hypot(A, B)) / (0.0 - B))) / (pi / 180.0);
	else
		tmp = atan(((B * -0.5) / (C - A))) / (pi / 180.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -2.1e-14], 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], If[LessEqual[C, 5e+30], N[(N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / N[(0.0 - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -2.0999999999999999e-14

   1. Initial program 83.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 94.7%

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

   if -2.0999999999999999e-14 < C < 4.9999999999999998e30

   1. Initial program 50.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 71.9%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 82.4%

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

   6. Applied egg-rr 82.4%

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

   7. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. unpow2 N/A

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

      7. accelerator-lowering-hypot.f64 82.4%

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

   9. Simplified 82.4%

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

   if 4.9999999999999998e30 < C

   1. Initial program 18.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 50.0%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 53.5%

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

   6. Applied egg-rr 53.5%

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

   7. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. --lowering--.f64 78.6%

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

   9. Simplified 78.6%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.1 \cdot 10^{-14}:\\ \;\;\;\;\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;C \leq 5 \cdot 10^{+30}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{0 - B}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -250000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{elif}\;C \leq 2.6 \cdot 10^{+30}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{0 - B}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -250000.0)
   (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
   (if (<= C 2.6e+30)
     (/ (atan (/ (+ A (hypot A B)) (- 0.0 B))) (/ PI 180.0))
     (/ (atan (/ (* B -0.5) (- C A))) (/ PI 180.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -250000.0) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / B));
	} else if (C <= 2.6e+30) {
		tmp = atan(((A + hypot(A, B)) / (0.0 - B))) / (((double) M_PI) / 180.0);
	} else {
		tmp = atan(((B * -0.5) / (C - A))) / (((double) M_PI) / 180.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -250000.0) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / B));
	} else if (C <= 2.6e+30) {
		tmp = Math.atan(((A + Math.hypot(A, B)) / (0.0 - B))) / (Math.PI / 180.0);
	} else {
		tmp = Math.atan(((B * -0.5) / (C - A))) / (Math.PI / 180.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -250000.0:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / B))
	elif C <= 2.6e+30:
		tmp = math.atan(((A + math.hypot(A, B)) / (0.0 - B))) / (math.pi / 180.0)
	else:
		tmp = math.atan(((B * -0.5) / (C - A))) / (math.pi / 180.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -250000.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / B)));
	elseif (C <= 2.6e+30)
		tmp = Float64(atan(Float64(Float64(A + hypot(A, B)) / Float64(0.0 - B))) / Float64(pi / 180.0));
	else
		tmp = Float64(atan(Float64(Float64(B * -0.5) / Float64(C - A))) / Float64(pi / 180.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -250000.0)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / B));
	elseif (C <= 2.6e+30)
		tmp = atan(((A + hypot(A, B)) / (0.0 - B))) / (pi / 180.0);
	else
		tmp = atan(((B * -0.5) / (C - A))) / (pi / 180.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -250000.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.6e+30], N[(N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / N[(0.0 - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -2.5e5

   1. Initial program 84.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 95.9%

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

   5. Taylor expanded in 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. unpow2 N/A

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

      4. unpow2 N/A

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

      5. accelerator-lowering-hypot.f64 94.8%

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

   7. Simplified 94.8%

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

   if -2.5e5 < C < 2.59999999999999988e30

   1. Initial program 50.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 71.6%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 81.9%

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

   6. Applied egg-rr 81.9%

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

   7. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. unpow2 N/A

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

      7. accelerator-lowering-hypot.f64 81.9%

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

   9. Simplified 81.9%

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

   if 2.59999999999999988e30 < C

   1. Initial program 18.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 50.0%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 53.5%

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

   6. Applied egg-rr 53.5%

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

   7. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. --lowering--.f64 78.6%

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

   9. Simplified 78.6%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -250000:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{elif}\;C \leq 2.6 \cdot 10^{+30}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{0 - B}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1 \cdot 10^{+73}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 1.46 \cdot 10^{+40}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1e+73)
   (/ (atan (/ (* B -0.5) (- C A))) (/ PI 180.0))
   (if (<= A 1.46e+40)
     (* (/ 180.0 PI) (atan (/ (- C (hypot B C)) B)))
     (* (/ 180.0 PI) (atan (+ 1.0 (/ (- C A) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1e+73) {
		tmp = atan(((B * -0.5) / (C - A))) / (((double) M_PI) / 180.0);
	} else if (A <= 1.46e+40) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(B, C)) / 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+73) {
		tmp = Math.atan(((B * -0.5) / (C - A))) / (Math.PI / 180.0);
	} else if (A <= 1.46e+40) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(B, C)) / 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+73:
		tmp = math.atan(((B * -0.5) / (C - A))) / (math.pi / 180.0)
	elif A <= 1.46e+40:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(B, C)) / 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+73)
		tmp = Float64(atan(Float64(Float64(B * -0.5) / Float64(C - A))) / Float64(pi / 180.0));
	elseif (A <= 1.46e+40)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(B, C)) / 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+73)
		tmp = atan(((B * -0.5) / (C - A))) / (pi / 180.0);
	elseif (A <= 1.46e+40)
		tmp = (180.0 / pi) * atan(((C - hypot(B, C)) / 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+73], N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.46e+40], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[B ^ 2 + C ^ 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 < -9.99999999999999983e72

   1. Initial program 22.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 30.4%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 58.5%

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

   6. Applied egg-rr 58.5%

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

   7. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. --lowering--.f64 76.4%

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

   9. Simplified 76.4%

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

   if -9.99999999999999983e72 < A < 1.46e40

   1. Initial program 52.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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. unpow2 N/A

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

      4. unpow2 N/A

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

      5. accelerator-lowering-hypot.f64 78.0%

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

   7. Simplified 78.0%

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

   if 1.46e40 < A

   1. Initial program 81.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 94.4%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 84.7%

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

   7. Simplified 84.7%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1 \cdot 10^{+73}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 1.46 \cdot 10^{+40}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(B, C\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 1.75 \cdot 10^{+28}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 1.75e+28)
   (/ (atan (/ (- (- C A) (hypot B (- C A))) B)) (/ PI 180.0))
   (/ (atan (/ (* B -0.5) (- C A))) (/ PI 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.75e+28) {
		tmp = atan((((C - A) - hypot(B, (C - A))) / B)) / (((double) M_PI) / 180.0);
	} else {
		tmp = atan(((B * -0.5) / (C - A))) / (((double) M_PI) / 180.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.75e+28) {
		tmp = Math.atan((((C - A) - Math.hypot(B, (C - A))) / B)) / (Math.PI / 180.0);
	} else {
		tmp = Math.atan(((B * -0.5) / (C - A))) / (Math.PI / 180.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 1.75e+28:
		tmp = math.atan((((C - A) - math.hypot(B, (C - A))) / B)) / (math.pi / 180.0)
	else:
		tmp = math.atan(((B * -0.5) / (C - A))) / (math.pi / 180.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 1.75e+28)
		tmp = Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(C - A))) / B)) / Float64(pi / 180.0));
	else
		tmp = Float64(atan(Float64(Float64(B * -0.5) / Float64(C - A))) / Float64(pi / 180.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 1.75e+28)
		tmp = atan((((C - A) - hypot(B, (C - A))) / B)) / (pi / 180.0);
	else
		tmp = atan(((B * -0.5) / (C - A))) / (pi / 180.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 1.75e+28], N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 1.75e28

   1. Initial program 63.2%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 87.7%

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

   6. Applied egg-rr 87.7%

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

   if 1.75e28 < C

   1. Initial program 18.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 50.0%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 53.5%

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

   6. Applied egg-rr 53.5%

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

   7. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. --lowering--.f64 78.6%

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

   9. Simplified 78.6%

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

Alternative 6: 77.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 2.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 2.4e+26)
   (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot B A))) B)))
   (/ (atan (/ (* B -0.5) (- C A))) (/ PI 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.4e+26) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(B, A))) / B));
	} else {
		tmp = atan(((B * -0.5) / (C - A))) / (((double) M_PI) / 180.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.4e+26) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(B, A))) / B));
	} else {
		tmp = Math.atan(((B * -0.5) / (C - A))) / (Math.PI / 180.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 2.4e+26:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(B, A))) / B))
	else:
		tmp = math.atan(((B * -0.5) / (C - A))) / (math.pi / 180.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 2.4e+26)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(B, A))) / B)));
	else
		tmp = Float64(atan(Float64(Float64(B * -0.5) / Float64(C - A))) / Float64(pi / 180.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 2.4e+26)
		tmp = (180.0 / pi) * atan(((C - (A + hypot(B, A))) / B));
	else
		tmp = atan(((B * -0.5) / (C - A))) / (pi / 180.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 2.4e+26], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 2.40000000000000005e26

   1. Initial program 63.2%

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

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

      3. unpow2 N/A

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

      4. unpow2 N/A

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

      5. accelerator-lowering-hypot.f64 80.1%

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

   7. Simplified 80.1%

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

   if 2.40000000000000005e26 < C

   1. Initial program 18.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 50.0%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 53.5%

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

   6. Applied egg-rr 53.5%

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

   7. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. --lowering--.f64 78.6%

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

   9. Simplified 78.6%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 2.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{if}\;B \leq -9 \cdot 10^{-139}:\\ \;\;\;\;\frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-204}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-203}:\\ \;\;\;\;\frac{\frac{\tan^{-1} 0}{\pi}}{0.005555555555555556}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-134}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (/ (* A -2.0) B)))))
   (if (<= B -9e-139)
     (/ (atan (+ 1.0 (/ C B))) (/ PI 180.0))
     (if (<= B -6.5e-204)
       t_0
       (if (<= B 3.9e-203)
         (/ (/ (atan 0.0) PI) 0.005555555555555556)
         (if (<= B 4.8e-134) t_0 (* (/ 180.0 PI) (atan (/ (- C B) B)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan(((A * -2.0) / B));
	double tmp;
	if (B <= -9e-139) {
		tmp = atan((1.0 + (C / B))) / (((double) M_PI) / 180.0);
	} else if (B <= -6.5e-204) {
		tmp = t_0;
	} else if (B <= 3.9e-203) {
		tmp = (atan(0.0) / ((double) M_PI)) / 0.005555555555555556;
	} else if (B <= 4.8e-134) {
		tmp = t_0;
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan(((A * -2.0) / B));
	double tmp;
	if (B <= -9e-139) {
		tmp = Math.atan((1.0 + (C / B))) / (Math.PI / 180.0);
	} else if (B <= -6.5e-204) {
		tmp = t_0;
	} else if (B <= 3.9e-203) {
		tmp = (Math.atan(0.0) / Math.PI) / 0.005555555555555556;
	} else if (B <= 4.8e-134) {
		tmp = t_0;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan(((A * -2.0) / B))
	tmp = 0
	if B <= -9e-139:
		tmp = math.atan((1.0 + (C / B))) / (math.pi / 180.0)
	elif B <= -6.5e-204:
		tmp = t_0
	elif B <= 3.9e-203:
		tmp = (math.atan(0.0) / math.pi) / 0.005555555555555556
	elif B <= 4.8e-134:
		tmp = t_0
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A * -2.0) / B)))
	tmp = 0.0
	if (B <= -9e-139)
		tmp = Float64(atan(Float64(1.0 + Float64(C / B))) / Float64(pi / 180.0));
	elseif (B <= -6.5e-204)
		tmp = t_0;
	elseif (B <= 3.9e-203)
		tmp = Float64(Float64(atan(0.0) / pi) / 0.005555555555555556);
	elseif (B <= 4.8e-134)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan(((A * -2.0) / B));
	tmp = 0.0;
	if (B <= -9e-139)
		tmp = atan((1.0 + (C / B))) / (pi / 180.0);
	elseif (B <= -6.5e-204)
		tmp = t_0;
	elseif (B <= 3.9e-203)
		tmp = (atan(0.0) / pi) / 0.005555555555555556;
	elseif (B <= 4.8e-134)
		tmp = t_0;
	else
		tmp = (180.0 / pi) * atan(((C - B) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[B, -9e-139], N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6.5e-204], t$95$0, If[LessEqual[B, 3.9e-203], N[(N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision] / 0.005555555555555556), $MachinePrecision], If[LessEqual[B, 4.8e-134], t$95$0, N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if B < -9.00000000000000046e-139

   1. Initial program 57.8%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 81.4%

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

   6. Applied egg-rr 81.4%

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

   7. Taylor expanded in A around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. unpow2 N/A

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

      5. unpow2 N/A

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

      6. accelerator-lowering-hypot.f64 72.8%

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

   9. Simplified 72.8%

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

   10. Taylor expanded in B around -inf

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

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

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

       2. /-lowering-/.f64 70.7%

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

   12. Simplified 70.7%

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

   if -9.00000000000000046e-139 < B < -6.49999999999999939e-204 or 3.8999999999999999e-203 < B < 4.80000000000000019e-134

   1. Initial program 68.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 72.1%

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

   5. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-lowering-*.f64 65.4%

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

   7. Simplified 65.4%

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

   if -6.49999999999999939e-204 < B < 3.8999999999999999e-203

   1. Initial program 45.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 60.1%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 79.6%

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

   6. Applied egg-rr 79.6%

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

   7. Taylor expanded in C around inf

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

      1. associate-*r/ N/A

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

      2. distribute-rgt1-in N/A

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

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-1 \cdot \left(0 \cdot A\right)}{B}\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

      4. mul0-lft N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-1 \cdot 0}{B}\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{0}{B}\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

      6. /-lowering-/.f64 47.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(0, B\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

   9. Simplified 47.3%

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

       1. div-inv N/A

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

       2. metadata-eval N/A

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

       3. associate-/r* N/A

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

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

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{\tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right)}\right), \color{blue}{\frac{1}{180}}\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\tan^{-1} \left(\frac{0}{B}\right), \mathsf{PI}\left(\right)\right), \frac{1}{180}\right) \]

       6. div0 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\tan^{-1} 0, \mathsf{PI}\left(\right)\right), \frac{1}{180}\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(0\right), \mathsf{PI}\left(\right)\right), \frac{1}{180}\right) \]

       8. PI-lowering-PI.f64 47.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(0\right), \mathsf{PI.f64}\left(\right)\right), \frac{1}{180}\right) \]

   11. Applied egg-rr 47.3%

       \[\leadsto \color{blue}{\frac{\frac{\tan^{-1} 0}{\pi}}{0.005555555555555556}} \]

   if 4.80000000000000019e-134 < B

   1. Initial program 42.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 72.7%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 65.5%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9 \cdot 10^{-139}:\\ \;\;\;\;\frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;B \leq -6.5 \cdot 10^{-204}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{elif}\;B \leq 3.9 \cdot 10^{-203}:\\ \;\;\;\;\frac{\frac{\tan^{-1} 0}{\pi}}{0.005555555555555556}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-134}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.6% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-203}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-133}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.6e-99)
   (/ (atan (+ 1.0 (/ C B))) (/ PI 180.0))
   (if (<= B 2.8e-203)
     (* (/ 180.0 PI) (atan (* B (/ 0.5 (- A C)))))
     (if (<= B 1.55e-133)
       (* (/ 180.0 PI) (atan (/ (* A -2.0) B)))
       (* (/ 180.0 PI) (atan (/ (- C B) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.6e-99) {
		tmp = atan((1.0 + (C / B))) / (((double) M_PI) / 180.0);
	} else if (B <= 2.8e-203) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / (A - C))));
	} else if (B <= 1.55e-133) {
		tmp = (180.0 / ((double) M_PI)) * atan(((A * -2.0) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.6e-99) {
		tmp = Math.atan((1.0 + (C / B))) / (Math.PI / 180.0);
	} else if (B <= 2.8e-203) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / (A - C))));
	} else if (B <= 1.55e-133) {
		tmp = (180.0 / Math.PI) * Math.atan(((A * -2.0) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.6e-99:
		tmp = math.atan((1.0 + (C / B))) / (math.pi / 180.0)
	elif B <= 2.8e-203:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / (A - C))))
	elif B <= 1.55e-133:
		tmp = (180.0 / math.pi) * math.atan(((A * -2.0) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.6e-99)
		tmp = Float64(atan(Float64(1.0 + Float64(C / B))) / Float64(pi / 180.0));
	elseif (B <= 2.8e-203)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / Float64(A - C)))));
	elseif (B <= 1.55e-133)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A * -2.0) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.6e-99)
		tmp = atan((1.0 + (C / B))) / (pi / 180.0);
	elseif (B <= 2.8e-203)
		tmp = (180.0 / pi) * atan((B * (0.5 / (A - C))));
	elseif (B <= 1.55e-133)
		tmp = (180.0 / pi) * atan(((A * -2.0) / B));
	else
		tmp = (180.0 / pi) * atan(((C - B) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.6e-99], N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.8e-203], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.55e-133], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -3.6000000000000001e-99

   1. Initial program 58.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 82.5%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 82.5%

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

   6. Applied egg-rr 82.5%

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

   7. Taylor expanded in A around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. unpow2 N/A

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

      5. unpow2 N/A

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

      6. accelerator-lowering-hypot.f64 75.6%

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

   9. Simplified 75.6%

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

   10. Taylor expanded in B around -inf

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

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

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

       2. /-lowering-/.f64 73.4%

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

   12. Simplified 73.4%

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

   if -3.6000000000000001e-99 < B < 2.80000000000000022e-203

   1. Initial program 49.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 60.9%

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

   5. Taylor expanded in B around 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. 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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. mul-1-neg N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. sub-neg N/A

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

      21. /-lowering-/.f64 N/A

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

      22. --lowering--.f64 61.5%

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

   7. Simplified 61.5%

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

   if 2.80000000000000022e-203 < B < 1.55000000000000008e-133

   1. Initial program 77.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 77.8%

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

   5. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-lowering-*.f64 75.9%

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

   7. Simplified 75.9%

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

   if 1.55000000000000008e-133 < B

   1. Initial program 42.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 72.7%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 65.5%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-203}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)\\ \mathbf{elif}\;B \leq 1.55 \cdot 10^{-133}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.7% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.08 \cdot 10^{+135}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{-52}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.08e+135)
   (* (/ 180.0 PI) (atan (/ (* B 0.5) A)))
   (if (<= A 1.35e-52)
     (* (/ 180.0 PI) (atan (/ (- C B) B)))
     (if (<= A 4.5e+39)
       (* (/ 180.0 PI) (atan (/ (* B -0.5) C)))
       (* (/ 180.0 PI) (atan (/ (* A -2.0) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.08e+135) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * 0.5) / A));
	} else if (A <= 1.35e-52) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	} else if (A <= 4.5e+39) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((A * -2.0) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.08e+135) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * 0.5) / A));
	} else if (A <= 1.35e-52) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	} else if (A <= 4.5e+39) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((A * -2.0) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.08e+135:
		tmp = (180.0 / math.pi) * math.atan(((B * 0.5) / A))
	elif A <= 1.35e-52:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	elif A <= 4.5e+39:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	else:
		tmp = (180.0 / math.pi) * math.atan(((A * -2.0) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.08e+135)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * 0.5) / A)));
	elseif (A <= 1.35e-52)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	elseif (A <= 4.5e+39)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A * -2.0) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.08e+135)
		tmp = (180.0 / pi) * atan(((B * 0.5) / A));
	elseif (A <= 1.35e-52)
		tmp = (180.0 / pi) * atan(((C - B) / B));
	elseif (A <= 4.5e+39)
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	else
		tmp = (180.0 / pi) * atan(((A * -2.0) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.08e+135], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.35e-52], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.5e+39], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.08e135

   1. Initial program 18.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 25.7%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 76.2%

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

   7. Simplified 76.2%

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

   if -1.08e135 < A < 1.35000000000000005e-52

   1. Initial program 50.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 80.0%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 49.8%

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

   if 1.35000000000000005e-52 < A < 4.49999999999999996e39

   1. Initial program 58.6%

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

   3. Taylor expanded in C around inf

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

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

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

      2. associate-*r/ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt1-in N/A

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

      5. metadata-eval N/A

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

      6. mul0-lft N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. metadata-eval N/A

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

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

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

      9. associate-*r/ N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 62.3%

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

   5. Simplified 62.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B} + \frac{B \cdot -0.5}{C}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\mathsf{PI}\left(\right)} \cdot \color{blue}{180} \]

      2. div-inv N/A

         \[\leadsto \left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}\right) \cdot 180 \]

      3. associate-*l* N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \color{blue}{\left(\frac{1}{\mathsf{PI}\left(\right)} \cdot 180\right)} \]

      4. associate-/r/ N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

      5. clear-num N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{180}{\color{blue}{\mathsf{PI}\left(\right)}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

      7. div0 N/A

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(0 + \frac{B \cdot \frac{-1}{2}}{C}\right), \left(\frac{180}{\mathsf{PI}\left(\right)}\right)\right) \]

      8. +-lft-identity N/A

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

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

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

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

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

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

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

      12. /-lowering-/.f64 N/A

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

      13. PI-lowering-PI.f64 62.5%

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

   7. Applied egg-rr 62.5%

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

   if 4.49999999999999996e39 < A

   1. Initial program 81.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 94.4%

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

   5. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-lowering-*.f64 74.7%

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

   7. Simplified 74.7%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.08 \cdot 10^{+135}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{-52}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.7% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.9 \cdot 10^{-105}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{\tan^{-1} 0}{\pi}}{0.005555555555555556}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{+129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.9e-105)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 5e-119)
     (/ (/ (atan 0.0) PI) 0.005555555555555556)
     (if (<= B 2.7e+129)
       (* 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 <= -2.9e-105) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 5e-119) {
		tmp = (atan(0.0) / ((double) M_PI)) / 0.005555555555555556;
	} else if (B <= 2.7e+129) {
		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 <= -2.9e-105) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 5e-119) {
		tmp = (Math.atan(0.0) / Math.PI) / 0.005555555555555556;
	} else if (B <= 2.7e+129) {
		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 <= -2.9e-105:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 5e-119:
		tmp = (math.atan(0.0) / math.pi) / 0.005555555555555556
	elif B <= 2.7e+129:
		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 <= -2.9e-105)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 5e-119)
		tmp = Float64(Float64(atan(0.0) / pi) / 0.005555555555555556);
	elseif (B <= 2.7e+129)
		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 <= -2.9e-105)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 5e-119)
		tmp = (atan(0.0) / pi) / 0.005555555555555556;
	elseif (B <= 2.7e+129)
		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, -2.9e-105], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5e-119], N[(N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision] / 0.005555555555555556), $MachinePrecision], If[LessEqual[B, 2.7e+129], 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 4 regimes

2. if B < -2.90000000000000003e-105

   1. Initial program 58.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 82.5%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 51.4%

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

   if -2.90000000000000003e-105 < B < 4.99999999999999993e-119

   1. Initial program 55.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 64.6%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 81.4%

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

   6. Applied egg-rr 81.4%

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

   7. Taylor expanded in C around inf

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

      1. associate-*r/ N/A

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

      2. distribute-rgt1-in N/A

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

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-1 \cdot \left(0 \cdot A\right)}{B}\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

      4. mul0-lft N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-1 \cdot 0}{B}\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{0}{B}\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

      6. /-lowering-/.f64 36.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(0, B\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

   9. Simplified 36.2%

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

       1. div-inv N/A

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

       2. metadata-eval N/A

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

       3. associate-/r* N/A

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

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

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{\tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right)}\right), \color{blue}{\frac{1}{180}}\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\tan^{-1} \left(\frac{0}{B}\right), \mathsf{PI}\left(\right)\right), \frac{1}{180}\right) \]

       6. div0 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\tan^{-1} 0, \mathsf{PI}\left(\right)\right), \frac{1}{180}\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(0\right), \mathsf{PI}\left(\right)\right), \frac{1}{180}\right) \]

       8. PI-lowering-PI.f64 36.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(0\right), \mathsf{PI.f64}\left(\right)\right), \frac{1}{180}\right) \]

   11. Applied egg-rr 36.2%

       \[\leadsto \color{blue}{\frac{\frac{\tan^{-1} 0}{\pi}}{0.005555555555555556}} \]

   if 4.99999999999999993e-119 < B < 2.7000000000000001e129

   1. Initial program 56.2%

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

   3. Taylor expanded in 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 34.7%

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

   5. Simplified 34.7%

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

   if 2.7000000000000001e129 < B

   1. Initial program 21.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 87.7%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 85.8%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.9 \cdot 10^{-105}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{\tan^{-1} 0}{\pi}}{0.005555555555555556}\\ \mathbf{elif}\;B \leq 2.7 \cdot 10^{+129}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -5.2 \cdot 10^{-199}:\\ \;\;\;\;\frac{\tan^{-1} \left(1 + t\_0\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-203}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(t\_0 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -5.2e-199)
     (/ (atan (+ 1.0 t_0)) (/ PI 180.0))
     (if (<= B 3.8e-203)
       (/ (atan (/ (* B -0.5) (- C A))) (/ PI 180.0))
       (* (/ 180.0 PI) (atan (+ t_0 -1.0)))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -5.2e-199) {
		tmp = atan((1.0 + t_0)) / (((double) M_PI) / 180.0);
	} else if (B <= 3.8e-203) {
		tmp = atan(((B * -0.5) / (C - A))) / (((double) M_PI) / 180.0);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((t_0 + -1.0));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -5.2e-199) {
		tmp = Math.atan((1.0 + t_0)) / (Math.PI / 180.0);
	} else if (B <= 3.8e-203) {
		tmp = Math.atan(((B * -0.5) / (C - A))) / (Math.PI / 180.0);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((t_0 + -1.0));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -5.2e-199:
		tmp = math.atan((1.0 + t_0)) / (math.pi / 180.0)
	elif B <= 3.8e-203:
		tmp = math.atan(((B * -0.5) / (C - A))) / (math.pi / 180.0)
	else:
		tmp = (180.0 / math.pi) * math.atan((t_0 + -1.0))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -5.2e-199)
		tmp = Float64(atan(Float64(1.0 + t_0)) / Float64(pi / 180.0));
	elseif (B <= 3.8e-203)
		tmp = Float64(atan(Float64(Float64(B * -0.5) / Float64(C - A))) / Float64(pi / 180.0));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(t_0 + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -5.2e-199)
		tmp = atan((1.0 + t_0)) / (pi / 180.0);
	elseif (B <= 3.8e-203)
		tmp = atan(((B * -0.5) / (C - A))) / (pi / 180.0);
	else
		tmp = (180.0 / pi) * atan((t_0 + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -5.2e-199], N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.8e-203], N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -5.2000000000000001e-199

   1. Initial program 59.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 78.8%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 82.0%

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

   6. Applied egg-rr 82.0%

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

   7. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

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

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

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

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

      5. --lowering--.f64 73.8%

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

   9. Simplified 73.8%

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

   if -5.2000000000000001e-199 < B < 3.80000000000000025e-203

   1. Initial program 44.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 59.0%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 78.1%

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

   6. Applied egg-rr 78.1%

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

   7. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. --lowering--.f64 67.9%

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

   9. Simplified 67.9%

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

   if 3.80000000000000025e-203 < B

   1. Initial program 47.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 73.4%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

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

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

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

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

      8. --lowering--.f64 70.9%

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

   7. Simplified 70.9%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.2 \cdot 10^{-199}:\\ \;\;\;\;\frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;B \leq 3.8 \cdot 10^{-203}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -1.3 \cdot 10^{-197}:\\ \;\;\;\;\frac{\tan^{-1} \left(1 + t\_0\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-202}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(t\_0 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -1.3e-197)
     (/ (atan (+ 1.0 t_0)) (/ PI 180.0))
     (if (<= B 1.25e-202)
       (* (/ 180.0 PI) (atan (* B (/ 0.5 (- A C)))))
       (* (/ 180.0 PI) (atan (+ t_0 -1.0)))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.3e-197) {
		tmp = atan((1.0 + t_0)) / (((double) M_PI) / 180.0);
	} else if (B <= 1.25e-202) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / (A - C))));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((t_0 + -1.0));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.3e-197) {
		tmp = Math.atan((1.0 + t_0)) / (Math.PI / 180.0);
	} else if (B <= 1.25e-202) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / (A - C))));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((t_0 + -1.0));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -1.3e-197:
		tmp = math.atan((1.0 + t_0)) / (math.pi / 180.0)
	elif B <= 1.25e-202:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / (A - C))))
	else:
		tmp = (180.0 / math.pi) * math.atan((t_0 + -1.0))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -1.3e-197)
		tmp = Float64(atan(Float64(1.0 + t_0)) / Float64(pi / 180.0));
	elseif (B <= 1.25e-202)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / Float64(A - C)))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(t_0 + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -1.3e-197)
		tmp = atan((1.0 + t_0)) / (pi / 180.0);
	elseif (B <= 1.25e-202)
		tmp = (180.0 / pi) * atan((B * (0.5 / (A - C))));
	else
		tmp = (180.0 / pi) * atan((t_0 + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -1.3e-197], N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.25e-202], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.3000000000000001e-197

   1. Initial program 59.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 78.8%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

      6. associate--r+ N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 82.0%

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

   6. Applied egg-rr 82.0%

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

   7. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

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

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

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

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

      5. --lowering--.f64 73.8%

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

   9. Simplified 73.8%

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

   if -1.3000000000000001e-197 < B < 1.24999999999999993e-202

   1. Initial program 44.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 59.0%

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

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. mul-1-neg N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. sub-neg N/A

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

      21. /-lowering-/.f64 N/A

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

      22. --lowering--.f64 67.9%

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

   7. Simplified 67.9%

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

   if 1.24999999999999993e-202 < B

   1. Initial program 47.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 73.4%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

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

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

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

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

      8. --lowering--.f64 70.9%

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

   7. Simplified 70.9%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.3 \cdot 10^{-197}:\\ \;\;\;\;\frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;B \leq 1.25 \cdot 10^{-202}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -1.14 \cdot 10^{-201}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + t\_0\right)\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-203}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(t\_0 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -1.14e-201)
     (* (/ 180.0 PI) (atan (+ 1.0 t_0)))
     (if (<= B 1.65e-203)
       (* (/ 180.0 PI) (atan (* B (/ 0.5 (- A C)))))
       (* (/ 180.0 PI) (atan (+ t_0 -1.0)))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.14e-201) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + t_0));
	} else if (B <= 1.65e-203) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / (A - C))));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((t_0 + -1.0));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.14e-201) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + t_0));
	} else if (B <= 1.65e-203) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / (A - C))));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((t_0 + -1.0));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -1.14e-201:
		tmp = (180.0 / math.pi) * math.atan((1.0 + t_0))
	elif B <= 1.65e-203:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / (A - C))))
	else:
		tmp = (180.0 / math.pi) * math.atan((t_0 + -1.0))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -1.14e-201)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + t_0)));
	elseif (B <= 1.65e-203)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / Float64(A - C)))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(t_0 + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -1.14e-201)
		tmp = (180.0 / pi) * atan((1.0 + t_0));
	elseif (B <= 1.65e-203)
		tmp = (180.0 / pi) * atan((B * (0.5 / (A - C))));
	else
		tmp = (180.0 / pi) * atan((t_0 + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -1.14e-201], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.65e-203], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.1400000000000001e-201

   1. Initial program 59.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 78.8%

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

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   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 73.8%

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

   7. Simplified 73.8%

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

   if -1.1400000000000001e-201 < B < 1.65000000000000012e-203

   1. Initial program 44.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 59.0%

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

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. mul-1-neg N/A

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

      16. mul-1-neg N/A

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

      17. associate-*r* N/A

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

      18. metadata-eval N/A

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

      19. *-lft-identity N/A

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

      20. sub-neg N/A

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

      21. /-lowering-/.f64 N/A

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

      22. --lowering--.f64 67.9%

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

   7. Simplified 67.9%

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

   if 1.65000000000000012e-203 < B

   1. Initial program 47.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 73.4%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

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

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

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

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

      8. --lowering--.f64 70.9%

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

   7. Simplified 70.9%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.14 \cdot 10^{-201}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \mathbf{elif}\;B \leq 1.65 \cdot 10^{-203}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.2 \cdot 10^{-228}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 9.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.2e-228)
   (* (/ 180.0 PI) (atan (/ (* B 0.5) A)))
   (if (<= A 9.4e+39)
     (* (/ 180.0 PI) (atan (/ (* B -0.5) C)))
     (* (/ 180.0 PI) (atan (/ (* A -2.0) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.2e-228) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * 0.5) / A));
	} else if (A <= 9.4e+39) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((A * -2.0) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.2e-228) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * 0.5) / A));
	} else if (A <= 9.4e+39) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((A * -2.0) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.2e-228:
		tmp = (180.0 / math.pi) * math.atan(((B * 0.5) / A))
	elif A <= 9.4e+39:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	else:
		tmp = (180.0 / math.pi) * math.atan(((A * -2.0) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.2e-228)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * 0.5) / A)));
	elseif (A <= 9.4e+39)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A * -2.0) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.2e-228)
		tmp = (180.0 / pi) * atan(((B * 0.5) / A));
	elseif (A <= 9.4e+39)
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	else
		tmp = (180.0 / pi) * atan(((A * -2.0) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.2e-228], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9.4e+39], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.19999999999999995e-228

   1. Initial program 34.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 55.6%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 51.9%

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

   7. Simplified 51.9%

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

   if -8.19999999999999995e-228 < A < 9.3999999999999998e39

   1. Initial program 55.7%

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

   3. Taylor expanded in C around inf

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

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

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

      2. associate-*r/ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt1-in N/A

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

      5. metadata-eval N/A

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

      6. mul0-lft N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(0\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. metadata-eval N/A

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

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

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

      9. associate-*r/ N/A

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

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

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 37.5%

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

   5. Simplified 37.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B} + \frac{B \cdot -0.5}{C}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\mathsf{PI}\left(\right)} \cdot \color{blue}{180} \]

      2. div-inv N/A

         \[\leadsto \left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\mathsf{PI}\left(\right)}\right) \cdot 180 \]

      3. associate-*l* N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \color{blue}{\left(\frac{1}{\mathsf{PI}\left(\right)} \cdot 180\right)} \]

      4. associate-/r/ N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{1}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

      5. clear-num N/A

         \[\leadsto \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right) \cdot \frac{180}{\color{blue}{\mathsf{PI}\left(\right)}} \]

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

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

      7. div0 N/A

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(0 + \frac{B \cdot \frac{-1}{2}}{C}\right), \left(\frac{180}{\mathsf{PI}\left(\right)}\right)\right) \]

      8. +-lft-identity N/A

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

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

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

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

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

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

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

      12. /-lowering-/.f64 N/A

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

      13. PI-lowering-PI.f64 37.7%

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

   7. Applied egg-rr 37.7%

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

   if 9.3999999999999998e39 < A

   1. Initial program 81.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 94.4%

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

   5. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-lowering-*.f64 74.7%

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

   7. Simplified 74.7%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.2 \cdot 10^{-228}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 9.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.4% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.2 \cdot 10^{-94}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-127}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.2e-94)
   (* (/ 180.0 PI) (atan (/ (* B 0.5) A)))
   (if (<= A 2e-127)
     (* (/ 180.0 PI) (atan -1.0))
     (* (/ 180.0 PI) (atan (/ (* A -2.0) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.2e-94) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * 0.5) / A));
	} else if (A <= 2e-127) {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((A * -2.0) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.2e-94) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * 0.5) / A));
	} else if (A <= 2e-127) {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((A * -2.0) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.2e-94:
		tmp = (180.0 / math.pi) * math.atan(((B * 0.5) / A))
	elif A <= 2e-127:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	else:
		tmp = (180.0 / math.pi) * math.atan(((A * -2.0) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.2e-94)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * 0.5) / A)));
	elseif (A <= 2e-127)
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A * -2.0) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.2e-94)
		tmp = (180.0 / pi) * atan(((B * 0.5) / A));
	elseif (A <= 2e-127)
		tmp = (180.0 / pi) * atan(-1.0);
	else
		tmp = (180.0 / pi) * atan(((A * -2.0) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.2e-94], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2e-127], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -4.2000000000000002e-94

   1. Initial program 28.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 45.6%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 58.0%

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

   7. Simplified 58.0%

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

   if -4.2000000000000002e-94 < A < 2.0000000000000001e-127

   1. Initial program 49.8%

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

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 31.0%

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

   if 2.0000000000000001e-127 < A

   1. Initial program 76.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 90.4%

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

   5. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-lowering-*.f64 57.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, A\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 57.7%

      \[\leadsto \tan^{-1} \color{blue}{\left(\frac{-2 \cdot A}{B}\right)} \cdot \frac{180}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.2 \cdot 10^{-94}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-127}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 48.4% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.25 \cdot 10^{-92}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{-132}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.25e-92)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 4.1e-132)
     (* (/ 180.0 PI) (atan -1.0))
     (* (/ 180.0 PI) (atan (/ (* A -2.0) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.25e-92) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 4.1e-132) {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((A * -2.0) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.25e-92) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 4.1e-132) {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((A * -2.0) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.25e-92:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 4.1e-132:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	else:
		tmp = (180.0 / math.pi) * math.atan(((A * -2.0) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.25e-92)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 4.1e-132)
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A * -2.0) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.25e-92)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 4.1e-132)
		tmp = (180.0 / pi) * atan(-1.0);
	else
		tmp = (180.0 / pi) * atan(((A * -2.0) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.25e-92], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 4.1e-132], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.25000000000000003e-92

   1. Initial program 28.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 57.9%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, B\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 57.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0.5 \cdot B}{A}\right)}}{\pi} \]

   if -1.25000000000000003e-92 < A < 4.10000000000000007e-132

   1. Initial program 49.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 82.8%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 31.0%

      \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\pi} \]

   if 4.10000000000000007e-132 < A

   1. Initial program 76.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 90.4%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in A around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-2 \cdot \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-2 \cdot A}{B}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(-2 \cdot A\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. *-lowering-*.f64 57.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, A\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 57.7%

      \[\leadsto \tan^{-1} \color{blue}{\left(\frac{-2 \cdot A}{B}\right)} \cdot \frac{180}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.25 \cdot 10^{-92}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 4.1 \cdot 10^{-132}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 63.0% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 2.5 \cdot 10^{+25}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 2.5e+25)
   (* (/ 180.0 PI) (atan (+ 1.0 (/ (- C A) B))))
   (* (/ 180.0 PI) (atan (* B (/ 0.5 (- A C)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.5e+25) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + ((C - A) / B)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / (A - C))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.5e+25) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + ((C - A) / B)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / (A - C))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 2.5e+25:
		tmp = (180.0 / math.pi) * math.atan((1.0 + ((C - A) / B)))
	else:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / (A - C))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 2.5e+25)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(Float64(C - A) / B))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / Float64(A - C)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 2.5e+25)
		tmp = (180.0 / pi) * atan((1.0 + ((C - A) / B)));
	else
		tmp = (180.0 / pi) * atan((B * (0.5 / (A - C))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 2.5e+25], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 2.50000000000000012e25

   1. Initial program 63.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   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 63.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 63.1%

      \[\leadsto \tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)} \cdot \frac{180}{\pi} \]

   if 2.50000000000000012e25 < C

   1. Initial program 18.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 50.0%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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. 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. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\frac{-1}{2}}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \frac{\mathsf{neg}\left(\frac{1}{2}\right)}{C - A}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2} \cdot 1}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\mathsf{neg}\left(\frac{\frac{1}{2}}{C - A}\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C - A\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(C + \left(\mathsf{neg}\left(A\right)\right)\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(A\right)\right) + C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(A\right)\right)\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(\mathsf{neg}\left(A\right)\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      16. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{-1 \cdot \left(-1 \cdot A\right) + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{\left(-1 \cdot -1\right) \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{1 \cdot A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      19. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A + \left(\mathsf{neg}\left(C\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\frac{\frac{1}{2}}{A - C}\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      21. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \left(A - C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      22. --lowering--.f64 78.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, \mathsf{\_.f64}\left(A, C\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 78.5%

      \[\leadsto \tan^{-1} \color{blue}{\left(B \cdot \frac{0.5}{A - C}\right)} \cdot \frac{180}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 2.5 \cdot 10^{+25}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 43.3% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.35 \cdot 10^{-103}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-129}:\\ \;\;\;\;\frac{\frac{\tan^{-1} 0}{\pi}}{0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.35e-103)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 7.8e-129)
     (/ (/ (atan 0.0) PI) 0.005555555555555556)
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.35e-103) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 7.8e-129) {
		tmp = (atan(0.0) / ((double) M_PI)) / 0.005555555555555556;
	} 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 <= -1.35e-103) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 7.8e-129) {
		tmp = (Math.atan(0.0) / Math.PI) / 0.005555555555555556;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.35e-103:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 7.8e-129:
		tmp = (math.atan(0.0) / math.pi) / 0.005555555555555556
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.35e-103)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 7.8e-129)
		tmp = Float64(Float64(atan(0.0) / pi) / 0.005555555555555556);
	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 <= -1.35e-103)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 7.8e-129)
		tmp = (atan(0.0) / pi) / 0.005555555555555556;
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.35e-103], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.8e-129], N[(N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision] / 0.005555555555555556), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.35000000000000005e-103

   1. Initial program 58.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 82.5%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 51.4%

      \[\leadsto \tan^{-1} \color{blue}{1} \cdot \frac{180}{\pi} \]

   if -1.35000000000000005e-103 < B < 7.80000000000000019e-129

   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 63.4%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}\right)}{B}\right) \cdot \frac{1}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

      2. un-div-inv N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}\right)}{B}\right)}{\color{blue}{\frac{\mathsf{PI}\left(\right)}{180}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}\right)}{B}\right), \color{blue}{\left(\frac{\mathsf{PI}\left(\right)}{180}\right)}\right) \]

      4. atan-lowering-atan.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C - \left(A + \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}\right)}{B}\right)\right), \left(\frac{\color{blue}{\mathsf{PI}\left(\right)}}{180}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(C - \left(A + \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}\right)\right), B\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      6. associate--r+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\left(C - A\right) - \sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}\right), B\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(C - A\right), \left(\sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}\right)\right), B\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \left(\sqrt{B \cdot B + \left(C - A\right) \cdot \left(C - A\right)}\right)\right), B\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      9. accelerator-lowering-hypot.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{hypot.f64}\left(B, \left(C - A\right)\right)\right), B\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(C, A\right)\right)\right), B\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(C, A\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(\mathsf{PI}\left(\right), \color{blue}{180}\right)\right) \]

      12. PI-lowering-PI.f64 80.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(C, A\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

   6. Applied egg-rr 80.8%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\frac{\pi}{180}}} \]

   7. Taylor expanded in C around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]
   8. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

      2. distribute-rgt1-in N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-1 \cdot \left(\left(-1 + 1\right) \cdot A\right)}{B}\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-1 \cdot \left(0 \cdot A\right)}{B}\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

      4. mul0-lft N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{-1 \cdot 0}{B}\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{0}{B}\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

      6. /-lowering-/.f64 37.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(0, B\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

   9. Simplified 37.4%

      \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\frac{\pi}{180}} \]
   10. Step-by-step derivation

       1. div-inv N/A

          \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right) \cdot \color{blue}{\frac{1}{180}}} \]

       2. metadata-eval N/A

          \[\leadsto \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right) \cdot \frac{1}{180}} \]

       3. associate-/r* N/A

          \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right)}}{\color{blue}{\frac{1}{180}}} \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{\tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right)}\right), \color{blue}{\frac{1}{180}}\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\tan^{-1} \left(\frac{0}{B}\right), \mathsf{PI}\left(\right)\right), \frac{1}{180}\right) \]

       6. div0 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\tan^{-1} 0, \mathsf{PI}\left(\right)\right), \frac{1}{180}\right) \]

       7. atan-lowering-atan.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(0\right), \mathsf{PI}\left(\right)\right), \frac{1}{180}\right) \]

       8. PI-lowering-PI.f64 37.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(0\right), \mathsf{PI.f64}\left(\right)\right), \frac{1}{180}\right) \]

   11. Applied egg-rr 37.4%

       \[\leadsto \color{blue}{\frac{\frac{\tan^{-1} 0}{\pi}}{0.005555555555555556}} \]

   if 7.80000000000000019e-129 < B

   1. Initial program 42.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 72.7%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 51.2%

      \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.35 \cdot 10^{-103}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-129}:\\ \;\;\;\;\frac{\frac{\tan^{-1} 0}{\pi}}{0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 38.9% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -9.8 \cdot 10^{-269}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -9.8e-269)
   (* (/ 180.0 PI) (atan 1.0))
   (* (/ 180.0 PI) (atan -1.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -9.8e-269) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} 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 <= -9.8e-269) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -9.8e-269:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -9.8e-269)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	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 <= -9.8e-269)
		tmp = (180.0 / pi) * atan(1.0);
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -9.8e-269], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -9.79999999999999999e-269

   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 74.4%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 37.1%

      \[\leadsto \tan^{-1} \color{blue}{1} \cdot \frac{180}{\pi} \]

   if -9.79999999999999999e-269 < B

   1. Initial program 45.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 71.0%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 37.7%

      \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9.8 \cdot 10^{-269}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 20.1% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \frac{180}{\pi} \cdot \tan^{-1} -1 \end{array} \]

FPCore

(FPCore (A B C) :precision binary64 (* (/ 180.0 PI) (atan -1.0)))

C

double code(double A, double B, double C) {
	return (180.0 / ((double) M_PI)) * atan(-1.0);
}

Java

public static double code(double A, double B, double C) {
	return (180.0 / Math.PI) * Math.atan(-1.0);
}

Python

def code(A, B, C):
	return (180.0 / math.pi) * math.atan(-1.0)

Julia

function code(A, B, C)
	return Float64(Float64(180.0 / pi) * atan(-1.0))
end

MATLAB

function tmp = code(A, B, C)
	tmp = (180.0 / pi) * atan(-1.0);
end

Wolfram

code[A_, B_, C_] := N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 51.5%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
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 72.7%

   \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
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 20.0%

   \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\pi} \]

8. Final simplification 20.0%

   \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} -1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024191 
(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)))