ABCF->ab-angle angle

Percentage Accurate: 54.3% → 88.7%

Time: 20.2s

Alternatives: 27

Speedup: 3.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.3% 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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_1 := \left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-8}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{t\_1}{B}\right)}}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{1}{\frac{B}{t\_1}}\right)}{\frac{\pi}{180}}\\ \end{array} \end{array} \]

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))))))
        (t_1 (- (- C A) (hypot (- C A) B))))
   (if (<= t_0 -1e-8)
     (/ 1.0 (/ (/ PI 180.0) (atan (/ t_1 B))))
     (if (<= t_0 0.0)
       (/ (atan (* -0.5 (/ B (- C A)))) (/ PI 180.0))
       (/ (atan (/ 1.0 (/ B t_1))) (/ 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 t_1 = (C - A) - hypot((C - A), B);
	double tmp;
	if (t_0 <= -1e-8) {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((t_1 / B)));
	} else if (t_0 <= 0.0) {
		tmp = atan((-0.5 * (B / (C - A)))) / (((double) M_PI) / 180.0);
	} else {
		tmp = atan((1.0 / (B / t_1))) / (((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 t_1 = (C - A) - Math.hypot((C - A), B);
	double tmp;
	if (t_0 <= -1e-8) {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((t_1 / B)));
	} else if (t_0 <= 0.0) {
		tmp = Math.atan((-0.5 * (B / (C - A)))) / (Math.PI / 180.0);
	} else {
		tmp = Math.atan((1.0 / (B / t_1))) / (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))))
	t_1 = (C - A) - math.hypot((C - A), B)
	tmp = 0
	if t_0 <= -1e-8:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((t_1 / B)))
	elif t_0 <= 0.0:
		tmp = math.atan((-0.5 * (B / (C - A)))) / (math.pi / 180.0)
	else:
		tmp = math.atan((1.0 / (B / t_1))) / (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)))))
	t_1 = Float64(Float64(C - A) - hypot(Float64(C - A), B))
	tmp = 0.0
	if (t_0 <= -1e-8)
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(t_1 / B))));
	elseif (t_0 <= 0.0)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / Float64(pi / 180.0));
	else
		tmp = Float64(atan(Float64(1.0 / Float64(B / t_1))) / 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))));
	t_1 = (C - A) - hypot((C - A), B);
	tmp = 0.0;
	if (t_0 <= -1e-8)
		tmp = 1.0 / ((pi / 180.0) / atan((t_1 / B)));
	elseif (t_0 <= 0.0)
		tmp = atan((-0.5 * (B / (C - A)))) / (pi / 180.0);
	else
		tmp = atan((1.0 / (B / t_1))) / (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]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-8], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(t$95$1 / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(1.0 / N[(B / t$95$1), $MachinePrecision]), $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)))))) < -1e-8

   1. Initial program 62.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 86.1%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 90.7%

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

   6. Applied egg-rr 90.7%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      10. +-commutative N/A

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

      11. hypot-define N/A

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

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

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

      13. --lowering--.f64 90.7%

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

   8. Applied egg-rr 90.7%

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

   if -1e-8 < (*.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 10.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 9.4%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 10.7%

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

   6. Applied egg-rr 10.7%

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

   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. *-lowering-*.f64 N/A

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

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

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

      3. --lowering--.f64 99.6%

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

   9. Simplified 99.6%

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

   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 62.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

   3. Simplified 82.9%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 87.5%

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

   6. Applied egg-rr 87.5%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

      6. +-commutative N/A

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

      7. hypot-define N/A

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

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

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

      9. --lowering--.f64 87.6%

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

   8. Applied egg-rr 87.6%

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

Alternative 2: 80.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.2 \cdot 10^{+62}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-92}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.2e+62)
   (/ (atan (* -0.5 (/ B (- C A)))) (/ PI 180.0))
   (if (<= A 2.1e-92)
     (/ (atan (/ (- C (hypot C B)) B)) (/ PI 180.0))
     (* (/ 180.0 PI) (atan (/ (- C (+ A (hypot A B))) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.2e+62) {
		tmp = atan((-0.5 * (B / (C - A)))) / (((double) M_PI) / 180.0);
	} else if (A <= 2.1e-92) {
		tmp = atan(((C - hypot(C, B)) / B)) / (((double) M_PI) / 180.0);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (A + hypot(A, B))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.2e+62) {
		tmp = Math.atan((-0.5 * (B / (C - A)))) / (Math.PI / 180.0);
	} else if (A <= 2.1e-92) {
		tmp = Math.atan(((C - Math.hypot(C, B)) / B)) / (Math.PI / 180.0);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (A + Math.hypot(A, B))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.2e+62:
		tmp = math.atan((-0.5 * (B / (C - A)))) / (math.pi / 180.0)
	elif A <= 2.1e-92:
		tmp = math.atan(((C - math.hypot(C, B)) / B)) / (math.pi / 180.0)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (A + math.hypot(A, B))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.2e+62)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / Float64(pi / 180.0));
	elseif (A <= 2.1e-92)
		tmp = Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / Float64(pi / 180.0));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(A + hypot(A, B))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.2e+62)
		tmp = atan((-0.5 * (B / (C - A)))) / (pi / 180.0);
	elseif (A <= 2.1e-92)
		tmp = atan(((C - hypot(C, B)) / B)) / (pi / 180.0);
	else
		tmp = (180.0 / pi) * atan(((C - (A + hypot(A, B))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.2e+62], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.1e-92], N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.19999999999999967e62

   1. Initial program 13.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 26.5%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 49.4%

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

   6. Applied egg-rr 49.4%

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

   7. Taylor expanded in 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. *-lowering-*.f64 N/A

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

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

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

      3. --lowering--.f64 85.4%

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

   9. Simplified 85.4%

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

   if -8.19999999999999967e62 < A < 2.1e-92

   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. 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 76.1%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 76.5%

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

   6. Applied egg-rr 76.5%

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

   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. hypot-define N/A

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

      7. hypot-lowering-hypot.f64 76.5%

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

   9. Simplified 76.5%

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

   if 2.1e-92 < A

   1. Initial program 74.0%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

   3. Simplified 91.7%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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. unpow2 N/A

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

      3. unpow2 N/A

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

      4. hypot-define N/A

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

      5. hypot-lowering-hypot.f64 88.6%

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

   7. Simplified 88.6%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.2 \cdot 10^{+62}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{-92}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(A, B\right)\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.8 \cdot 10^{+66}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.8e+66)
   (/ (atan (* -0.5 (/ B (- C A)))) (/ PI 180.0))
   (/ 1.0 (/ (/ PI 180.0) (atan (/ (- (- C A) (hypot (- C A) B)) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.8e+66) {
		tmp = atan((-0.5 * (B / (C - A)))) / (((double) M_PI) / 180.0);
	} else {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((((C - A) - hypot((C - A), B)) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.8e+66) {
		tmp = Math.atan((-0.5 * (B / (C - A)))) / (Math.PI / 180.0);
	} else {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((((C - A) - Math.hypot((C - A), B)) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.8e+66:
		tmp = math.atan((-0.5 * (B / (C - A)))) / (math.pi / 180.0)
	else:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((((C - A) - math.hypot((C - A), B)) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.8e+66)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / Float64(pi / 180.0));
	else
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(Float64(Float64(C - A) - hypot(Float64(C - A), B)) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.8e+66)
		tmp = atan((-0.5 * (B / (C - A)))) / (pi / 180.0);
	else
		tmp = 1.0 / ((pi / 180.0) / atan((((C - A) - hypot((C - A), B)) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.8e+66], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -3.8000000000000002e66

   1. Initial program 13.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 26.5%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 49.4%

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

   6. Applied egg-rr 49.4%

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

   7. Taylor expanded in 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. *-lowering-*.f64 N/A

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

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

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

      3. --lowering--.f64 85.4%

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

   9. Simplified 85.4%

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

   if -3.8000000000000002e66 < A

   1. Initial program 62.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 81.8%

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

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

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

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

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

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

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

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

      13. 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. Step-by-step derivation

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      10. +-commutative N/A

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

      11. hypot-define N/A

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

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

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

      13. --lowering--.f64 82.0%

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

   8. Applied egg-rr 82.0%

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

Alternative 4: 77.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3 \cdot 10^{+64}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 1.02 \cdot 10^{+63}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3e+64)
   (/ (atan (* -0.5 (/ B (- C A)))) (/ PI 180.0))
   (if (<= A 1.02e+63)
     (/ (atan (/ (- C (hypot C B)) B)) (/ PI 180.0))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3e+64) {
		tmp = atan((-0.5 * (B / (C - A)))) / (((double) M_PI) / 180.0);
	} else if (A <= 1.02e+63) {
		tmp = atan(((C - hypot(C, B)) / B)) / (((double) M_PI) / 180.0);
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3e+64) {
		tmp = Math.atan((-0.5 * (B / (C - A)))) / (Math.PI / 180.0);
	} else if (A <= 1.02e+63) {
		tmp = Math.atan(((C - Math.hypot(C, B)) / B)) / (Math.PI / 180.0);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3e+64:
		tmp = math.atan((-0.5 * (B / (C - A)))) / (math.pi / 180.0)
	elif A <= 1.02e+63:
		tmp = math.atan(((C - math.hypot(C, B)) / B)) / (math.pi / 180.0)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3e+64)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / Float64(pi / 180.0));
	elseif (A <= 1.02e+63)
		tmp = Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / Float64(pi / 180.0));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3e+64)
		tmp = atan((-0.5 * (B / (C - A)))) / (pi / 180.0);
	elseif (A <= 1.02e+63)
		tmp = atan(((C - hypot(C, B)) / B)) / (pi / 180.0);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3e+64], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.02e+63], N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.0000000000000002e64

   1. Initial program 13.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 26.5%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 49.4%

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

   6. Applied egg-rr 49.4%

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

   7. Taylor expanded in 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. *-lowering-*.f64 N/A

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

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

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

      3. --lowering--.f64 85.4%

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

   9. Simplified 85.4%

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

   if -3.0000000000000002e64 < A < 1.02e63

   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. 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 77.4%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 77.8%

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

   6. Applied egg-rr 77.8%

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

   7. Taylor expanded in 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. hypot-define N/A

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

      7. hypot-lowering-hypot.f64 75.9%

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

   9. Simplified 75.9%

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

   if 1.02e63 < A

   1. Initial program 85.3%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

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

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

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

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

      5. --lowering--.f64 86.9%

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

   5. Simplified 86.9%

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

Alternative 5: 77.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{+64}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.1e+63)
   (/ (atan (* -0.5 (/ B (- C A)))) (/ PI 180.0))
   (if (<= A 1.55e+64)
     (* (/ 180.0 PI) (atan (/ (- C (hypot C B)) B)))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e+63) {
		tmp = atan((-0.5 * (B / (C - A)))) / (((double) M_PI) / 180.0);
	} else if (A <= 1.55e+64) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(C, B)) / B));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e+63) {
		tmp = Math.atan((-0.5 * (B / (C - A)))) / (Math.PI / 180.0);
	} else if (A <= 1.55e+64) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(C, B)) / B));
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.1e+63:
		tmp = math.atan((-0.5 * (B / (C - A)))) / (math.pi / 180.0)
	elif A <= 1.55e+64:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(C, B)) / B))
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.1e+63)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / Float64(pi / 180.0));
	elseif (A <= 1.55e+64)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(C, B)) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.1e+63)
		tmp = atan((-0.5 * (B / (C - A)))) / (pi / 180.0);
	elseif (A <= 1.55e+64)
		tmp = (180.0 / pi) * atan(((C - hypot(C, B)) / B));
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.1e+63], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.55e+64], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.1000000000000001e63

   1. Initial program 13.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 26.5%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 49.4%

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

   6. Applied egg-rr 49.4%

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

   7. Taylor expanded in 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. *-lowering-*.f64 N/A

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

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

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

      3. --lowering--.f64 85.4%

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

   9. Simplified 85.4%

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

   if -3.1000000000000001e63 < A < 1.55e64

   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. 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 77.4%

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

   5. Taylor expanded in A around 0

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

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

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

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

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

      3. +-commutative N/A

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

      4. unpow2 N/A

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

      5. unpow2 N/A

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

      6. hypot-define N/A

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

      7. hypot-lowering-hypot.f64 75.8%

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

   7. Simplified 75.8%

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

   if 1.55e64 < A

   1. Initial program 85.3%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

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

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

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

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

      5. --lowering--.f64 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 1.55 \cdot 10^{+64}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.6 \cdot 10^{+66}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\frac{\pi}{180}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.6e+66)
   (/ (atan (* -0.5 (/ B (- 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 tmp;
	if (A <= -1.6e+66) {
		tmp = atan((-0.5 * (B / (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 tmp;
	if (A <= -1.6e+66) {
		tmp = Math.atan((-0.5 * (B / (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):
	tmp = 0
	if A <= -1.6e+66:
		tmp = math.atan((-0.5 * (B / (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)
	tmp = 0.0
	if (A <= -1.6e+66)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / 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)
	tmp = 0.0;
	if (A <= -1.6e+66)
		tmp = atan((-0.5 * (B / (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_] := If[LessEqual[A, -1.6e+66], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $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 2 regimes

2. if A < -1.6e66

   1. Initial program 13.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 26.5%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 49.4%

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

   6. Applied egg-rr 49.4%

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

   7. Taylor expanded in 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. *-lowering-*.f64 N/A

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

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

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

      3. --lowering--.f64 85.4%

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

   9. Simplified 85.4%

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

   if -1.6e66 < A

   1. Initial program 62.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 81.8%

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

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

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

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

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

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

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

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

      13. 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%

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

Alternative 7: 82.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.55 \cdot 10^{+62}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.55e+62)
   (/ (atan (* -0.5 (/ B (- C A)))) (/ PI 180.0))
   (* (atan (/ (- C (+ A (hypot B (- C A)))) B)) (/ 180.0 PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.55e+62) {
		tmp = atan((-0.5 * (B / (C - A)))) / (((double) M_PI) / 180.0);
	} else {
		tmp = atan(((C - (A + hypot(B, (C - A)))) / B)) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.55e+62) {
		tmp = Math.atan((-0.5 * (B / (C - A)))) / (Math.PI / 180.0);
	} else {
		tmp = Math.atan(((C - (A + Math.hypot(B, (C - A)))) / B)) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.55e+62:
		tmp = math.atan((-0.5 * (B / (C - A)))) / (math.pi / 180.0)
	else:
		tmp = math.atan(((C - (A + math.hypot(B, (C - A)))) / B)) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.55e+62)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / Float64(pi / 180.0));
	else
		tmp = Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(C - A)))) / B)) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.55e+62)
		tmp = atan((-0.5 * (B / (C - A)))) / (pi / 180.0);
	else
		tmp = atan(((C - (A + hypot(B, (C - A)))) / B)) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.55e+62], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if A < -1.55000000000000007e62

   1. Initial program 13.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 26.5%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 49.4%

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

   6. Applied egg-rr 49.4%

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

   7. Taylor expanded in 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. *-lowering-*.f64 N/A

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

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

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

      3. --lowering--.f64 85.4%

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

   9. Simplified 85.4%

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

   if -1.55000000000000007e62 < A

   1. Initial program 62.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 81.8%

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

Alternative 8: 66.7% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -1.25 \cdot 10^{-300}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-213}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{-0.5}{t\_0}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(-0.5 \cdot \left(t\_0 \cdot t\_0\right) + \left(\left(\frac{C}{B} + -1\right) - \frac{A}{B}\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -1.25e-300)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 1.6e-213)
       (/ 1.0 (/ (/ PI 180.0) (atan (/ -0.5 t_0))))
       (/
        1.0
        (/
         (/ PI 180.0)
         (atan (+ (* -0.5 (* t_0 t_0)) (- (+ (/ C B) -1.0) (/ A B))))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.25e-300) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 1.6e-213) {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((-0.5 / t_0)));
	} else {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan(((-0.5 * (t_0 * t_0)) + (((C / B) + -1.0) - (A / B)))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.25e-300) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 1.6e-213) {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((-0.5 / t_0)));
	} else {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan(((-0.5 * (t_0 * t_0)) + (((C / B) + -1.0) - (A / B)))));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -1.25e-300:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 1.6e-213:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((-0.5 / t_0)))
	else:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan(((-0.5 * (t_0 * t_0)) + (((C / B) + -1.0) - (A / B)))))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -1.25e-300)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 1.6e-213)
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(-0.5 / t_0))));
	else
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(Float64(-0.5 * Float64(t_0 * t_0)) + Float64(Float64(Float64(C / B) + -1.0) - Float64(A / B))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -1.25e-300)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 1.6e-213)
		tmp = 1.0 / ((pi / 180.0) / atan((-0.5 / t_0)));
	else
		tmp = 1.0 / ((pi / 180.0) / atan(((-0.5 * (t_0 * t_0)) + (((C / B) + -1.0) - (A / B)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -1.25e-300], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.6e-213], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(-0.5 / t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(N[(-0.5 * N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision] - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.24999999999999999e-300

   1. Initial program 55.4%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

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

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

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

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

      5. --lowering--.f64 66.0%

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

   5. Simplified 66.0%

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

   if -1.24999999999999999e-300 < B < 1.59999999999999986e-213

   1. Initial program 35.8%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 77.4%

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

   6. Applied egg-rr 77.4%

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

   7. Taylor expanded in 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. *-lowering-*.f64 N/A

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

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

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

      3. --lowering--.f64 72.1%

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

   9. Simplified 72.1%

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

       1. clear-num N/A

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

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

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

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

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

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

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

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

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

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

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

       7. clear-num N/A

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

       8. un-div-inv N/A

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

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

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

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

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

       11. --lowering--.f64 72.3%

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

   11. Applied egg-rr 72.3%

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

   if 1.59999999999999986e-213 < B

   1. Initial program 56.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 76.5%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 78.3%

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

   6. Applied egg-rr 78.3%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      10. +-commutative N/A

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

      11. hypot-define N/A

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

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

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

      13. --lowering--.f64 78.3%

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

   8. Applied egg-rr 78.3%

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

   9. Taylor expanded in B around inf

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

       1. associate--l+ N/A

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

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

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

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

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

       4. unpow2 N/A

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

       5. unpow2 N/A

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

       6. times-frac N/A

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

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

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

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

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

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

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

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

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

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

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

       12. associate--r+ N/A

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

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

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

       14. sub-neg N/A

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

       15. metadata-eval N/A

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

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

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

       17. /-lowering-/.f64 N/A

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

       18. /-lowering-/.f64 74.2%

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

   11. Simplified 74.2%

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

Alternative 9: 66.8% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -3.9 \cdot 10^{-296}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-213}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{-0.5}{t\_0}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{B} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right) + \left(t\_0 + -1\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -3.9e-296)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 3.2e-213)
       (/ 1.0 (/ (/ PI 180.0) (atan (/ -0.5 t_0))))
       (*
        180.0
        (/
         (atan (+ (* (/ -0.5 B) (* (- A C) (/ (- A C) B))) (+ t_0 -1.0)))
         PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -3.9e-296) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 3.2e-213) {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((-0.5 / t_0)));
	} else {
		tmp = 180.0 * (atan((((-0.5 / B) * ((A - C) * ((A - C) / B))) + (t_0 + -1.0))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -3.9e-296) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 3.2e-213) {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((-0.5 / t_0)));
	} else {
		tmp = 180.0 * (Math.atan((((-0.5 / B) * ((A - C) * ((A - C) / B))) + (t_0 + -1.0))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -3.9e-296:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 3.2e-213:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((-0.5 / t_0)))
	else:
		tmp = 180.0 * (math.atan((((-0.5 / B) * ((A - C) * ((A - C) / B))) + (t_0 + -1.0))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -3.9e-296)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 3.2e-213)
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(-0.5 / t_0))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-0.5 / B) * Float64(Float64(A - C) * Float64(Float64(A - C) / B))) + Float64(t_0 + -1.0))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -3.9e-296)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 3.2e-213)
		tmp = 1.0 / ((pi / 180.0) / atan((-0.5 / t_0)));
	else
		tmp = 180.0 * (atan((((-0.5 / B) * ((A - C) * ((A - C) / B))) + (t_0 + -1.0))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -3.9e-296], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.2e-213], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(-0.5 / t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(-0.5 / B), $MachinePrecision] * N[(N[(A - C), $MachinePrecision] * N[(N[(A - C), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.9000000000000001e-296

   1. Initial program 55.4%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

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

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

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

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

      5. --lowering--.f64 66.0%

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

   5. Simplified 66.0%

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

   if -3.9000000000000001e-296 < B < 3.19999999999999972e-213

   1. Initial program 35.8%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 77.4%

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

   6. Applied egg-rr 77.4%

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

   7. Taylor expanded in 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. *-lowering-*.f64 N/A

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

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

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

      3. --lowering--.f64 72.1%

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

   9. Simplified 72.1%

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

       1. clear-num N/A

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

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

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

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

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

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

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

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

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

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

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

       7. clear-num N/A

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

       8. un-div-inv N/A

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

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

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

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

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

       11. --lowering--.f64 72.3%

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

   11. Applied egg-rr 72.3%

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

   if 3.19999999999999972e-213 < B

   1. Initial program 56.3%

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

   3. Taylor expanded in B around inf

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

      1. associate--l+ N/A

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

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

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

   5. Simplified 74.1%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.9 \cdot 10^{-296}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.2 \cdot 10^{-213}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5}{B} \cdot \left(\left(A - C\right) \cdot \frac{A - C}{B}\right) + \left(\frac{C - A}{B} + -1\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.4% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -1.5 \cdot 10^{-301}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-203}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{-0.5}{t\_0}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\left(\frac{C}{B} + -1\right) - \frac{A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -1.5e-301)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 7e-203)
       (/ 1.0 (/ (/ PI 180.0) (atan (/ -0.5 t_0))))
       (/ 1.0 (/ (/ PI 180.0) (atan (- (+ (/ C B) -1.0) (/ A B)))))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.5e-301) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 7e-203) {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((-0.5 / t_0)));
	} else {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((((C / B) + -1.0) - (A / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.5e-301) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 7e-203) {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((-0.5 / t_0)));
	} else {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((((C / B) + -1.0) - (A / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -1.5e-301:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 7e-203:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((-0.5 / t_0)))
	else:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((((C / B) + -1.0) - (A / B))))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -1.5e-301)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 7e-203)
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(-0.5 / t_0))));
	else
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(Float64(Float64(C / B) + -1.0) - Float64(A / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -1.5e-301)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 7e-203)
		tmp = 1.0 / ((pi / 180.0) / atan((-0.5 / t_0)));
	else
		tmp = 1.0 / ((pi / 180.0) / atan((((C / B) + -1.0) - (A / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -1.5e-301], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7e-203], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(-0.5 / t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(N[(N[(C / B), $MachinePrecision] + -1.0), $MachinePrecision] - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.5e-301

   1. Initial program 55.4%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

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

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

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

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

      5. --lowering--.f64 66.0%

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

   5. Simplified 66.0%

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

   if -1.5e-301 < B < 7.0000000000000003e-203

   1. Initial program 38.4%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

   3. Simplified 57.9%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 73.4%

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

   6. Applied egg-rr 73.4%

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

   7. Taylor expanded in 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. *-lowering-*.f64 N/A

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

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

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

      3. --lowering--.f64 68.8%

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

   9. Simplified 68.8%

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

       1. clear-num N/A

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

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

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

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

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

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

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

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

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

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

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

       7. clear-num N/A

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

       8. un-div-inv N/A

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

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

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

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

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

       11. --lowering--.f64 68.9%

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

   11. Applied egg-rr 68.9%

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

   if 7.0000000000000003e-203 < B

   1. Initial program 56.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 77.5%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 79.3%

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

   6. Applied egg-rr 79.3%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

      10. +-commutative N/A

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

      11. hypot-define N/A

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

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

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

      13. --lowering--.f64 79.3%

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

   8. Applied egg-rr 79.3%

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

   9. Taylor expanded in B around inf

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

       1. associate--r+ N/A

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

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

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

       3. sub-neg N/A

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

       4. metadata-eval N/A

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

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

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

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

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

       7. /-lowering-/.f64 74.2%

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

   11. Simplified 74.2%

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

Alternative 11: 66.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -5.6 \cdot 10^{-300}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-149}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{-0.5}{t\_0}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(t\_0 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -5.6e-300)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 8.5e-149)
       (/ 1.0 (/ (/ PI 180.0) (atan (/ -0.5 t_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 <= -5.6e-300) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 8.5e-149) {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((-0.5 / t_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 <= -5.6e-300) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 8.5e-149) {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((-0.5 / t_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 <= -5.6e-300:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 8.5e-149:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((-0.5 / t_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 <= -5.6e-300)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 8.5e-149)
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(-0.5 / t_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 <= -5.6e-300)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 8.5e-149)
		tmp = 1.0 / ((pi / 180.0) / atan((-0.5 / t_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, -5.6e-300], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.5e-149], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(-0.5 / t$95$0), $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 < -5.59999999999999988e-300

   1. Initial program 55.4%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

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

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

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

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

      5. --lowering--.f64 66.0%

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

   5. Simplified 66.0%

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

   if -5.59999999999999988e-300 < B < 8.5000000000000006e-149

   1. Initial program 39.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 59.3%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 74.0%

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

   6. Applied egg-rr 74.0%

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

   7. Taylor expanded in B around 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. *-lowering-*.f64 N/A

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

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

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

      3. --lowering--.f64 64.5%

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

   9. Simplified 64.5%

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

       1. clear-num N/A

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

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

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

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

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

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

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

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

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

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

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

       7. clear-num N/A

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

       8. un-div-inv N/A

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

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

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

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

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

       11. --lowering--.f64 64.6%

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

   11. Applied egg-rr 64.6%

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

   if 8.5000000000000006e-149 < B

   1. Initial program 57.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 78.6%

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

   5. Taylor expanded in 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. --lowering--.f64 N/A

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

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

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

      6. --lowering--.f64 76.1%

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

   7. Simplified 76.1%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.6 \cdot 10^{-300}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-149}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.2% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -6 \cdot 10^{-297}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-152}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5}{t\_0}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(t\_0 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -6e-297)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 1.15e-152)
       (/ (* 180.0 (atan (/ -0.5 t_0))) PI)
       (* (/ 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 <= -6e-297) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 1.15e-152) {
		tmp = (180.0 * atan((-0.5 / t_0))) / ((double) M_PI);
	} 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 <= -6e-297) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 1.15e-152) {
		tmp = (180.0 * Math.atan((-0.5 / t_0))) / Math.PI;
	} 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 <= -6e-297:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 1.15e-152:
		tmp = (180.0 * math.atan((-0.5 / t_0))) / math.pi
	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 <= -6e-297)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 1.15e-152)
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 / t_0))) / pi);
	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 <= -6e-297)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 1.15e-152)
		tmp = (180.0 * atan((-0.5 / t_0))) / pi;
	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, -6e-297], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.15e-152], N[(N[(180.0 * N[ArcTan[N[(-0.5 / t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $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 < -5.9999999999999999e-297

   1. Initial program 55.4%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

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

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

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

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

      5. --lowering--.f64 66.0%

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

   5. Simplified 66.0%

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

   if -5.9999999999999999e-297 < B < 1.1500000000000001e-152

   1. Initial program 39.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 59.3%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 74.0%

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

   6. Applied egg-rr 74.0%

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

   7. Taylor expanded in B around 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. *-lowering-*.f64 N/A

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

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

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

      3. --lowering--.f64 64.5%

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

   9. Simplified 64.5%

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

       1. associate-/r/ N/A

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

       2. associate-*l/ N/A

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

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

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

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

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

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

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

       6. clear-num N/A

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

       7. un-div-inv N/A

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

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

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

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

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

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

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

       11. PI-lowering-PI.f64 64.6%

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

   11. Applied egg-rr 64.6%

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

   if 1.1500000000000001e-152 < B

   1. Initial program 57.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 78.6%

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

   5. Taylor expanded in 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. --lowering--.f64 N/A

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

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

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

      6. --lowering--.f64 76.1%

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

   7. Simplified 76.1%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6 \cdot 10^{-297}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{-152}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-0.5}{\frac{C - A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -1.25 \cdot 10^{-301}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-160}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(t\_0 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -1.25e-301)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 9.2e-160)
       (/ (* 180.0 (atan (* B (/ -0.5 (- C A))))) PI)
       (* (/ 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 <= -1.25e-301) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 9.2e-160) {
		tmp = (180.0 * atan((B * (-0.5 / (C - A))))) / ((double) M_PI);
	} 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 <= -1.25e-301) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 9.2e-160) {
		tmp = (180.0 * Math.atan((B * (-0.5 / (C - A))))) / Math.PI;
	} 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 <= -1.25e-301:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 9.2e-160:
		tmp = (180.0 * math.atan((B * (-0.5 / (C - A))))) / math.pi
	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 <= -1.25e-301)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 9.2e-160)
		tmp = Float64(Float64(180.0 * atan(Float64(B * Float64(-0.5 / Float64(C - A))))) / pi);
	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 <= -1.25e-301)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 9.2e-160)
		tmp = (180.0 * atan((B * (-0.5 / (C - A))))) / pi;
	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, -1.25e-301], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.2e-160], N[(N[(180.0 * N[ArcTan[N[(B * N[(-0.5 / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $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 < -1.25000000000000003e-301

   1. Initial program 55.4%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

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

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

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

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

      5. --lowering--.f64 66.0%

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

   5. Simplified 66.0%

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

   if -1.25000000000000003e-301 < B < 9.19999999999999939e-160

   1. Initial program 39.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 59.3%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 74.0%

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

   6. Applied egg-rr 74.0%

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

   7. Taylor expanded in B around 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. *-lowering-*.f64 N/A

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

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

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

      3. --lowering--.f64 64.5%

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

   9. Simplified 64.5%

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

       1. associate-/r/ N/A

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

       2. associate-*l/ N/A

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

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

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

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

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

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

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

       6. clear-num N/A

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

       7. un-div-inv N/A

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

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

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

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

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

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

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

       11. PI-lowering-PI.f64 64.6%

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

   11. Applied egg-rr 64.6%

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

       1. associate-/r/ N/A

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

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

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

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

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

       4. --lowering--.f64 64.5%

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

   13. Applied egg-rr 64.5%

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

   if 9.19999999999999939e-160 < B

   1. Initial program 57.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 78.6%

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

   5. Taylor expanded in 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. --lowering--.f64 N/A

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

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

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

      6. --lowering--.f64 76.1%

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

   7. Simplified 76.1%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.25 \cdot 10^{-301}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-160}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 66.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -3.6 \cdot 10^{-300}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(t\_0 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -3.6e-300)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 9.5e-203)
       (/ (atan (* -0.5 (/ B (- 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 <= -3.6e-300) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 9.5e-203) {
		tmp = atan((-0.5 * (B / (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 <= -3.6e-300) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 9.5e-203) {
		tmp = Math.atan((-0.5 * (B / (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 <= -3.6e-300:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 9.5e-203:
		tmp = math.atan((-0.5 * (B / (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 <= -3.6e-300)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 9.5e-203)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / 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 <= -3.6e-300)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 9.5e-203)
		tmp = atan((-0.5 * (B / (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, -3.6e-300], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.5e-203], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $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 < -3.60000000000000016e-300

   1. Initial program 55.4%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

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

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

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

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

      5. --lowering--.f64 66.0%

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

   5. Simplified 66.0%

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

   if -3.60000000000000016e-300 < B < 9.50000000000000035e-203

   1. Initial program 38.4%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

   3. Simplified 57.9%

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

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

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

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

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

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

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

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

      13. PI-lowering-PI.f64 73.4%

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

   6. Applied egg-rr 73.4%

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

   7. Taylor expanded in 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. *-lowering-*.f64 N/A

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

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

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

      3. --lowering--.f64 68.8%

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

   9. Simplified 68.8%

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

   if 9.50000000000000035e-203 < B

   1. Initial program 56.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 77.5%

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

   5. Taylor expanded in B around inf

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

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

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

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

      6. --lowering--.f64 74.2%

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

   7. Simplified 74.2%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.6 \cdot 10^{-300}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 66.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -1.38 \cdot 10^{-297}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-203}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(t\_0 + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -1.38e-297)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 2.6e-203)
       (* (atan (* -0.5 (/ B (- C A)))) (/ 180.0 PI))
       (* (/ 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 <= -1.38e-297) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 2.6e-203) {
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / ((double) M_PI));
	} 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 <= -1.38e-297) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 2.6e-203) {
		tmp = Math.atan((-0.5 * (B / (C - A)))) * (180.0 / Math.PI);
	} 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 <= -1.38e-297:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 2.6e-203:
		tmp = math.atan((-0.5 * (B / (C - A)))) * (180.0 / math.pi)
	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 <= -1.38e-297)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 2.6e-203)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) * Float64(180.0 / pi));
	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 <= -1.38e-297)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 2.6e-203)
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / pi);
	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, -1.38e-297], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.6e-203], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $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 < -1.38000000000000004e-297

   1. Initial program 55.4%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

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

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

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

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

      5. --lowering--.f64 66.0%

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

   5. Simplified 66.0%

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

   if -1.38000000000000004e-297 < B < 2.59999999999999975e-203

   1. Initial program 38.4%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

   3. Simplified 57.9%

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

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

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

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

      3. --lowering--.f64 68.8%

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

   7. Simplified 68.8%

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

   if 2.59999999999999975e-203 < B

   1. Initial program 56.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 77.5%

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

   5. Taylor expanded in B around inf

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

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

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

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

      6. --lowering--.f64 74.2%

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

   7. Simplified 74.2%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.38 \cdot 10^{-297}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-203}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 66.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -1.3 \cdot 10^{-301}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-203}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_0 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -1.3e-301)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 2.5e-203)
       (* (atan (* -0.5 (/ B (- C A)))) (/ 180.0 PI))
       (* 180.0 (/ (atan (+ t_0 -1.0)) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -1.3e-301) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 2.5e-203) {
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((t_0 + -1.0)) / ((double) M_PI));
	}
	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-301) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 2.5e-203) {
		tmp = Math.atan((-0.5 * (B / (C - A)))) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((t_0 + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -1.3e-301:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 2.5e-203:
		tmp = math.atan((-0.5 * (B / (C - A)))) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan((t_0 + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -1.3e-301)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 2.5e-203)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -1.3e-301)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 2.5e-203)
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / pi);
	else
		tmp = 180.0 * (atan((t_0 + -1.0)) / pi);
	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-301], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.5e-203], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.2999999999999999e-301

   1. Initial program 55.4%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

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

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

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

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

      5. --lowering--.f64 66.0%

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

   5. Simplified 66.0%

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

   if -1.2999999999999999e-301 < B < 2.5000000000000001e-203

   1. Initial program 38.4%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

   3. Simplified 57.9%

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

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

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

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

      3. --lowering--.f64 68.8%

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

   7. Simplified 68.8%

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

   if 2.5000000000000001e-203 < B

   1. Initial program 56.5%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

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

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

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

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

      6. --lowering--.f64 74.2%

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

   5. Simplified 74.2%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.3 \cdot 10^{-301}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-203}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 65.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -2.3 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 10^{-250}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_0 + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -2.3e-302)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 1e-250)
       (* (/ 180.0 PI) (atan (* B (/ 0.5 A))))
       (* 180.0 (/ (atan (+ t_0 -1.0)) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -2.3e-302) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 1e-250) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / A)));
	} else {
		tmp = 180.0 * (atan((t_0 + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -2.3e-302) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 1e-250) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / A)));
	} else {
		tmp = 180.0 * (Math.atan((t_0 + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -2.3e-302:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 1e-250:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / A)))
	else:
		tmp = 180.0 * (math.atan((t_0 + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -2.3e-302)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 1e-250)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / A))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -2.3e-302)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 1e-250)
		tmp = (180.0 / pi) * atan((B * (0.5 / A)));
	else
		tmp = 180.0 * (atan((t_0 + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[B, -2.3e-302], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1e-250], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.30000000000000002e-302

   1. Initial program 55.4%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 66.0%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 66.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   if -2.30000000000000002e-302 < B < 1.0000000000000001e-250

   1. Initial program 29.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 49.0%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(B \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} - \frac{1}{2} \cdot \frac{1}{C - A}\right)\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\frac{\frac{1}{8} \cdot {B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\frac{\frac{1}{8}}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\frac{\frac{1}{8} \cdot 1}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{+.f64}\left(\left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2}\right), \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 60.5%

      \[\leadsto \tan^{-1} \color{blue}{\left(B \cdot \left(\left(B \cdot B\right) \cdot \frac{\frac{0.125}{C - A}}{\left(C - A\right) \cdot \left(C - A\right)} + \frac{-0.5}{C - A}\right)\right)} \cdot \frac{180}{\pi} \]

   8. Taylor expanded in A around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \color{blue}{\left(\frac{\frac{1}{2}}{A}\right)}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 60.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 60.9%

       \[\leadsto \tan^{-1} \left(B \cdot \color{blue}{\frac{0.5}{A}}\right) \cdot \frac{180}{\pi} \]

   if 1.0000000000000001e-250 < B

   1. Initial program 56.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C}{B} - \left(\frac{A}{B} + 1\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate--r+ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\left(\frac{C}{B} - \frac{A}{B}\right) - 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{C - A}{B} - 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\left(\frac{C - A}{B}\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(C - A\right), B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. --lowering--.f64 71.3%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right), 1\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 71.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C - A}{B} - 1\right)}}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.3 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 10^{-250}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 60.9% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -9.5 \cdot 10^{-303}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-247}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -9.5e-303)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= B 3.7e-247)
     (* (/ 180.0 PI) (atan (* B (/ 0.5 A))))
     (* (/ 180.0 PI) (atan (/ (- C B) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -9.5e-303) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= 3.7e-247) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / A)));
	} 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 <= -9.5e-303) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= 3.7e-247) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / A)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -9.5e-303:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= 3.7e-247:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / A)))
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -9.5e-303)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= 3.7e-247)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / A))));
	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 <= -9.5e-303)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= 3.7e-247)
		tmp = (180.0 / pi) * atan((B * (0.5 / A)));
	else
		tmp = (180.0 / pi) * atan(((C - B) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -9.5e-303], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.7e-247], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $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 3 regimes

2. if B < -9.4999999999999999e-303

   1. Initial program 55.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(1 + \frac{C - A}{B}\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{C - A}{B}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(C - A\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. --lowering--.f64 66.0%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, A\right), B\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 66.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   if -9.4999999999999999e-303 < B < 3.7000000000000001e-247

   1. Initial program 29.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 49.0%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(B \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} - \frac{1}{2} \cdot \frac{1}{C - A}\right)\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\frac{\frac{1}{8} \cdot {B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\frac{\frac{1}{8}}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\frac{\frac{1}{8} \cdot 1}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{+.f64}\left(\left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2}\right), \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 60.5%

      \[\leadsto \tan^{-1} \color{blue}{\left(B \cdot \left(\left(B \cdot B\right) \cdot \frac{\frac{0.125}{C - A}}{\left(C - A\right) \cdot \left(C - A\right)} + \frac{-0.5}{C - A}\right)\right)} \cdot \frac{180}{\pi} \]

   8. Taylor expanded in A around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \color{blue}{\left(\frac{\frac{1}{2}}{A}\right)}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 60.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 60.9%

       \[\leadsto \tan^{-1} \left(B \cdot \color{blue}{\frac{0.5}{A}}\right) \cdot \frac{180}{\pi} \]

   if 3.7000000000000001e-247 < B

   1. Initial program 56.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 76.9%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \color{blue}{B}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 63.5%

      \[\leadsto \tan^{-1} \left(\frac{C - \color{blue}{B}}{B}\right) \cdot \frac{180}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9.5 \cdot 10^{-303}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{-247}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 47.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 5.9 \cdot 10^{-10}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.8e-22)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 5.9e-10)
     (* (/ 180.0 PI) (atan (* B (/ 0.5 A))))
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.8e-22) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 5.9e-10) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / A)));
	} 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 <= -1.8e-22) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 5.9e-10) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / A)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.8e-22:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 5.9e-10:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / A)))
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.8e-22)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 5.9e-10)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / A))));
	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 <= -1.8e-22)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 5.9e-10)
		tmp = (180.0 / pi) * atan((B * (0.5 / A)));
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.8e-22], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.9e-10], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.7999999999999999e-22

   1. Initial program 55.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 80.2%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 60.1%

      \[\leadsto \tan^{-1} \color{blue}{1} \cdot \frac{180}{\pi} \]

   if -1.7999999999999999e-22 < B < 5.9000000000000003e-10

   1. Initial program 51.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 59.7%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(B \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} - \frac{1}{2} \cdot \frac{1}{C - A}\right)\right)}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\frac{1}{8} \cdot \frac{{B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\frac{\frac{1}{8} \cdot {B}^{2}}{{\left(C - A\right)}^{3}} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\frac{\frac{1}{8}}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\frac{\frac{1}{8} \cdot 1}{{\left(C - A\right)}^{3}} \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\left(B \cdot \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2} + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{+.f64}\left(\left(\left(\frac{1}{8} \cdot \frac{1}{{\left(C - A\right)}^{3}}\right) \cdot {B}^{2}\right), \left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{C - A}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   7. Simplified 49.7%

      \[\leadsto \tan^{-1} \color{blue}{\left(B \cdot \left(\left(B \cdot B\right) \cdot \frac{\frac{0.125}{C - A}}{\left(C - A\right) \cdot \left(C - A\right)} + \frac{-0.5}{C - A}\right)\right)} \cdot \frac{180}{\pi} \]

   8. Taylor expanded in A around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \color{blue}{\left(\frac{\frac{1}{2}}{A}\right)}\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 34.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(B, \mathsf{/.f64}\left(\frac{1}{2}, A\right)\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]

   10. Simplified 34.5%

       \[\leadsto \tan^{-1} \left(B \cdot \color{blue}{\frac{0.5}{A}}\right) \cdot \frac{180}{\pi} \]

   if 5.9000000000000003e-10 < B

   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. 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 86.4%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 67.5%

      \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 5.9 \cdot 10^{-10}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 47.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.7 \cdot 10^{-22}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-12}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.7e-22)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 7.8e-12)
     (* 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 <= -2.7e-22) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 7.8e-12) {
		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 <= -2.7e-22) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 7.8e-12) {
		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 <= -2.7e-22:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 7.8e-12:
		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 <= -2.7e-22)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 7.8e-12)
		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 <= -2.7e-22)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 7.8e-12)
		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, -2.7e-22], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 7.8e-12], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.7000000000000002e-22

   1. Initial program 55.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 80.2%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 60.1%

      \[\leadsto \tan^{-1} \color{blue}{1} \cdot \frac{180}{\pi} \]

   if -2.7000000000000002e-22 < B < 7.79999999999999988e-12

   1. Initial program 51.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in A around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   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 34.4%

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, B\right), A\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 34.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0.5 \cdot B}{A}\right)}}{\pi} \]

   if 7.79999999999999988e-12 < B

   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. 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 86.4%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 67.5%

      \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.7 \cdot 10^{-22}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 7.8 \cdot 10^{-12}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 45.1% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.8 \cdot 10^{-117}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-144}:\\ \;\;\;\;\frac{\frac{\tan^{-1} 0}{\pi}}{0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.8e-117)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 2.15e-144)
     (/ (/ (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 <= -3.8e-117) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 2.15e-144) {
		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 <= -3.8e-117) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 2.15e-144) {
		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 <= -3.8e-117:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 2.15e-144:
		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 <= -3.8e-117)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 2.15e-144)
		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 <= -3.8e-117)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 2.15e-144)
		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, -3.8e-117], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.15e-144], 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 < -3.79999999999999972e-117

   1. Initial program 54.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 74.9%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\color{blue}{1}\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 53.4%

      \[\leadsto \tan^{-1} \color{blue}{1} \cdot \frac{180}{\pi} \]

   if -3.79999999999999972e-117 < B < 2.14999999999999995e-144

   1. Initial program 48.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 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. 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. hypot-define N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \left(\mathsf{hypot}\left(B, C - A\right)\right)\right), B\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      10. hypot-lowering-hypot.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{hypot.f64}\left(B, \left(C - A\right)\right)\right), B\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(C, A\right)\right)\right), B\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(C, A\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(\mathsf{PI}\left(\right), \color{blue}{180}\right)\right) \]

      13. PI-lowering-PI.f64 73.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(C, A\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

   6. Applied egg-rr 73.5%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\frac{\pi}{180}}} \]

   7. Taylor expanded in 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 29.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(0, B\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

   9. Simplified 29.7%

      \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B}\right)}}{\frac{\pi}{180}} \]
   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. associate-/r* N/A

          \[\leadsto \frac{\frac{\tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right)}}{\color{blue}{\frac{1}{180}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{\tan^{-1} \left(\frac{0}{B}\right)}{\mathsf{PI}\left(\right)}\right), \color{blue}{\left(\frac{1}{180}\right)}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\tan^{-1} \left(\frac{0}{B}\right), \mathsf{PI}\left(\right)\right), \left(\frac{\color{blue}{1}}{180}\right)\right) \]

       5. div0 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\tan^{-1} 0, \mathsf{PI}\left(\right)\right), \left(\frac{1}{180}\right)\right) \]

       6. atan-lowering-atan.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(0\right), \mathsf{PI}\left(\right)\right), \left(\frac{1}{180}\right)\right) \]

       7. PI-lowering-PI.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(0\right), \mathsf{PI.f64}\left(\right)\right), \left(\frac{1}{180}\right)\right) \]

       8. metadata-eval 29.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(0\right), \mathsf{PI.f64}\left(\right)\right), \frac{1}{180}\right) \]

   11. Applied egg-rr 29.7%

       \[\leadsto \color{blue}{\frac{\frac{\tan^{-1} 0}{\pi}}{0.005555555555555556}} \]

   if 2.14999999999999995e-144 < B

   1. Initial program 57.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\mathsf{PI}\left(\right)} \cdot \color{blue}{180} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot 180}{\color{blue}{\mathsf{PI}\left(\right)}} \]

      3. associate-/l* N/A

         \[\leadsto \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \color{blue}{\frac{180}{\mathsf{PI}\left(\right)}} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 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. 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 57.7%

      \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.8 \cdot 10^{-117}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 2.15 \cdot 10^{-144}:\\ \;\;\;\;\frac{\frac{\tan^{-1} 0}{\pi}}{0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 54.0% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 1.35 \cdot 10^{-152}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 1.35e-152)
   (* (/ 180.0 PI) (atan (/ (- C B) B)))
   (/ (* 180.0 (atan (/ (* B -0.5) C))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.35e-152) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	} else {
		tmp = (180.0 * atan(((B * -0.5) / C))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.35e-152) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	} else {
		tmp = (180.0 * Math.atan(((B * -0.5) / C))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 1.35e-152:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	else:
		tmp = (180.0 * math.atan(((B * -0.5) / C))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 1.35e-152)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / C))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 1.35e-152)
		tmp = (180.0 / pi) * atan(((C - B) / B));
	else
		tmp = (180.0 * atan(((B * -0.5) / C))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 1.35e-152], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 1.34999999999999999e-152

   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 84.3%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \color{blue}{B}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 57.9%

      \[\leadsto \tan^{-1} \left(\frac{C - \color{blue}{B}}{B}\right) \cdot \frac{180}{\pi} \]

   if 1.34999999999999999e-152 < C

   1. Initial program 30.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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. distribute-rgt1-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(\left(-1 + 1\right) \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(0 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. mul0-lft N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{-1 \cdot 0}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{0}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{\frac{-1}{2} \cdot B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. *-lowering-*.f64 61.7%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 61.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B} + \frac{B \cdot -0.5}{C}\right)}}{\pi} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\color{blue}{\mathsf{PI}\left(\right)}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(180 \cdot \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)\right), \color{blue}{\mathsf{PI}\left(\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(180, \tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)\right), \mathsf{PI}\left(\right)\right) \]

      4. div0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(180, \tan^{-1} \left(0 + \frac{B \cdot \frac{-1}{2}}{C}\right)\right), \mathsf{PI}\left(\right)\right) \]

      5. +-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(180, \tan^{-1} \left(\frac{B \cdot \frac{-1}{2}}{C}\right)\right), \mathsf{PI}\left(\right)\right) \]

      6. atan-lowering-atan.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(180, \mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C}\right)\right)\right), \mathsf{PI}\left(\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(180, \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI}\left(\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(180, \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI}\left(\right)\right) \]

      9. PI-lowering-PI.f64 61.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(180, \mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right) \]

   7. Applied egg-rr 61.7%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 1.35 \cdot 10^{-152}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 54.0% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 1.82 \cdot 10^{-152}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\frac{\pi}{180}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 1.82e-152)
   (* (/ 180.0 PI) (atan (/ (- C B) B)))
   (/ (atan (/ (* B -0.5) C)) (/ PI 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.82e-152) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	} else {
		tmp = atan(((B * -0.5) / C)) / (((double) M_PI) / 180.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.82e-152) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	} else {
		tmp = Math.atan(((B * -0.5) / C)) / (Math.PI / 180.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 1.82e-152:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	else:
		tmp = math.atan(((B * -0.5) / C)) / (math.pi / 180.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 1.82e-152)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	else
		tmp = Float64(atan(Float64(Float64(B * -0.5) / C)) / Float64(pi / 180.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 1.82e-152)
		tmp = (180.0 / pi) * atan(((C - B) / B));
	else
		tmp = atan(((B * -0.5) / C)) / (pi / 180.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 1.82e-152], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / N[(Pi / 180.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 1.82000000000000009e-152

   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 84.3%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \color{blue}{B}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 57.9%

      \[\leadsto \tan^{-1} \left(\frac{C - \color{blue}{B}}{B}\right) \cdot \frac{180}{\pi} \]

   if 1.82000000000000009e-152 < C

   1. Initial program 30.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 53.8%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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. hypot-define N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \left(\mathsf{hypot}\left(B, C - A\right)\right)\right), B\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      10. hypot-lowering-hypot.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{hypot.f64}\left(B, \left(C - A\right)\right)\right), B\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(C, A\right)\right)\right), B\right)\right), \left(\frac{\mathsf{PI}\left(\right)}{180}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(C, A\right), \mathsf{hypot.f64}\left(B, \mathsf{\_.f64}\left(C, A\right)\right)\right), B\right)\right), \mathsf{/.f64}\left(\mathsf{PI}\left(\right), \color{blue}{180}\right)\right) \]

      13. 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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \left(\frac{B}{C - A}\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{/.f64}\left(B, \left(C - A\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

      3. --lowering--.f64 63.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{*.f64}\left(\frac{-1}{2}, \mathsf{/.f64}\left(B, \mathsf{\_.f64}\left(C, A\right)\right)\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

   9. Simplified 63.9%

      \[\leadsto \frac{\tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{B}{C - A}\right)}}{\frac{\pi}{180}} \]

   10. Taylor expanded in C around inf

       \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\frac{-1}{2} \cdot \frac{B}{C}\right)}\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]
   11. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{\frac{-1}{2} \cdot B}{C}\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), C\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), C\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

       4. *-lowering-*.f64 61.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right), \mathsf{/.f64}\left(\mathsf{PI.f64}\left(\right), 180\right)\right) \]

   12. Simplified 61.7%

       \[\leadsto \frac{\tan^{-1} \color{blue}{\left(\frac{B \cdot -0.5}{C}\right)}}{\frac{\pi}{180}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 1.82 \cdot 10^{-152}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\frac{\pi}{180}}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 54.0% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 1.4 \cdot 10^{-152}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 1.4e-152)
   (* (/ 180.0 PI) (atan (/ (- C B) B)))
   (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.4e-152) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	} else {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.4e-152) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	} else {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 1.4e-152:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	else:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 1.4e-152)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 1.4e-152)
		tmp = (180.0 / pi) * atan(((C - B) / B));
	else
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 1.4e-152], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 1.39999999999999992e-152

   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 84.3%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in B around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(C, \color{blue}{B}\right), B\right)\right), \mathsf{/.f64}\left(180, \mathsf{PI.f64}\left(\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 57.9%

      \[\leadsto \tan^{-1} \left(\frac{C - \color{blue}{B}}{B}\right) \cdot \frac{180}{\pi} \]

   if 1.39999999999999992e-152 < C

   1. Initial program 30.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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. distribute-rgt1-in N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(\left(-1 + 1\right) \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{-1 \cdot \left(0 \cdot A\right)}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      5. mul0-lft N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{-1 \cdot 0}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\left(\frac{0}{B}\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{-1}{2} \cdot \frac{B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \left(\frac{\frac{-1}{2} \cdot B}{C}\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(\frac{-1}{2} \cdot B\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

      11. *-lowering-*.f64 61.7%

          \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(0, B\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right)\right), \mathsf{PI.f64}\left(\right)\right)\right) \]

   5. Simplified 61.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{0}{B} + \frac{B \cdot -0.5}{C}\right)}}{\pi} \]
   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right)}{\mathsf{PI}\left(\right)}\right), \color{blue}{180}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\tan^{-1} \left(\frac{0}{B} + \frac{B \cdot \frac{-1}{2}}{C}\right), \mathsf{PI}\left(\right)\right), 180\right) \]

      4. div0 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\tan^{-1} \left(0 + \frac{B \cdot \frac{-1}{2}}{C}\right), \mathsf{PI}\left(\right)\right), 180\right) \]

      5. +-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\tan^{-1} \left(\frac{B \cdot \frac{-1}{2}}{C}\right), \mathsf{PI}\left(\right)\right), 180\right) \]

      6. atan-lowering-atan.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(\left(\frac{B \cdot \frac{-1}{2}}{C}\right)\right), \mathsf{PI}\left(\right)\right), 180\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\left(B \cdot \frac{-1}{2}\right), C\right)\right), \mathsf{PI}\left(\right)\right), 180\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right), \mathsf{PI}\left(\right)\right), 180\right) \]

      9. PI-lowering-PI.f64 61.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{atan.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(B, \frac{-1}{2}\right), C\right)\right), \mathsf{PI.f64}\left(\right)\right), 180\right) \]

   7. Applied egg-rr 61.7%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi} \cdot 180} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 1.4 \cdot 10^{-152}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 51.1% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{-146}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.8e-146)
   (* (/ 180.0 PI) (atan 1.0))
   (* (/ 180.0 PI) (atan (/ (- C B) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.8e-146) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} 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 tmp;
	if (B <= -6.8e-146) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -6.8e-146:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -6.8e-146)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	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)
	tmp = 0.0;
	if (B <= -6.8e-146)
		tmp = (180.0 / pi) * atan(1.0);
	else
		tmp = (180.0 / pi) * atan(((C - B) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -6.8e-146], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -6.8000000000000001e-146

   1. Initial program 51.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 71.5%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 50.3%

      \[\leadsto \tan^{-1} \color{blue}{1} \cdot \frac{180}{\pi} \]

   if -6.8000000000000001e-146 < B

   1. Initial program 55.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 73.0%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 59.0%

      \[\leadsto \tan^{-1} \left(\frac{C - \color{blue}{B}}{B}\right) \cdot \frac{180}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{-146}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 39.7% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-310) (* (/ 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 <= -5e-310) {
		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 <= -5e-310) {
		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 <= -5e-310:
		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 <= -5e-310)
		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 <= -5e-310)
		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, -5e-310], 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 < -4.999999999999985e-310

   1. Initial program 54.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\mathsf{PI}\left(\right)} \cdot \color{blue}{180} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot 180}{\color{blue}{\mathsf{PI}\left(\right)}} \]

      3. associate-/l* N/A

         \[\leadsto \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \color{blue}{\frac{180}{\mathsf{PI}\left(\right)}} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 70.4%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 40.7%

      \[\leadsto \tan^{-1} \color{blue}{1} \cdot \frac{180}{\pi} \]

   if -4.999999999999985e-310 < B

   1. Initial program 54.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\mathsf{PI}\left(\right)} \cdot \color{blue}{180} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot 180}{\color{blue}{\mathsf{PI}\left(\right)}} \]

      3. associate-/l* N/A

         \[\leadsto \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \color{blue}{\frac{180}{\mathsf{PI}\left(\right)}} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

   3. Simplified 74.6%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   4. Add Preprocessing

   5. Taylor expanded in 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 45.9%

      \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 20.6% 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 54.2%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
2. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\mathsf{PI}\left(\right)} \cdot \color{blue}{180} \]

   2. associate-*l/ N/A

      \[\leadsto \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot 180}{\color{blue}{\mathsf{PI}\left(\right)}} \]

   3. associate-/l* N/A

      \[\leadsto \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \color{blue}{\frac{180}{\mathsf{PI}\left(\right)}} \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right), \color{blue}{\left(\frac{180}{\mathsf{PI}\left(\right)}\right)}\right) \]

3. Simplified 72.5%

   \[\leadsto \color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, C - A\right)\right)}{B}\right) \cdot \frac{180}{\pi}} \]
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 23.5%

   \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\pi} \]

8. Final simplification 23.5%

   \[\leadsto \frac{180}{\pi} \cdot \tan^{-1} -1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024148 
(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)))