ABCF->ab-angle angle

Percentage Accurate: 53.5% → 88.3%

Time: 19.8s

Alternatives: 19

Speedup: 3.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -0.5)
     (/ 180.0 (/ PI (atan (/ (- (- C A) (hypot B (- A C))) B))))
     (if (<= t_0 2e-5)
       (/ 1.0 (/ (/ PI 180.0) (atan (* -0.5 (/ B (- C A))))))
       (* (atan (/ 1.0 (/ B (- (- C A) (hypot B (- C A)))))) (/ 180.0 PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 / (((double) M_PI) / atan((((C - A) - hypot(B, (A - C))) / B)));
	} else if (t_0 <= 2e-5) {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((-0.5 * (B / (C - A)))));
	} else {
		tmp = atan((1.0 / (B / ((C - A) - hypot(B, (C - A)))))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 / (Math.PI / Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)));
	} else if (t_0 <= 2e-5) {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((-0.5 * (B / (C - A)))));
	} else {
		tmp = Math.atan((1.0 / (B / ((C - A) - Math.hypot(B, (C - A)))))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_0 <= -0.5:
		tmp = 180.0 / (math.pi / math.atan((((C - A) - math.hypot(B, (A - C))) / B)))
	elif t_0 <= 2e-5:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((-0.5 * (B / (C - A)))))
	else:
		tmp = math.atan((1.0 / (B / ((C - A) - math.hypot(B, (C - A)))))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B))));
	elseif (t_0 <= 2e-5)
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(-0.5 * Float64(B / Float64(C - A))))));
	else
		tmp = Float64(atan(Float64(1.0 / Float64(B / Float64(Float64(C - A) - hypot(B, Float64(C - A)))))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = 180.0 / (pi / atan((((C - A) - hypot(B, (A - C))) / B)));
	elseif (t_0 <= 2e-5)
		tmp = 1.0 / ((pi / 180.0) / atan((-0.5 * (B / (C - A)))));
	else
		tmp = atan((1.0 / (B / ((C - A) - hypot(B, (C - A)))))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 55.6%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. un-div-inv N/A

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

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

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

   4. Applied egg-rr 89.4%

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

   if -0.5 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 2.00000000000000016e-5

   1. Initial program 15.3%

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

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

   5. Taylor expanded in B around 0

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

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

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

      2. unpow2 N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. --lowering--.f64 55.5%

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

   7. Simplified 55.5%

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

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

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

      6. associate-/l* N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 55.4%

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

   9. Applied egg-rr 55.4%

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

       1. div-inv N/A

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

       2. associate-*r/ N/A

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

       3. associate-*l/ N/A

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

       4. pow2 N/A

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

       5. inv-pow N/A

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

       6. pow-prod-up N/A

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

       7. metadata-eval N/A

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

       8. unpow1 N/A

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

       9. clear-num N/A

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

       10. associate-/r/ N/A

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

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

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

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

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

       13. --lowering--.f64 98.5%

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

   11. Applied egg-rr 98.5%

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

       1. clear-num N/A

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

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

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

       3. associate-/r* N/A

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

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

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

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

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

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

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

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

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

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

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

       9. *-commutative N/A

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

       10. un-div-inv N/A

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

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

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

       12. --lowering--.f64 98.8%

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

   13. Applied egg-rr 98.8%

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

   if 2.00000000000000016e-5 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 66.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 89.9%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

      6. hypot-define N/A

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

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

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

      8. --lowering--.f64 89.9%

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

   6. Applied egg-rr 89.9%

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

Alternative 2: 77.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.12 \cdot 10^{+24}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}}\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{+29}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{0 - B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.12e+24)
   (/ 1.0 (/ (/ PI 180.0) (atan (* -0.5 (/ B (- C A))))))
   (if (<= A 1.35e+29)
     (* (/ 180.0 PI) (atan (/ (- C (hypot C B)) B)))
     (* (/ 180.0 PI) (atan (/ (+ A (hypot A B)) (- 0.0 B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.12e+24) {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((-0.5 * (B / (C - A)))));
	} else if (A <= 1.35e+29) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(C, B)) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((A + hypot(A, B)) / (0.0 - B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.12e+24) {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((-0.5 * (B / (C - A)))));
	} else if (A <= 1.35e+29) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(C, B)) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((A + Math.hypot(A, B)) / (0.0 - B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.12e+24:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((-0.5 * (B / (C - A)))))
	elif A <= 1.35e+29:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(C, B)) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan(((A + math.hypot(A, B)) / (0.0 - B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.12e+24)
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(-0.5 * Float64(B / Float64(C - A))))));
	elseif (A <= 1.35e+29)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(C, B)) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(A + hypot(A, B)) / Float64(0.0 - B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.12e+24)
		tmp = 1.0 / ((pi / 180.0) / atan((-0.5 * (B / (C - A)))));
	elseif (A <= 1.35e+29)
		tmp = (180.0 / pi) * atan(((C - hypot(C, B)) / B));
	else
		tmp = (180.0 / pi) * atan(((A + hypot(A, B)) / (0.0 - B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.12e+24], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.35e+29], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / N[(0.0 - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.12e24

   1. Initial program 20.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 54.2%

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

   5. Taylor expanded in B around 0

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

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

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

      2. unpow2 N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. --lowering--.f64 63.0%

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

   7. Simplified 63.0%

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

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

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

      6. associate-/l* N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 62.9%

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

   9. Applied egg-rr 62.9%

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

       1. div-inv N/A

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

       2. associate-*r/ N/A

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

       3. associate-*l/ N/A

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

       4. pow2 N/A

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

       5. inv-pow N/A

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

       6. pow-prod-up N/A

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

       7. metadata-eval N/A

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

       8. unpow1 N/A

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

       9. clear-num N/A

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

       10. associate-/r/ N/A

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

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

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

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

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

       13. --lowering--.f64 71.3%

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

   11. Applied egg-rr 71.3%

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

       1. clear-num N/A

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

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

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

       3. associate-/r* N/A

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

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

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

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

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

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

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

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

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

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

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

       9. *-commutative N/A

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

       10. un-div-inv N/A

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

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

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

       12. --lowering--.f64 71.5%

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

   13. Applied egg-rr 71.5%

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

   if -1.12e24 < A < 1.35e29

   1. Initial program 54.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 77.1%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 74.8%

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

   7. Simplified 74.8%

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

   if 1.35e29 < A

   1. Initial program 79.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 96.8%

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

   5. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

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

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

      5. unpow2 N/A

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

      6. unpow2 N/A

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

      7. hypot-define N/A

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

      8. hypot-lowering-hypot.f64 92.2%

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

   7. Simplified 92.2%

      \[\leadsto \tan^{-1} \left(\frac{\color{blue}{0 - \left(A + \mathsf{hypot}\left(A, B\right)\right)}}{B}\right) \cdot \frac{180}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.12 \cdot 10^{+24}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}}\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{+29}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{0 - B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -7.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}}\\ \mathbf{elif}\;A \leq 1.6 \cdot 10^{+132}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -7.5e+20)
   (/ 1.0 (/ (/ PI 180.0) (atan (* -0.5 (/ B (- C A))))))
   (if (<= A 1.6e+132)
     (* (/ 180.0 PI) (atan (/ (- C (hypot C B)) B)))
     (* (/ 180.0 PI) (atan (- -1.0 (/ A B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -7.5e+20) {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((-0.5 * (B / (C - A)))));
	} else if (A <= 1.6e+132) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - hypot(C, B)) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -7.5e+20) {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((-0.5 * (B / (C - A)))));
	} else if (A <= 1.6e+132) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - Math.hypot(C, B)) / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -7.5e+20:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((-0.5 * (B / (C - A)))))
	elif A <= 1.6e+132:
		tmp = (180.0 / math.pi) * math.atan(((C - math.hypot(C, B)) / B))
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -7.5e+20)
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(-0.5 * Float64(B / Float64(C - A))))));
	elseif (A <= 1.6e+132)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - hypot(C, B)) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -7.5e+20)
		tmp = 1.0 / ((pi / 180.0) / atan((-0.5 * (B / (C - A)))));
	elseif (A <= 1.6e+132)
		tmp = (180.0 / pi) * atan(((C - hypot(C, B)) / B));
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -7.5e+20], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.6e+132], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -7.5e20

   1. Initial program 20.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 54.2%

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

   5. Taylor expanded in B around 0

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

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

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

      2. unpow2 N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. --lowering--.f64 63.0%

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

   7. Simplified 63.0%

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

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

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

      6. associate-/l* N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 62.9%

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

   9. Applied egg-rr 62.9%

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

       1. div-inv N/A

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

       2. associate-*r/ N/A

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

       3. associate-*l/ N/A

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

       4. pow2 N/A

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

       5. inv-pow N/A

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

       6. pow-prod-up N/A

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

       7. metadata-eval N/A

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

       8. unpow1 N/A

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

       9. clear-num N/A

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

       10. associate-/r/ N/A

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

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

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

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

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

       13. --lowering--.f64 71.3%

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

   11. Applied egg-rr 71.3%

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

       1. clear-num N/A

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

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

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

       3. associate-/r* N/A

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

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

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

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

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

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

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

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

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

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

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

       9. *-commutative N/A

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

       10. un-div-inv N/A

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

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

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

       12. --lowering--.f64 71.5%

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

   13. Applied egg-rr 71.5%

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

   if -7.5e20 < A < 1.5999999999999999e132

   1. Initial program 54.7%

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

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 74.7%

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

   7. Simplified 74.7%

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

   if 1.5999999999999999e132 < A

   1. Initial program 86.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 97.9%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 91.3%

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

   7. Simplified 91.3%

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

   8. Taylor expanded in C around 0

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

      1. distribute-lft-in N/A

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

      2. metadata-eval N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. /-lowering-/.f64 91.3%

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

   10. Simplified 91.3%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -7.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}}\\ \mathbf{elif}\;A \leq 1.6 \cdot 10^{+132}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.4 \cdot 10^{+86}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.4e+86)
   (/ 1.0 (/ (/ PI 180.0) (atan (* -0.5 (/ B (- C A))))))
   (* (/ 180.0 PI) (atan (/ (- (- C A) (hypot B (- C A))) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.4e+86) {
		tmp = 1.0 / ((((double) M_PI) / 180.0) / atan((-0.5 * (B / (C - A)))));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((((C - A) - hypot(B, (C - A))) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.4e+86) {
		tmp = 1.0 / ((Math.PI / 180.0) / Math.atan((-0.5 * (B / (C - A)))));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((((C - A) - Math.hypot(B, (C - A))) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.4e+86:
		tmp = 1.0 / ((math.pi / 180.0) / math.atan((-0.5 * (B / (C - A)))))
	else:
		tmp = (180.0 / math.pi) * math.atan((((C - A) - math.hypot(B, (C - A))) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.4e+86)
		tmp = Float64(1.0 / Float64(Float64(pi / 180.0) / atan(Float64(-0.5 * Float64(B / Float64(C - A))))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(C - A))) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.4e+86)
		tmp = 1.0 / ((pi / 180.0) / atan((-0.5 * (B / (C - A)))));
	else
		tmp = (180.0 / pi) * atan((((C - A) - hypot(B, (C - A))) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.4e+86], N[(1.0 / N[(N[(Pi / 180.0), $MachinePrecision] / N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(C - A), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -4.40000000000000006e86

   1. Initial program 18.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 52.5%

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

   5. Taylor expanded in B around 0

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

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

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

      2. unpow2 N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. --lowering--.f64 66.3%

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

   7. Simplified 66.3%

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

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

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

      6. associate-/l* N/A

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

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

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

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

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

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

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

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

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

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

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

      12. PI-lowering-PI.f64 66.2%

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

   9. Applied egg-rr 66.2%

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

       1. div-inv N/A

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

       2. associate-*r/ N/A

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

       3. associate-*l/ N/A

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

       4. pow2 N/A

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

       5. inv-pow N/A

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

       6. pow-prod-up N/A

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

       7. metadata-eval N/A

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

       8. unpow1 N/A

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

       9. clear-num N/A

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

       10. associate-/r/ N/A

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

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

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

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

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

       13. --lowering--.f64 74.7%

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

   11. Applied egg-rr 74.7%

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

       1. clear-num N/A

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

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

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

       3. associate-/r* N/A

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

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

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

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

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

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

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

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

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

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

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

       9. *-commutative N/A

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

       10. un-div-inv N/A

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

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

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

       12. --lowering--.f64 75.0%

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

   13. Applied egg-rr 75.0%

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

   if -4.40000000000000006e86 < A

   1. Initial program 59.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

   3. Simplified 81.7%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.4 \cdot 10^{+86}:\\ \;\;\;\;\frac{1}{\frac{\frac{\pi}{180}}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.36 \cdot 10^{-45}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -6 \cdot 10^{-170}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-229}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 2100000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.36e-45)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B -6e-170)
     (* (/ 180.0 PI) (atan (/ C B)))
     (if (<= B 1.8e-229)
       (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
       (if (<= B 2100000.0)
         (* 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 <= -1.36e-45) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= -6e-170) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / B));
	} else if (B <= 1.8e-229) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else if (B <= 2100000.0) {
		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 <= -1.36e-45) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= -6e-170) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else if (B <= 1.8e-229) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else if (B <= 2100000.0) {
		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 <= -1.36e-45:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= -6e-170:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	elif B <= 1.8e-229:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	elif B <= 2100000.0:
		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 <= -1.36e-45)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= -6e-170)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / B)));
	elseif (B <= 1.8e-229)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	elseif (B <= 2100000.0)
		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 <= -1.36e-45)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= -6e-170)
		tmp = (180.0 / pi) * atan((C / B));
	elseif (B <= 1.8e-229)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	elseif (B <= 2100000.0)
		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, -1.36e-45], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -6e-170], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.8e-229], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2100000.0], 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 5 regimes

2. if B < -1.35999999999999998e-45

   1. Initial program 52.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

   3. Simplified 79.1%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 56.1%

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

   if -1.35999999999999998e-45 < B < -6.00000000000000027e-170

   1. Initial program 68.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 71.8%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in C around inf

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

      1. /-lowering-/.f64 48.1%

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

   10. Simplified 48.1%

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

   if -6.00000000000000027e-170 < B < 1.80000000000000001e-229

   1. Initial program 56.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

   3. Simplified 77.9%

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

   5. Taylor expanded in B around 0

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

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

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

      2. unpow2 N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. --lowering--.f64 34.3%

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

   7. Simplified 34.3%

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

   8. Taylor expanded in C around inf

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

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

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

      2. /-lowering-/.f64 45.0%

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

   10. Simplified 45.0%

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

   if 1.80000000000000001e-229 < B < 2.1e6

   1. Initial program 49.6%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      4. *-lowering-*.f64 47.1%

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

   5. Simplified 47.1%

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

   if 2.1e6 < B

   1. Initial program 47.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 83.3%

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

   5. Taylor expanded in B around inf

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

   7. Simplified 62.8%

      \[\leadsto \tan^{-1} \color{blue}{-1} \cdot \frac{180}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.36 \cdot 10^{-45}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq -6 \cdot 10^{-170}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-229}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 2100000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.05 \cdot 10^{-264}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{\left(C - A\right) + -0.5 \cdot \left(\left(A - C\right) \cdot \frac{C - A}{B}\right)}{B}\right)\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-110}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{\frac{1}{\frac{C - \left(B + A\right)}{B}}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.05e-264)
   (*
    (/ 180.0 PI)
    (atan (+ 1.0 (/ (+ (- C A) (* -0.5 (* (- A C) (/ (- C A) B)))) B))))
   (if (<= B 1.4e-110)
     (* (/ 180.0 PI) (atan (* B (/ -0.5 (- C A)))))
     (* (/ 180.0 PI) (atan (/ 1.0 (/ 1.0 (/ (- C (+ B A)) B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.05e-264) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + (((C - A) + (-0.5 * ((A - C) * ((C - A) / B)))) / B)));
	} else if (B <= 1.4e-110) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / (C - A))));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 / (1.0 / ((C - (B + A)) / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.05e-264) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + (((C - A) + (-0.5 * ((A - C) * ((C - A) / B)))) / B)));
	} else if (B <= 1.4e-110) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / (C - A))));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 / (1.0 / ((C - (B + A)) / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.05e-264:
		tmp = (180.0 / math.pi) * math.atan((1.0 + (((C - A) + (-0.5 * ((A - C) * ((C - A) / B)))) / B)))
	elif B <= 1.4e-110:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / (C - A))))
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 / (1.0 / ((C - (B + A)) / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.05e-264)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(Float64(Float64(C - A) + Float64(-0.5 * Float64(Float64(A - C) * Float64(Float64(C - A) / B)))) / B))));
	elseif (B <= 1.4e-110)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / Float64(C - A)))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 / Float64(1.0 / Float64(Float64(C - Float64(B + A)) / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.05e-264)
		tmp = (180.0 / pi) * atan((1.0 + (((C - A) + (-0.5 * ((A - C) * ((C - A) / B)))) / B)));
	elseif (B <= 1.4e-110)
		tmp = (180.0 / pi) * atan((B * (-0.5 / (C - A))));
	else
		tmp = (180.0 / pi) * atan((1.0 / (1.0 / ((C - (B + A)) / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.05e-264], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(N[(N[(C - A), $MachinePrecision] + N[(-0.5 * N[(N[(A - C), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.4e-110], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 / N[(1.0 / N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.0500000000000001e-264

   1. Initial program 59.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 78.5%

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

   5. Taylor expanded in B around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

   7. Simplified 71.8%

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

   if -1.0500000000000001e-264 < B < 1.4e-110

   1. Initial program 38.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 64.7%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

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

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

      14. --lowering--.f64 70.7%

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

   7. Simplified 70.7%

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

   if 1.4e-110 < B

   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 79.9%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

      6. hypot-define N/A

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

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

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

      8. --lowering--.f64 79.9%

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

   6. Applied egg-rr 79.9%

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

      1. clear-num N/A

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

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

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

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

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

      4. associate--l- N/A

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

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

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

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

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

      7. hypot-define N/A

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

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

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

      9. --lowering--.f64 79.9%

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

   8. Applied egg-rr 79.9%

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

   9. Taylor expanded in B around inf

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

   11. Simplified 76.7%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.05 \cdot 10^{-264}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{\left(C - A\right) + -0.5 \cdot \left(\left(A - C\right) \cdot \frac{C - A}{B}\right)}{B}\right)\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-110}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{\frac{1}{\frac{C - \left(B + A\right)}{B}}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.6% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -9 \cdot 10^{-196}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-110}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{\frac{1}{\frac{C - \left(B + A\right)}{B}}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -9e-196)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= B 2.4e-110)
     (* (/ 180.0 PI) (atan (* B (/ -0.5 (- C A)))))
     (* (/ 180.0 PI) (atan (/ 1.0 (/ 1.0 (/ (- C (+ B A)) B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -9e-196) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= 2.4e-110) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / (C - A))));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 / (1.0 / ((C - (B + A)) / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -9e-196) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= 2.4e-110) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / (C - A))));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 / (1.0 / ((C - (B + A)) / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -9e-196:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= 2.4e-110:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / (C - A))))
	else:
		tmp = (180.0 / math.pi) * math.atan((1.0 / (1.0 / ((C - (B + A)) / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -9e-196)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= 2.4e-110)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / Float64(C - A)))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 / Float64(1.0 / Float64(Float64(C - Float64(B + A)) / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -9e-196)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= 2.4e-110)
		tmp = (180.0 / pi) * atan((B * (-0.5 / (C - A))));
	else
		tmp = (180.0 / pi) * atan((1.0 / (1.0 / ((C - (B + A)) / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -9e-196], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.4e-110], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 / N[(1.0 / N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -9e-196

   1. Initial program 58.1%

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

   3. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   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 73.1%

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

   5. Simplified 73.1%

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

   if -9e-196 < B < 2.40000000000000006e-110

   1. Initial program 45.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 70.7%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

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

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

      14. --lowering--.f64 65.8%

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

   7. Simplified 65.8%

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

   if 2.40000000000000006e-110 < B

   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 79.9%

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

      1. clear-num N/A

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

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

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

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

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

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

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

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

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

      6. hypot-define N/A

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

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

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

      8. --lowering--.f64 79.9%

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

   6. Applied egg-rr 79.9%

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

      1. clear-num N/A

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

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

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

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

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

      4. associate--l- N/A

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

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

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

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

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

      7. hypot-define N/A

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

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

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

      9. --lowering--.f64 79.9%

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

   8. Applied egg-rr 79.9%

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

   9. Taylor expanded in B around inf

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

   11. Simplified 76.7%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9 \cdot 10^{-196}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-110}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{\frac{1}{\frac{C - \left(B + A\right)}{B}}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.32 \cdot 10^{-58}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq -7 \cdot 10^{-102}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 4.9 \cdot 10^{-151}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.32e-58)
   (* (/ 180.0 PI) (atan (/ (- C B) B)))
   (if (<= C -7e-102)
     (* (/ 180.0 PI) (atan (+ 1.0 (/ C B))))
     (if (<= C 4.9e-151)
       (* (/ 180.0 PI) (atan (- -1.0 (/ A B))))
       (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.32e-58) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	} else if (C <= -7e-102) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + (C / B)));
	} else if (C <= 4.9e-151) {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.32e-58) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	} else if (C <= -7e-102) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + (C / B)));
	} else if (C <= 4.9e-151) {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.32e-58:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	elif C <= -7e-102:
		tmp = (180.0 / math.pi) * math.atan((1.0 + (C / B)))
	elif C <= 4.9e-151:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	else:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.32e-58)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	elseif (C <= -7e-102)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(C / B))));
	elseif (C <= 4.9e-151)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.32e-58)
		tmp = (180.0 / pi) * atan(((C - B) / B));
	elseif (C <= -7e-102)
		tmp = (180.0 / pi) * atan((1.0 + (C / B)));
	elseif (C <= 4.9e-151)
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	else
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.32e-58], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -7e-102], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4.9e-151], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.31999999999999993e-58

   1. Initial program 74.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 94.0%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 85.5%

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

   7. Simplified 85.5%

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

   8. Taylor expanded in C around 0

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

      1. --lowering--.f64 79.4%

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

   10. Simplified 79.4%

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

   if -1.31999999999999993e-58 < C < -6.99999999999999973e-102

   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 78.0%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 62.1%

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

   7. Simplified 62.1%

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

   8. Taylor expanded in B around -inf

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

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

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

      2. /-lowering-/.f64 55.2%

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

   10. Simplified 55.2%

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

   if -6.99999999999999973e-102 < C < 4.89999999999999966e-151

   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 79.4%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 61.2%

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

   7. Simplified 61.2%

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

   8. Taylor expanded in C around 0

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

      1. distribute-lft-in N/A

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

      2. metadata-eval N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. /-lowering-/.f64 61.2%

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

   10. Simplified 61.2%

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

   if 4.89999999999999966e-151 < C

   1. Initial program 31.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 60.4%

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

   5. Taylor expanded in B around 0

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

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

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

      2. unpow2 N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. --lowering--.f64 45.4%

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

   7. Simplified 45.4%

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

   8. Taylor expanded in C around inf

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

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

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

      2. /-lowering-/.f64 52.2%

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

   10. Simplified 52.2%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.32 \cdot 10^{-58}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq -7 \cdot 10^{-102}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 4.9 \cdot 10^{-151}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.1 \cdot 10^{-169}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-229}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 3200000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.1e-169)
   (* (/ 180.0 PI) (atan (+ 1.0 (/ C B))))
   (if (<= B 8.5e-229)
     (* (/ 180.0 PI) (atan (* -0.5 (/ B C))))
     (if (<= B 3200000.0)
       (* 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 <= -2.1e-169) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + (C / B)));
	} else if (B <= 8.5e-229) {
		tmp = (180.0 / ((double) M_PI)) * atan((-0.5 * (B / C)));
	} else if (B <= 3200000.0) {
		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 <= -2.1e-169) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + (C / B)));
	} else if (B <= 8.5e-229) {
		tmp = (180.0 / Math.PI) * Math.atan((-0.5 * (B / C)));
	} else if (B <= 3200000.0) {
		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 <= -2.1e-169:
		tmp = (180.0 / math.pi) * math.atan((1.0 + (C / B)))
	elif B <= 8.5e-229:
		tmp = (180.0 / math.pi) * math.atan((-0.5 * (B / C)))
	elif B <= 3200000.0:
		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 <= -2.1e-169)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(C / B))));
	elseif (B <= 8.5e-229)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-0.5 * Float64(B / C))));
	elseif (B <= 3200000.0)
		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 <= -2.1e-169)
		tmp = (180.0 / pi) * atan((1.0 + (C / B)));
	elseif (B <= 8.5e-229)
		tmp = (180.0 / pi) * atan((-0.5 * (B / C)));
	elseif (B <= 3200000.0)
		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, -2.1e-169], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.5e-229], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3200000.0], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -2.1000000000000001e-169

   1. Initial program 56.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

   3. Simplified 77.0%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in B around -inf

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

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

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

      2. /-lowering-/.f64 61.8%

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

   10. Simplified 61.8%

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

   if -2.1000000000000001e-169 < B < 8.49999999999999977e-229

   1. Initial program 56.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

   3. Simplified 77.9%

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

   5. Taylor expanded in B around 0

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

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

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

      2. unpow2 N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. --lowering--.f64 34.3%

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

   7. Simplified 34.3%

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

   8. Taylor expanded in C around inf

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

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

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

      2. /-lowering-/.f64 45.0%

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

   10. Simplified 45.0%

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

   if 8.49999999999999977e-229 < B < 3.2e6

   1. Initial program 49.6%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      4. *-lowering-*.f64 47.1%

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

   5. Simplified 47.1%

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

   if 3.2e6 < B

   1. Initial program 47.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 83.3%

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

   5. Taylor expanded in B around inf

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

   7. Simplified 62.8%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.1 \cdot 10^{-169}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-229}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)\\ \mathbf{elif}\;B \leq 3200000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.8% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -9.8 \cdot 10^{-46}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-308}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 3900000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -9.8e-46)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 1.5e-308)
     (* (/ 180.0 PI) (atan (/ C B)))
     (if (<= B 3900000.0)
       (* 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 <= -9.8e-46) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 1.5e-308) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / B));
	} else if (B <= 3900000.0) {
		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 <= -9.8e-46) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 1.5e-308) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else if (B <= 3900000.0) {
		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 <= -9.8e-46:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 1.5e-308:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	elif B <= 3900000.0:
		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 <= -9.8e-46)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 1.5e-308)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / B)));
	elseif (B <= 3900000.0)
		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 <= -9.8e-46)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 1.5e-308)
		tmp = (180.0 / pi) * atan((C / B));
	elseif (B <= 3900000.0)
		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, -9.8e-46], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.5e-308], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3900000.0], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -9.8000000000000002e-46

   1. Initial program 52.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

   3. Simplified 79.1%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 56.1%

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

   if -9.8000000000000002e-46 < B < 1.4999999999999999e-308

   1. Initial program 65.6%

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

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 58.3%

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

   7. Simplified 58.3%

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

   8. Taylor expanded in C around inf

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

      1. /-lowering-/.f64 41.2%

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

   10. Simplified 41.2%

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

   if 1.4999999999999999e-308 < B < 3.9e6

   1. Initial program 48.7%

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

   3. Taylor expanded in A around -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. *-commutative N/A

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

      4. *-lowering-*.f64 41.9%

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

   5. Simplified 41.9%

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

   if 3.9e6 < B

   1. Initial program 47.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 83.3%

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

   5. Taylor expanded in B around inf

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

   7. Simplified 62.8%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9.8 \cdot 10^{-46}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-308}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;B \leq 3900000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -6.8 \cdot 10^{-196}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + t\_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-113}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 + t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (- C A) B)))
   (if (<= B -6.8e-196)
     (* 180.0 (/ (atan (+ 1.0 t_0)) PI))
     (if (<= B 1.2e-113)
       (* (/ 180.0 PI) (atan (* B (/ -0.5 (- C A)))))
       (* (/ 180.0 PI) (atan (+ -1.0 t_0)))))))

C

double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -6.8e-196) {
		tmp = 180.0 * (atan((1.0 + t_0)) / ((double) M_PI));
	} else if (B <= 1.2e-113) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / (C - A))));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 + t_0));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (C - A) / B;
	double tmp;
	if (B <= -6.8e-196) {
		tmp = 180.0 * (Math.atan((1.0 + t_0)) / Math.PI);
	} else if (B <= 1.2e-113) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / (C - A))));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 + t_0));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (C - A) / B
	tmp = 0
	if B <= -6.8e-196:
		tmp = 180.0 * (math.atan((1.0 + t_0)) / math.pi)
	elif B <= 1.2e-113:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / (C - A))))
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 + t_0))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (B <= -6.8e-196)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + t_0)) / pi));
	elseif (B <= 1.2e-113)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / Float64(C - A)))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 + t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (C - A) / B;
	tmp = 0.0;
	if (B <= -6.8e-196)
		tmp = 180.0 * (atan((1.0 + t_0)) / pi);
	elseif (B <= 1.2e-113)
		tmp = (180.0 / pi) * atan((B * (-0.5 / (C - A))));
	else
		tmp = (180.0 / pi) * atan((-1.0 + t_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, -6.8e-196], N[(180.0 * N[(N[ArcTan[N[(1.0 + t$95$0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.2e-113], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 + t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if B < -6.8e-196

   1. Initial program 58.1%

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

   3. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   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 73.1%

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

   5. Simplified 73.1%

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

   if -6.8e-196 < B < 1.20000000000000006e-113

   1. Initial program 45.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 70.7%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

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

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

      14. --lowering--.f64 65.8%

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

   7. Simplified 65.8%

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

   if 1.20000000000000006e-113 < B

   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 79.9%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 76.7%

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

   7. Simplified 76.7%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.8 \cdot 10^{-196}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-113}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 + \frac{C - A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.6% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.1 \cdot 10^{-195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-109}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.1e-195)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= B 1.45e-109)
     (* (/ 180.0 PI) (atan (* B (/ -0.5 (- C A)))))
     (* (/ 180.0 PI) (atan (/ (- C B) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.1e-195) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= 1.45e-109) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (-0.5 / (C - 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 <= -2.1e-195) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= 1.45e-109) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (-0.5 / (C - A))));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.1e-195:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= 1.45e-109:
		tmp = (180.0 / math.pi) * math.atan((B * (-0.5 / (C - 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 <= -2.1e-195)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= 1.45e-109)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(-0.5 / Float64(C - 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 <= -2.1e-195)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= 1.45e-109)
		tmp = (180.0 / pi) * atan((B * (-0.5 / (C - A))));
	else
		tmp = (180.0 / pi) * atan(((C - B) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.1e-195], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.45e-109], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(-0.5 / N[(C - A), $MachinePrecision]), $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 < -2.1e-195

   1. Initial program 58.1%

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

   3. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   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 73.1%

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

   5. Simplified 73.1%

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

   if -2.1e-195 < B < 1.45e-109

   1. Initial program 45.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 70.7%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

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

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

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

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

      14. --lowering--.f64 65.8%

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

   7. Simplified 65.8%

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

   if 1.45e-109 < B

   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 79.9%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in C around 0

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

      1. --lowering--.f64 68.1%

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

   10. Simplified 68.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.1 \cdot 10^{-195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.45 \cdot 10^{-109}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{-0.5}{C - A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.5 \cdot 10^{-124}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{+15}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.5e-124)
   (* (/ 180.0 PI) (atan (/ (* B 0.5) A)))
   (if (<= A 1.4e+15)
     (* (/ 180.0 PI) (atan (+ 1.0 (/ C B))))
     (* (/ 180.0 PI) (atan (- -1.0 (/ A B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.5e-124) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * 0.5) / A));
	} else if (A <= 1.4e+15) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + (C / B)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.5e-124) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * 0.5) / A));
	} else if (A <= 1.4e+15) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + (C / B)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.5e-124:
		tmp = (180.0 / math.pi) * math.atan(((B * 0.5) / A))
	elif A <= 1.4e+15:
		tmp = (180.0 / math.pi) * math.atan((1.0 + (C / B)))
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.5e-124)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * 0.5) / A)));
	elseif (A <= 1.4e+15)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(C / B))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.5e-124)
		tmp = (180.0 / pi) * atan(((B * 0.5) / A));
	elseif (A <= 1.4e+15)
		tmp = (180.0 / pi) * atan((1.0 + (C / B)));
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.5e-124], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.4e+15], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.5000000000000001e-124

   1. Initial program 28.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 58.2%

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

   5. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 59.3%

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

   7. Simplified 59.3%

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

   if -2.5000000000000001e-124 < A < 1.4e15

   1. Initial program 56.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

   3. Simplified 80.5%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 77.6%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in B around -inf

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

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

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

      2. /-lowering-/.f64 45.5%

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

   10. Simplified 45.5%

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

   if 1.4e15 < A

   1. Initial program 79.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 95.5%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 83.4%

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

   7. Simplified 83.4%

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

   8. Taylor expanded in C around 0

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

      1. distribute-lft-in N/A

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

      2. metadata-eval N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. /-lowering-/.f64 81.9%

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

   10. Simplified 81.9%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.5 \cdot 10^{-124}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{+15}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3 \cdot 10^{-122}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3e-122)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 5.6e+15)
     (* (/ 180.0 PI) (atan (+ 1.0 (/ C B))))
     (* (/ 180.0 PI) (atan (- -1.0 (/ A B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3e-122) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 5.6e+15) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 + (C / B)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((-1.0 - (A / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3e-122) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 5.6e+15) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 + (C / B)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((-1.0 - (A / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3e-122:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 5.6e+15:
		tmp = (180.0 / math.pi) * math.atan((1.0 + (C / B)))
	else:
		tmp = (180.0 / math.pi) * math.atan((-1.0 - (A / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3e-122)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 5.6e+15)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 + Float64(C / B))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(-1.0 - Float64(A / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3e-122)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 5.6e+15)
		tmp = (180.0 / pi) * atan((1.0 + (C / B)));
	else
		tmp = (180.0 / pi) * atan((-1.0 - (A / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3e-122], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.6e+15], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.00000000000000004e-122

   1. Initial program 28.5%

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

   3. Taylor expanded in A around -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. *-commutative N/A

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

      4. *-lowering-*.f64 59.2%

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

   5. Simplified 59.2%

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

   if -3.00000000000000004e-122 < A < 5.6e15

   1. Initial program 56.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

   3. Simplified 80.5%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 77.6%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in B around -inf

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

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

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

      2. /-lowering-/.f64 45.5%

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

   10. Simplified 45.5%

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

   if 5.6e15 < A

   1. Initial program 79.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 95.5%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 83.4%

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

   7. Simplified 83.4%

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

   8. Taylor expanded in C around 0

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

      1. distribute-lft-in N/A

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

      2. metadata-eval N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. /-lowering-/.f64 81.9%

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

   10. Simplified 81.9%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3 \cdot 10^{-122}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 47.0% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.7 \cdot 10^{-46}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{+15}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.7e-46)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 3.7e+15)
     (* (/ 180.0 PI) (atan (/ C B)))
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.7e-46) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 3.7e+15) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.7e-46) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 3.7e+15) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -6.7e-46:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 3.7e+15:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -6.7e-46)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 3.7e+15)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -6.7e-46)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 3.7e+15)
		tmp = (180.0 / pi) * atan((C / B));
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -6.7e-46], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.7e+15], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -6.7000000000000001e-46

   1. Initial program 52.2%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

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

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

   3. Simplified 79.1%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 56.1%

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

   if -6.7000000000000001e-46 < B < 3.7e15

   1. Initial program 58.2%

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

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 51.9%

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

   7. Simplified 51.9%

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

   8. Taylor expanded in C around inf

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

      1. /-lowering-/.f64 33.9%

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

   10. Simplified 33.9%

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

   if 3.7e15 < B

   1. Initial program 45.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 83.5%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 64.9%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.7 \cdot 10^{-46}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 3.7 \cdot 10^{+15}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.9% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 4.6 \cdot 10^{-48}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 4.6e-48)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (* (/ 180.0 PI) (atan (/ (- C B) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 4.6e-48) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} 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 <= 4.6e-48) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 4.6e-48:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 4.6e-48)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	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 <= 4.6e-48)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	else
		tmp = (180.0 / pi) * atan(((C - B) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 4.6e-48], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 4.6000000000000001e-48

   1. Initial program 54.6%

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

   3. Taylor expanded in B around -inf

      \[\leadsto \mathsf{*.f64}\left(180, \mathsf{/.f64}\left(\mathsf{atan.f64}\left(\color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}\right), \mathsf{PI.f64}\left(\right)\right)\right) \]
   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 61.4%

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

   5. Simplified 61.4%

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

   if 4.6000000000000001e-48 < B

   1. Initial program 49.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 81.0%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in C around 0

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

      1. --lowering--.f64 70.9%

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

   10. Simplified 70.9%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 4.6 \cdot 10^{-48}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 44.7% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.2 \cdot 10^{-176}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-118}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.2e-176)
   (* (/ 180.0 PI) (atan 1.0))
   (if (<= B 3.1e-118)
     (/ (* 180.0 (atan 0.0)) PI)
     (* (/ 180.0 PI) (atan -1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.2e-176) {
		tmp = (180.0 / ((double) M_PI)) * atan(1.0);
	} else if (B <= 3.1e-118) {
		tmp = (180.0 * atan(0.0)) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(-1.0);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.2e-176) {
		tmp = (180.0 / Math.PI) * Math.atan(1.0);
	} else if (B <= 3.1e-118) {
		tmp = (180.0 * Math.atan(0.0)) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(-1.0);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.2e-176:
		tmp = (180.0 / math.pi) * math.atan(1.0)
	elif B <= 3.1e-118:
		tmp = (180.0 * math.atan(0.0)) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan(-1.0)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.2e-176)
		tmp = Float64(Float64(180.0 / pi) * atan(1.0));
	elseif (B <= 3.1e-118)
		tmp = Float64(Float64(180.0 * atan(0.0)) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(-1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.2e-176)
		tmp = (180.0 / pi) * atan(1.0);
	elseif (B <= 3.1e-118)
		tmp = (180.0 * atan(0.0)) / pi;
	else
		tmp = (180.0 / pi) * atan(-1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.2e-176], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.1e-118], N[(N[(180.0 * N[ArcTan[0.0], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[-1.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.20000000000000003e-176

   1. Initial program 57.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 77.2%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 44.5%

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

   if -1.20000000000000003e-176 < B < 3.1000000000000001e-118

   1. Initial program 48.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 71.8%

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

   5. Taylor expanded in C around inf

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

      1. associate-*r/ N/A

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

      2. distribute-rgt1-in N/A

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

      3. metadata-eval N/A

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

      4. mul0-lft N/A

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

      5. metadata-eval N/A

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

      6. /-lowering-/.f64 33.4%

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

   7. Simplified 33.4%

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

      1. associate-*r/ N/A

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

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

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

      3. *-commutative N/A

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

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

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

      5. div0 N/A

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

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

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

      7. PI-lowering-PI.f64 33.4%

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

   9. Applied egg-rr 33.4%

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

   if 3.1000000000000001e-118 < B

   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 79.9%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 54.2%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.2 \cdot 10^{-176}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{elif}\;B \leq 3.1 \cdot 10^{-118}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 40.2% 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 58.2%

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

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

   5. Taylor expanded in B around -inf

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

   7. Simplified 37.3%

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

   if -4.999999999999985e-310 < B

   1. Initial program 48.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 76.0%

      \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
   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 41.7%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} -1\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 21.2% 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 53.1%

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

   \[\leadsto \color{blue}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right) \cdot \frac{180}{\pi}} \]
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 22.2%

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

8. Final simplification 22.2%

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

Reproduce

herbie shell --seed 2024155 
(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)))