ABCF->ab-angle angle

Percentage Accurate: 54.2% → 81.6%

Time: 13.6s

Alternatives: 17

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.2% 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: 81.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6 \cdot 10^{+176}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6e+176)
   (/ 180.0 (/ PI (atan (/ (* B 0.5) A))))
   (* (/ 180.0 PI) (atan (/ (- (- C A) (hypot (- A C) B)) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6e+176) {
		tmp = 180.0 / (((double) M_PI) / atan(((B * 0.5) / A)));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((((C - A) - hypot((A - C), B)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6e+176) {
		tmp = 180.0 / (Math.PI / Math.atan(((B * 0.5) / A)));
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((((C - A) - Math.hypot((A - C), B)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6e+176:
		tmp = 180.0 / (math.pi / math.atan(((B * 0.5) / A)))
	else:
		tmp = (180.0 / math.pi) * math.atan((((C - A) - math.hypot((A - C), B)) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6e+176)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(B * 0.5) / A))));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6e+176)
		tmp = 180.0 / (pi / atan(((B * 0.5) / A)));
	else
		tmp = (180.0 / pi) * atan((((C - A) - hypot((A - C), B)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6e+176], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -6e176

   1. Initial program 5.9%

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

   3. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 86.9

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

   5. Simplified 86.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-atan.f64 N/A

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

      4. lift-PI.f64 N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 87.0

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

   7. Applied egg-rr 87.0%

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

   if -6e176 < A

   1. Initial program 63.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-sqrt.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-atan.f64 N/A

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

      11. lift-PI.f64 N/A

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

   4. Applied egg-rr 63.8%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lower-hypot.f64 84.2

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

   6. Applied egg-rr 84.2%

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

Alternative 2: 73.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

function code(A, B, C)
	t_0 = atan(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 <= -5e-39)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(C - A) / B) + -1.0)));
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - Float64(fma(-0.5, Float64(Float64(A - C) * Float64(Float64(A - C) / B)), Float64(A - C)) / B))));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-sqrt.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-atan.f64 N/A

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

      11. lift-PI.f64 N/A

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

   4. Applied egg-rr 64.2%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 77.3

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

   7. Simplified 77.3%

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

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

   1. Initial program 16.6%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. --rgt-identity N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 30.7

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

   5. Simplified 30.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-atan.f64 N/A

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

      7. lift-PI.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 30.7

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

   7. Applied egg-rr 60.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-atan.f64 N/A

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

      4. lift-PI.f64 N/A

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

      5. clear-num N/A

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

      6. associate-/r/ N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. lift-/.f64 N/A

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

      12. associate-/r/ N/A

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

      13. clear-num N/A

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

      14. lift-/.f64 N/A

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

      15. lower-*.f64 60.5

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

   9. Applied egg-rr 60.5%

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

   if -0.0 < (atan.f64 (*.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 64.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-sqrt.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-atan.f64 N/A

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

      11. lift-PI.f64 N/A

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

   4. Applied egg-rr 64.8%

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

   5. Taylor expanded in B around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   7. Simplified 82.3%

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

Alternative 3: 73.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-sqrt.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-atan.f64 N/A

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

      11. lift-PI.f64 N/A

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

   4. Applied egg-rr 64.2%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 77.3

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

   7. Simplified 77.3%

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

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

   1. Initial program 16.6%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. --rgt-identity N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 30.7

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

   5. Simplified 30.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-atan.f64 N/A

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

      7. lift-PI.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 30.7

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

   7. Applied egg-rr 60.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-atan.f64 N/A

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

      4. lift-PI.f64 N/A

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

      5. clear-num N/A

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

      6. associate-/r/ N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. lift-/.f64 N/A

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

      12. associate-/r/ N/A

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

      13. clear-num N/A

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

      14. lift-/.f64 N/A

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

      15. lower-*.f64 60.5

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

   9. Applied egg-rr 60.5%

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

   if -0.0 < (atan.f64 (*.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 64.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-sqrt.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-atan.f64 N/A

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

      11. lift-PI.f64 N/A

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

   4. Applied egg-rr 64.8%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 80.6

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

   7. Simplified 80.6%

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

Alternative 4: 73.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-sqrt.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-atan.f64 N/A

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

      11. lift-PI.f64 N/A

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

   4. Applied egg-rr 64.2%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 77.3

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

   7. Simplified 77.3%

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

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

   1. Initial program 16.6%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. --rgt-identity N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 30.7

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

   5. Simplified 30.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-atan.f64 N/A

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

      7. lift-PI.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 30.7

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

   7. Applied egg-rr 60.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-atan.f64 N/A

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

      4. lift-PI.f64 N/A

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

      5. clear-num N/A

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

      6. associate-/r/ N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. lift-/.f64 N/A

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

      12. associate-/r/ N/A

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

      13. clear-num N/A

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

      14. lift-/.f64 N/A

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

      15. lower-*.f64 60.5

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

   9. Applied egg-rr 60.5%

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

   if -0.0 < (atan.f64 (*.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 64.7%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 80.6

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

   5. Simplified 80.6%

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

Alternative 5: 73.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.2%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 77.3

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

   5. Simplified 77.3%

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

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

   1. Initial program 16.6%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. --rgt-identity N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 30.7

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

   5. Simplified 30.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-atan.f64 N/A

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

      7. lift-PI.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 30.7

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

   7. Applied egg-rr 60.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-atan.f64 N/A

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

      4. lift-PI.f64 N/A

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

      5. clear-num N/A

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

      6. associate-/r/ N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. lift-/.f64 N/A

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

      12. associate-/r/ N/A

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

      13. clear-num N/A

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

      14. lift-/.f64 N/A

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

      15. lower-*.f64 60.5

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

   9. Applied egg-rr 60.5%

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

   if -0.0 < (atan.f64 (*.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 64.7%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 80.6

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

   5. Simplified 80.6%

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

Alternative 6: 67.5% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-sqrt.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-atan.f64 N/A

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

      11. lift-PI.f64 N/A

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

   4. Applied egg-rr 64.2%

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

   5. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-in N/A

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

      3. unsub-neg N/A

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

      4. lower--.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-sqrt.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-fma.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 53.4

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

   7. Simplified 53.4%

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

   8. Taylor expanded in A around 0

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

      1. lower--.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 63.0

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

   10. Simplified 63.0%

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

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

   1. Initial program 16.6%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. --rgt-identity N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 30.7

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

   5. Simplified 30.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-atan.f64 N/A

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

      7. lift-PI.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 30.7

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

   7. Applied egg-rr 60.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-atan.f64 N/A

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

      4. lift-PI.f64 N/A

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

      5. clear-num N/A

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

      6. associate-/r/ N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. lift-/.f64 N/A

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

      12. associate-/r/ N/A

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

      13. clear-num N/A

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

      14. lift-/.f64 N/A

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

      15. lower-*.f64 60.5

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

   9. Applied egg-rr 60.5%

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

   if -0.0 < (atan.f64 (*.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 64.7%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 80.6

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

   5. Simplified 80.6%

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

Alternative 7: 62.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(A, B, C)
	t_0 = atan(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 <= -5e-39)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(-A) - B) / B))) / pi);
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-sqrt.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-atan.f64 N/A

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

      11. lift-PI.f64 N/A

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

   4. Applied egg-rr 64.2%

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

   5. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-in N/A

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

      3. unsub-neg N/A

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

      4. lower--.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-sqrt.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-fma.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 53.4

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

   7. Simplified 53.4%

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

   8. Taylor expanded in A around 0

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

      1. lower--.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 63.0

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

   10. Simplified 63.0%

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

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

   1. Initial program 16.6%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. --rgt-identity N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 30.7

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

   5. Simplified 30.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-atan.f64 N/A

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

      7. lift-PI.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 30.7

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

   7. Applied egg-rr 60.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-atan.f64 N/A

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

      4. lift-PI.f64 N/A

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

      5. clear-num N/A

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

      6. associate-/r/ N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. lift-/.f64 N/A

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

      12. associate-/r/ N/A

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

      13. clear-num N/A

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

      14. lift-/.f64 N/A

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

      15. lower-*.f64 60.5

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

   9. Applied egg-rr 60.5%

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

   if -0.0 < (atan.f64 (*.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 64.7%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 80.6

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

   5. Simplified 80.6%

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

   6. Taylor expanded in C around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 70.8

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

   8. Simplified 70.8%

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

Alternative 8: 73.3% accurate, 0.6× speedup

Math

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

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))))))
        (t_1 (/ (- C A) B)))
   (if (<= t_0 -5e-39)
     (* (/ 180.0 PI) (atan (+ t_1 -1.0)))
     (if (<= t_0 0.0)
       (* (/ 180.0 PI) (atan (/ (* B -0.5) C)))
       (* (* 180.0 (atan (+ 1.0 t_1))) (/ 1.0 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 t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -5e-39) {
		tmp = (180.0 / ((double) M_PI)) * atan((t_1 + -1.0));
	} else if (t_0 <= 0.0) {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 * atan((1.0 + t_1))) * (1.0 / ((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 t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -5e-39) {
		tmp = (180.0 / Math.PI) * Math.atan((t_1 + -1.0));
	} else if (t_0 <= 0.0) {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	} else {
		tmp = (180.0 * Math.atan((1.0 + t_1))) * (1.0 / 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))))
	t_1 = (C - A) / B
	tmp = 0
	if t_0 <= -5e-39:
		tmp = (180.0 / math.pi) * math.atan((t_1 + -1.0))
	elif t_0 <= 0.0:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	else:
		tmp = (180.0 * math.atan((1.0 + t_1))) * (1.0 / 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)))))
	t_1 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (t_0 <= -5e-39)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(t_1 + -1.0)));
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + t_1))) * Float64(1.0 / 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))));
	t_1 = (C - A) / B;
	tmp = 0.0;
	if (t_0 <= -5e-39)
		tmp = (180.0 / pi) * atan((t_1 + -1.0));
	elseif (t_0 <= 0.0)
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	else
		tmp = (180.0 * atan((1.0 + t_1))) * (1.0 / 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]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[t$95$0, -5e-39], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(t$95$1 + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(1.0 + t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 / 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)))))) < -4.9999999999999998e-39

   1. Initial program 64.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-sqrt.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-atan.f64 N/A

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

      11. lift-PI.f64 N/A

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

   4. Applied egg-rr 64.2%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 77.3

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

   7. Simplified 77.3%

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

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

   1. Initial program 16.6%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. --rgt-identity N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 30.7

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

   5. Simplified 30.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-atan.f64 N/A

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

      7. lift-PI.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 30.7

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

   7. Applied egg-rr 60.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-atan.f64 N/A

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

      4. lift-PI.f64 N/A

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

      5. clear-num N/A

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

      6. associate-/r/ N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. lift-/.f64 N/A

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

      12. associate-/r/ N/A

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

      13. clear-num N/A

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

      14. lift-/.f64 N/A

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

      15. lower-*.f64 60.5

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

   9. Applied egg-rr 60.5%

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

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

   1. Initial program 64.7%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 80.6

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

   5. Simplified 80.6%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-atan.f64 N/A

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

      5. lift-PI.f64 N/A

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

      6. associate-*r/ N/A

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

      7. div-inv N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 80.6

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

   7. Applied egg-rr 80.6%

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

Alternative 9: 59.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.2 \cdot 10^{-62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.85 \cdot 10^{-84}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.2e-62)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= C 1.85e-84)
     (/ (* 180.0 (atan (- 1.0 (/ A B)))) PI)
     (* (/ 180.0 PI) (atan (/ (* B -0.5) C))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.2e-62) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (C <= 1.85e-84) {
		tmp = (180.0 * atan((1.0 - (A / B)))) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((B * -0.5) / C));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.2e-62) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (C <= 1.85e-84) {
		tmp = (180.0 * Math.atan((1.0 - (A / B)))) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((B * -0.5) / C));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.2e-62:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif C <= 1.85e-84:
		tmp = (180.0 * math.atan((1.0 - (A / B)))) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan(((B * -0.5) / C))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.2e-62)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (C <= 1.85e-84)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 - Float64(A / B)))) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(B * -0.5) / C)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.2e-62)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (C <= 1.85e-84)
		tmp = (180.0 * atan((1.0 - (A / B)))) / pi;
	else
		tmp = (180.0 / pi) * atan(((B * -0.5) / C));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.2e-62], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.85e-84], N[(N[(180.0 * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.19999999999999992e-62

   1. Initial program 76.9%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 81.7

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

   5. Simplified 81.7%

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

   6. Taylor expanded in A around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 79.4

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

   8. Simplified 79.4%

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

   if -1.19999999999999992e-62 < C < 1.85e-84

   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. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-sqrt.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-atan.f64 N/A

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

      11. lift-PI.f64 N/A

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

   4. Applied egg-rr 68.0%

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

   5. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-in N/A

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

      3. unsub-neg N/A

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

      4. lower--.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-sqrt.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-fma.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 68.1

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

   7. Simplified 68.1%

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

   8. Taylor expanded in B around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 60.7

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

   10. Simplified 60.7%

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

   if 1.85e-84 < C

   1. Initial program 31.2%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. --rgt-identity N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. metadata-eval N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. unpow2 N/A

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

      12. lower-*.f64 45.2

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

   5. Simplified 45.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-atan.f64 N/A

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

      7. lift-PI.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 45.2

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

   7. Applied egg-rr 58.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-atan.f64 N/A

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

      4. lift-PI.f64 N/A

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

      5. clear-num N/A

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

      6. associate-/r/ N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. lift-/.f64 N/A

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

      12. associate-/r/ N/A

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

      13. clear-num N/A

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

      14. lift-/.f64 N/A

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

      15. lower-*.f64 58.7

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

   9. Applied egg-rr 58.7%

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

Alternative 10: 59.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9.6 \cdot 10^{+74}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.55 \cdot 10^{-114}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9.6e+74)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 2.55e-114)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.6e+74) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 2.55e-114) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.6e+74) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 2.55e-114) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -9.6e+74:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 2.55e-114:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -9.6e+74)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 2.55e-114)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -9.6e+74)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 2.55e-114)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -9.6e+74], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.55e-114], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -9.60000000000000034e74

   1. Initial program 18.7%

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

   3. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 73.8

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

   5. Simplified 73.8%

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

   if -9.60000000000000034e74 < A < 2.55e-114

   1. Initial program 57.0%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 49.3

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

   5. Simplified 49.3%

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

   6. Taylor expanded in A around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 48.4

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

   8. Simplified 48.4%

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

   if 2.55e-114 < A

   1. Initial program 75.5%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 78.0

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

   5. Simplified 78.0%

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

   6. Taylor expanded in C around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 72.8

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

   8. Simplified 72.8%

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

Alternative 11: 52.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.5 \cdot 10^{-62}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.2 \cdot 10^{+173}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.5e-62)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= C 1.2e+173)
     (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
     (* 180.0 (/ (atan 0.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.5e-62) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (C <= 1.2e+173) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.5e-62) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else if (C <= 1.2e+173) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.5e-62:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	elif C <= 1.2e+173:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.5e-62)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (C <= 1.2e+173)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.5e-62)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	elseif (C <= 1.2e+173)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	else
		tmp = 180.0 * (atan(0.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.5e-62], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.2e+173], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.5000000000000001e-62

   1. Initial program 76.9%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 81.7

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

   5. Simplified 81.7%

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

   6. Taylor expanded in A around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 79.4

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

   8. Simplified 79.4%

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

   if -1.5000000000000001e-62 < C < 1.2e173

   1. Initial program 59.6%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 52.0

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

   5. Simplified 52.0%

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

   6. Taylor expanded in C around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 52.1

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

   8. Simplified 52.1%

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

   if 1.2e173 < C

   1. Initial program 12.5%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 35.6

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

   5. Simplified 35.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 50.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.4 \cdot 10^{+143}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;A \leq 6 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.4e+143)
   (* 180.0 (/ (atan 0.0) PI))
   (if (<= A 6e+25)
     (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (/ A (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.4e+143) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (A <= 6e+25) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.4e+143) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (A <= 6e+25) {
		tmp = 180.0 * (Math.atan((1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.4e+143:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif A <= 6e+25:
		tmp = 180.0 * (math.atan((1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.4e+143)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (A <= 6e+25)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.4e+143)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (A <= 6e+25)
		tmp = 180.0 * (atan((1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan((A / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.4e+143], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 6e+25], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.39999999999999999e143

   1. Initial program 14.7%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B}\right)}{\mathsf{PI}\left(\right)} \]

      4. div0 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \color{blue}{0}\right)}{\mathsf{PI}\left(\right)} \]

      5. metadata-eval 33.6

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   5. Simplified 33.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   if -1.39999999999999999e143 < A < 6.00000000000000011e25

   1. Initial program 55.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)}}{\mathsf{PI}\left(\right)} \]

      2. div-sub N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\mathsf{PI}\left(\right)} \]

      3. lower-+.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\mathsf{PI}\left(\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\mathsf{PI}\left(\right)} \]

      5. lower--.f64 50.7

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \frac{\color{blue}{C - A}}{B}\right)}{\pi} \]

   5. Simplified 50.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   6. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C}{B}\right)}}{\mathsf{PI}\left(\right)} \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C}{B}\right)}}{\mathsf{PI}\left(\right)} \]

      2. lower-/.f64 46.8

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C}{B}}\right)}{\pi} \]

   8. Simplified 46.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C}{B}\right)}}{\pi} \]

   if 6.00000000000000011e25 < A

   1. Initial program 80.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)}}{\mathsf{PI}\left(\right)} \]

      2. div-sub N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\mathsf{PI}\left(\right)} \]

      3. lower-+.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\mathsf{PI}\left(\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\mathsf{PI}\left(\right)} \]

      5. lower--.f64 83.7

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \frac{\color{blue}{C - A}}{B}\right)}{\pi} \]

   5. Simplified 83.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   6. Taylor expanded in A around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A}{B}\right)}}{\mathsf{PI}\left(\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{neg}\left(\frac{A}{B}\right)\right)}}{\mathsf{PI}\left(\right)} \]

      2. distribute-neg-frac2 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{A}{\mathsf{neg}\left(B\right)}\right)}}{\mathsf{PI}\left(\right)} \]

      3. mul-1-neg N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A}{\color{blue}{-1 \cdot B}}\right)}{\mathsf{PI}\left(\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{A}{-1 \cdot B}\right)}}{\mathsf{PI}\left(\right)} \]

      5. mul-1-neg N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A}{\color{blue}{\mathsf{neg}\left(B\right)}}\right)}{\mathsf{PI}\left(\right)} \]

      6. lower-neg.f64 73.0

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A}{\color{blue}{-B}}\right)}{\pi} \]

   8. Simplified 73.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{A}{-B}\right)}}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 46.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -9.5 \cdot 10^{+33}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-74}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -9.5e+33)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.5e-74)
     (* 180.0 (/ (atan (/ A (- B))) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -9.5e+33) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.5e-74) {
		tmp = 180.0 * (atan((A / -B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -9.5e+33) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.5e-74) {
		tmp = 180.0 * (Math.atan((A / -B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -9.5e+33:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.5e-74:
		tmp = 180.0 * (math.atan((A / -B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -9.5e+33)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.5e-74)
		tmp = Float64(180.0 * Float64(atan(Float64(A / Float64(-B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -9.5e+33)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.5e-74)
		tmp = 180.0 * (atan((A / -B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -9.5e+33], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.5e-74], N[(180.0 * N[(N[ArcTan[N[(A / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -9.5000000000000003e33

   1. Initial program 52.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Simplified 64.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -9.5000000000000003e33 < B < 2.49999999999999999e-74

   1. Initial program 62.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)}}{\mathsf{PI}\left(\right)} \]

      2. div-sub N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\mathsf{PI}\left(\right)} \]

      3. lower-+.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\mathsf{PI}\left(\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\mathsf{PI}\left(\right)} \]

      5. lower--.f64 56.8

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \frac{\color{blue}{C - A}}{B}\right)}{\pi} \]

   5. Simplified 56.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   6. Taylor expanded in A around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A}{B}\right)}}{\mathsf{PI}\left(\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{neg}\left(\frac{A}{B}\right)\right)}}{\mathsf{PI}\left(\right)} \]

      2. distribute-neg-frac2 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{A}{\mathsf{neg}\left(B\right)}\right)}}{\mathsf{PI}\left(\right)} \]

      3. mul-1-neg N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A}{\color{blue}{-1 \cdot B}}\right)}{\mathsf{PI}\left(\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{A}{-1 \cdot B}\right)}}{\mathsf{PI}\left(\right)} \]

      5. mul-1-neg N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A}{\color{blue}{\mathsf{neg}\left(B\right)}}\right)}{\mathsf{PI}\left(\right)} \]

      6. lower-neg.f64 39.7

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A}{\color{blue}{-B}}\right)}{\pi} \]

   8. Simplified 39.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{A}{-B}\right)}}{\pi} \]

   if 2.49999999999999999e-74 < B

   1. Initial program 60.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Simplified 52.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 47.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.2 \cdot 10^{-118}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-105}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.2e-118)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.35e-105)
     (* 180.0 (/ (atan (/ C B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.2e-118) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.35e-105) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.2e-118) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.35e-105) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.2e-118:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.35e-105:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.2e-118)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.35e-105)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.2e-118)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.35e-105)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.2e-118], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.35e-105], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.20000000000000004e-118

   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

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Simplified 53.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -3.20000000000000004e-118 < B < 1.34999999999999996e-105

   1. Initial program 58.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(1 + \frac{C}{B}\right) - \frac{A}{B}\right)}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \left(\frac{C}{B} - \frac{A}{B}\right)\right)}}{\mathsf{PI}\left(\right)} \]

      2. div-sub N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\mathsf{PI}\left(\right)} \]

      3. lower-+.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\mathsf{PI}\left(\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \color{blue}{\frac{C - A}{B}}\right)}{\mathsf{PI}\left(\right)} \]

      5. lower--.f64 53.8

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(1 + \frac{\color{blue}{C - A}}{B}\right)}{\pi} \]

   5. Simplified 53.8%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(1 + \frac{C - A}{B}\right)}}{\pi} \]

   6. Taylor expanded in C around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B}\right)}}{\mathsf{PI}\left(\right)} \]
   7. Step-by-step derivation

      1. lower-/.f64 35.9

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B}\right)}}{\pi} \]

   8. Simplified 35.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B}\right)}}{\pi} \]

   if 1.34999999999999996e-105 < B

   1. Initial program 60.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Simplified 50.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 45.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.15 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{-74}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.15e-145)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 5.4e-74)
     (* 180.0 (/ (atan 0.0) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.15e-145) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 5.4e-74) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.15e-145) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 5.4e-74) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.15e-145:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 5.4e-74:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.15e-145)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 5.4e-74)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.15e-145)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 5.4e-74)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.15e-145], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 5.4e-74], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.15e-145

   1. Initial program 59.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Simplified 53.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\pi} \]

   if -2.15e-145 < B < 5.40000000000000036e-74

   1. Initial program 57.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in C around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

      1. distribute-rgt1-in N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{\left(-1 + 1\right) \cdot A}}{B}\right)}{\mathsf{PI}\left(\right)} \]

      2. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B}\right)}{\mathsf{PI}\left(\right)} \]

      3. mul0-lft N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B}\right)}{\mathsf{PI}\left(\right)} \]

      4. div0 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \color{blue}{0}\right)}{\mathsf{PI}\left(\right)} \]

      5. metadata-eval 25.4

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   5. Simplified 25.4%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   if 5.40000000000000036e-74 < B

   1. Initial program 61.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Simplified 52.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 28.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 5.4 \cdot 10^{-74}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 5.4e-74) (* 180.0 (/ (atan 0.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.4e-74) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 5.4e-74) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 5.4e-74:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 5.4e-74)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 5.4e-74)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 5.4e-74], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 5.40000000000000036e-74

   1. Initial program 58.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in C around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

      1. distribute-rgt1-in N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{\left(-1 + 1\right) \cdot A}}{B}\right)}{\mathsf{PI}\left(\right)} \]

      2. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B}\right)}{\mathsf{PI}\left(\right)} \]

      3. mul0-lft N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B}\right)}{\mathsf{PI}\left(\right)} \]

      4. div0 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \color{blue}{0}\right)}{\mathsf{PI}\left(\right)} \]

      5. metadata-eval 13.9

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   5. Simplified 13.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   if 5.40000000000000036e-74 < B

   1. Initial program 61.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. Add Preprocessing

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Simplified 52.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 20.6% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ 180 \cdot \frac{\tan^{-1} -1}{\pi} \end{array} \]

FPCore

(FPCore (A B C) :precision binary64 (* 180.0 (/ (atan -1.0) PI)))

C

double code(double A, double B, double C) {
	return 180.0 * (atan(-1.0) / ((double) M_PI));
}

Java

public static double code(double A, double B, double C) {
	return 180.0 * (Math.atan(-1.0) / Math.PI);
}

Python

def code(A, B, C):
	return 180.0 * (math.atan(-1.0) / math.pi)

Julia

function code(A, B, C)
	return Float64(180.0 * Float64(atan(-1.0) / pi))
end

MATLAB

function tmp = code(A, B, C)
	tmp = 180.0 * (atan(-1.0) / pi);
end

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 59.2%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
2. Add Preprocessing

3. Taylor expanded in B around inf

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\mathsf{PI}\left(\right)} \]
4. Step-by-step derivation

5. Simplified 19.6%

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024207 
(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)))