ABCF->ab-angle angle

Percentage Accurate: 53.4% → 79.7%

Time: 23.3s

Alternatives: 18

Speedup: 3.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.4% 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: 79.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.8 \cdot 10^{+154}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{-245} \lor \neg \left(A \leq -9.5 \cdot 10^{-269}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.8e+154)
   (/ (* 180.0 (atan (* B (/ 0.5 A)))) PI)
   (if (or (<= A -2.4e-245) (not (<= A -9.5e-269)))
     (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))
     (* 180.0 (/ (atan (* B (/ -0.5 C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.8e+154) {
		tmp = (180.0 * atan((B * (0.5 / A)))) / ((double) M_PI);
	} else if ((A <= -2.4e-245) || !(A <= -9.5e-269)) {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.8e+154) {
		tmp = (180.0 * Math.atan((B * (0.5 / A)))) / Math.PI;
	} else if ((A <= -2.4e-245) || !(A <= -9.5e-269)) {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.8e+154:
		tmp = (180.0 * math.atan((B * (0.5 / A)))) / math.pi
	elif (A <= -2.4e-245) or not (A <= -9.5e-269):
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.8e+154)
		tmp = Float64(Float64(180.0 * atan(Float64(B * Float64(0.5 / A)))) / pi);
	elseif ((A <= -2.4e-245) || !(A <= -9.5e-269))
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.8e+154)
		tmp = (180.0 * atan((B * (0.5 / A)))) / pi;
	elseif ((A <= -2.4e-245) || ~((A <= -9.5e-269)))
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	else
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.8e+154], N[(N[(180.0 * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[Or[LessEqual[A, -2.4e-245], N[Not[LessEqual[A, -9.5e-269]], $MachinePrecision]], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -4.8000000000000003e154

   1. Initial program 13.2%

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

      1. associate-*l/ 13.2%

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

      2. *-lft-identity 13.2%

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

      3. +-commutative 13.2%

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

      4. unpow2 13.2%

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

      5. unpow2 13.2%

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

      6. hypot-define 57.7%

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

   3. Simplified 57.7%

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

      1. clear-num 57.7%

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

      2. un-div-inv 57.7%

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

      3. hypot-undefine 13.2%

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

      4. unpow2 13.2%

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

      5. unpow2 13.2%

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

      6. +-commutative 13.2%

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

      7. unpow2 13.2%

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

      8. unpow2 13.2%

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

      9. hypot-define 57.7%

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

   6. Applied egg-rr 57.7%

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

      1. associate-/r/ 57.7%

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

      2. sub-neg 57.7%

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

      3. associate-+l- 24.1%

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

      4. sub-neg 24.1%

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

      5. remove-double-neg 24.1%

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

      6. hypot-undefine 13.2%

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

      7. unpow2 13.2%

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

      8. unpow2 13.2%

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

      9. +-commutative 13.2%

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

      10. unpow2 13.2%

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

      11. unpow2 13.2%

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

      12. hypot-undefine 24.1%

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

   8. Simplified 24.1%

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

   9. Taylor expanded in C around 0 13.2%

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

       1. mul-1-neg 13.2%

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

       2. distribute-neg-in 13.2%

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

       3. unsub-neg 13.2%

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

       4. unpow2 13.2%

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

       5. unpow2 13.2%

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

       6. hypot-define 50.4%

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

   11. Simplified 50.4%

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

   12. Taylor expanded in A around -inf 78.8%

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

       1. associate-*r/ 78.8%

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

       2. *-commutative 78.8%

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

       3. associate-/l* 78.7%

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

   14. Simplified 78.7%

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

       1. associate-*l/ 78.8%

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

   16. Applied egg-rr 78.8%

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

   if -4.8000000000000003e154 < A < -2.4e-245 or -9.5000000000000006e-269 < A

   1. Initial program 62.9%

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

   3. Simplified 84.7%

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

   if -2.4e-245 < A < -9.5000000000000006e-269

   1. Initial program 25.8%

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

   3. Taylor expanded in C around inf 79.5%

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

   4. Taylor expanded in A around inf 79.5%

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

      1. associate-*r/ 79.5%

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

      2. *-commutative 79.5%

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

      3. associate-/l* 79.7%

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

   6. Simplified 79.7%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.8 \cdot 10^{+154}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -2.4 \cdot 10^{-245} \lor \neg \left(A \leq -9.5 \cdot 10^{-269}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -7.8 \cdot 10^{+42}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)\\ \mathbf{elif}\;C \leq 2.05 \cdot 10^{+159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -7.8e+42)
   (* (/ 180.0 PI) (atan (/ (- (+ C B) A) B)))
   (if (<= C 2.05e+159)
     (* 180.0 (/ (atan (/ (+ A (hypot B A)) (- B))) PI))
     (/ 1.0 (* 0.005555555555555556 (/ PI (atan (* B (/ -0.5 C)))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -7.8e+42) {
		tmp = (180.0 / ((double) M_PI)) * atan((((C + B) - A) / B));
	} else if (C <= 2.05e+159) {
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / ((double) M_PI));
	} else {
		tmp = 1.0 / (0.005555555555555556 * (((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 <= -7.8e+42) {
		tmp = (180.0 / Math.PI) * Math.atan((((C + B) - A) / B));
	} else if (C <= 2.05e+159) {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(B, A)) / -B)) / Math.PI);
	} else {
		tmp = 1.0 / (0.005555555555555556 * (Math.PI / Math.atan((B * (-0.5 / C)))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -7.8e+42:
		tmp = (180.0 / math.pi) * math.atan((((C + B) - A) / B))
	elif C <= 2.05e+159:
		tmp = 180.0 * (math.atan(((A + math.hypot(B, A)) / -B)) / math.pi)
	else:
		tmp = 1.0 / (0.005555555555555556 * (math.pi / math.atan((B * (-0.5 / C)))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -7.8e+42)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(C + B) - A) / B)));
	elseif (C <= 2.05e+159)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(B, A)) / Float64(-B))) / pi));
	else
		tmp = Float64(1.0 / Float64(0.005555555555555556 * Float64(pi / atan(Float64(B * Float64(-0.5 / C))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -7.8e+42)
		tmp = (180.0 / pi) * atan((((C + B) - A) / B));
	elseif (C <= 2.05e+159)
		tmp = 180.0 * (atan(((A + hypot(B, A)) / -B)) / pi);
	else
		tmp = 1.0 / (0.005555555555555556 * (pi / atan((B * (-0.5 / C)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -7.8e+42], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(N[(C + B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.05e+159], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(0.005555555555555556 * N[(Pi / N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -7.79999999999999939e42

   1. Initial program 83.3%

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

      1. associate-*l/ 83.3%

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

      2. *-lft-identity 83.3%

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

      3. +-commutative 83.3%

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

      4. unpow2 83.3%

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

      5. unpow2 83.3%

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

      6. hypot-define 95.1%

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

   3. Simplified 95.1%

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

      1. clear-num 95.1%

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

      2. un-div-inv 95.1%

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

      3. hypot-undefine 83.3%

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

      4. unpow2 83.3%

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

      5. unpow2 83.3%

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

      6. +-commutative 83.3%

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

      7. unpow2 83.3%

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

      8. unpow2 83.3%

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

      9. hypot-define 95.1%

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

   6. Applied egg-rr 95.1%

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

      1. associate-/r/ 95.1%

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

      2. sub-neg 95.1%

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

      3. associate-+l- 91.7%

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

      4. sub-neg 91.7%

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

      5. remove-double-neg 91.7%

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

      6. hypot-undefine 83.3%

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

      7. unpow2 83.3%

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

      8. unpow2 83.3%

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

      9. +-commutative 83.3%

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

      10. unpow2 83.3%

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

      11. unpow2 83.3%

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

      12. hypot-undefine 91.7%

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

   8. Simplified 91.7%

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

   9. Taylor expanded in B around -inf 85.6%

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

   if -7.79999999999999939e42 < C < 2.05000000000000007e159

   1. Initial program 51.8%

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

   3. Taylor expanded in C around 0 48.4%

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

      1. mul-1-neg 48.4%

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

      2. distribute-neg-frac2 48.4%

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

      3. +-commutative 48.4%

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

      4. unpow2 48.4%

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

      5. unpow2 48.4%

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

      6. hypot-define 74.9%

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

   5. Simplified 74.9%

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

   if 2.05000000000000007e159 < C

   1. Initial program 8.7%

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

   3. Taylor expanded in C around inf 88.8%

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

   4. Taylor expanded in A around inf 88.8%

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

      1. associate-*r/ 88.9%

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

   6. Simplified 88.9%

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

      1. clear-num 88.9%

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

      2. inv-pow 88.9%

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

      3. *-un-lft-identity 88.9%

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

      4. times-frac 89.0%

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

      5. metadata-eval 89.0%

         \[\leadsto {\left(\color{blue}{0.005555555555555556} \cdot \frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}\right)}^{-1} \]

   8. Applied egg-rr 89.0%

      \[\leadsto \color{blue}{{\left(0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}\right)}^{-1}} \]
   9. Step-by-step derivation

      1. unpow-1 89.0%

         \[\leadsto \color{blue}{\frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}} \]

      2. *-commutative 89.0%

         \[\leadsto \frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \color{blue}{\left(\frac{B}{C} \cdot -0.5\right)}}} \]

      3. associate-*l/ 89.0%

         \[\leadsto \frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \color{blue}{\left(\frac{B \cdot -0.5}{C}\right)}}} \]

      4. associate-*r/ 89.0%

         \[\leadsto \frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \color{blue}{\left(B \cdot \frac{-0.5}{C}\right)}}} \]

   10. Simplified 89.0%

       \[\leadsto \color{blue}{\frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -7.8 \cdot 10^{+42}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)\\ \mathbf{elif}\;C \leq 2.05 \cdot 10^{+159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := A + \mathsf{hypot}\left(B, A\right)\\ \mathbf{if}\;C \leq -1.3 \cdot 10^{-77}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - t\_0}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.6 \cdot 10^{+159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{t\_0}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (+ A (hypot B A))))
   (if (<= C -1.3e-77)
     (* 180.0 (/ (atan (/ (- C t_0) B)) PI))
     (if (<= C 3.6e+159)
       (* 180.0 (/ (atan (/ t_0 (- B))) PI))
       (/ 1.0 (* 0.005555555555555556 (/ PI (atan (* B (/ -0.5 C))))))))))

C

double code(double A, double B, double C) {
	double t_0 = A + hypot(B, A);
	double tmp;
	if (C <= -1.3e-77) {
		tmp = 180.0 * (atan(((C - t_0) / B)) / ((double) M_PI));
	} else if (C <= 3.6e+159) {
		tmp = 180.0 * (atan((t_0 / -B)) / ((double) M_PI));
	} else {
		tmp = 1.0 / (0.005555555555555556 * (((double) M_PI) / atan((B * (-0.5 / C)))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = A + Math.hypot(B, A);
	double tmp;
	if (C <= -1.3e-77) {
		tmp = 180.0 * (Math.atan(((C - t_0) / B)) / Math.PI);
	} else if (C <= 3.6e+159) {
		tmp = 180.0 * (Math.atan((t_0 / -B)) / Math.PI);
	} else {
		tmp = 1.0 / (0.005555555555555556 * (Math.PI / Math.atan((B * (-0.5 / C)))));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = A + math.hypot(B, A)
	tmp = 0
	if C <= -1.3e-77:
		tmp = 180.0 * (math.atan(((C - t_0) / B)) / math.pi)
	elif C <= 3.6e+159:
		tmp = 180.0 * (math.atan((t_0 / -B)) / math.pi)
	else:
		tmp = 1.0 / (0.005555555555555556 * (math.pi / math.atan((B * (-0.5 / C)))))
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(A + hypot(B, A))
	tmp = 0.0
	if (C <= -1.3e-77)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - t_0) / B)) / pi));
	elseif (C <= 3.6e+159)
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 / Float64(-B))) / pi));
	else
		tmp = Float64(1.0 / Float64(0.005555555555555556 * Float64(pi / atan(Float64(B * Float64(-0.5 / C))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = A + hypot(B, A);
	tmp = 0.0;
	if (C <= -1.3e-77)
		tmp = 180.0 * (atan(((C - t_0) / B)) / pi);
	elseif (C <= 3.6e+159)
		tmp = 180.0 * (atan((t_0 / -B)) / pi);
	else
		tmp = 1.0 / (0.005555555555555556 * (pi / atan((B * (-0.5 / C)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(A + N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.3e-77], N[(180.0 * N[(N[ArcTan[N[(N[(C - t$95$0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.6e+159], N[(180.0 * N[(N[ArcTan[N[(t$95$0 / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(0.005555555555555556 * N[(Pi / N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.3000000000000001e-77

   1. Initial program 74.3%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in C around 0 73.3%

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

      1. +-commutative 73.3%

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

      2. unpow2 73.3%

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

      3. unpow2 73.3%

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

      4. hypot-define 84.9%

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

   7. Simplified 84.9%

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

   if -1.3000000000000001e-77 < C < 3.60000000000000037e159

   1. Initial program 51.4%

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

   3. Taylor expanded in C around 0 49.2%

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

      1. mul-1-neg 49.2%

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

      2. distribute-neg-frac2 49.2%

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

      3. +-commutative 49.2%

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

      4. unpow2 49.2%

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

      5. unpow2 49.2%

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

      6. hypot-define 76.9%

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

   5. Simplified 76.9%

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

   if 3.60000000000000037e159 < C

   1. Initial program 8.7%

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

   3. Taylor expanded in C around inf 88.8%

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

   4. Taylor expanded in A around inf 88.8%

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

      1. associate-*r/ 88.9%

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

   6. Simplified 88.9%

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

      1. clear-num 88.9%

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

      2. inv-pow 88.9%

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

      3. *-un-lft-identity 88.9%

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

      4. times-frac 89.0%

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

      5. metadata-eval 89.0%

         \[\leadsto {\left(\color{blue}{0.005555555555555556} \cdot \frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}\right)}^{-1} \]

   8. Applied egg-rr 89.0%

      \[\leadsto \color{blue}{{\left(0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}\right)}^{-1}} \]
   9. Step-by-step derivation

      1. unpow-1 89.0%

         \[\leadsto \color{blue}{\frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}} \]

      2. *-commutative 89.0%

         \[\leadsto \frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \color{blue}{\left(\frac{B}{C} \cdot -0.5\right)}}} \]

      3. associate-*l/ 89.0%

         \[\leadsto \frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \color{blue}{\left(\frac{B \cdot -0.5}{C}\right)}}} \]

      4. associate-*r/ 89.0%

         \[\leadsto \frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \color{blue}{\left(B \cdot \frac{-0.5}{C}\right)}}} \]

   10. Simplified 89.0%

       \[\leadsto \color{blue}{\frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.3 \cdot 10^{-77}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A\right)\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.6 \cdot 10^{+159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(B, A\right)}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 5.1 \cdot 10^{+159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 5.1e+159)
   (* 180.0 (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) PI))
   (/ 1.0 (* 0.005555555555555556 (/ PI (atan (* B (/ -0.5 C))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 5.1e+159) {
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / ((double) M_PI));
	} else {
		tmp = 1.0 / (0.005555555555555556 * (((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 <= 5.1e+159) {
		tmp = 180.0 * (Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)) / Math.PI);
	} else {
		tmp = 1.0 / (0.005555555555555556 * (Math.PI / Math.atan((B * (-0.5 / C)))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 5.1e+159:
		tmp = 180.0 * (math.atan((((C - A) - math.hypot(B, (A - C))) / B)) / math.pi)
	else:
		tmp = 1.0 / (0.005555555555555556 * (math.pi / math.atan((B * (-0.5 / C)))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 5.1e+159)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / pi));
	else
		tmp = Float64(1.0 / Float64(0.005555555555555556 * Float64(pi / atan(Float64(B * Float64(-0.5 / C))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 5.1e+159)
		tmp = 180.0 * (atan((((C - A) - hypot(B, (A - C))) / B)) / pi);
	else
		tmp = 1.0 / (0.005555555555555556 * (pi / atan((B * (-0.5 / C)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 5.1e+159], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(0.005555555555555556 * N[(Pi / N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 5.09999999999999967e159

   1. Initial program 59.8%

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

      1. associate-*l/ 59.8%

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

      2. *-lft-identity 59.8%

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

      3. +-commutative 59.8%

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

      4. unpow2 59.8%

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

      5. unpow2 59.8%

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

      6. hypot-define 82.4%

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

   3. Simplified 82.4%

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

   if 5.09999999999999967e159 < C

   1. Initial program 8.7%

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

   3. Taylor expanded in C around inf 88.8%

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

   4. Taylor expanded in A around inf 88.8%

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

      1. associate-*r/ 88.9%

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

   6. Simplified 88.9%

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

      1. clear-num 88.9%

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

      2. inv-pow 88.9%

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

      3. *-un-lft-identity 88.9%

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

      4. times-frac 89.0%

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

      5. metadata-eval 89.0%

         \[\leadsto {\left(\color{blue}{0.005555555555555556} \cdot \frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}\right)}^{-1} \]

   8. Applied egg-rr 89.0%

      \[\leadsto \color{blue}{{\left(0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}\right)}^{-1}} \]
   9. Step-by-step derivation

      1. unpow-1 89.0%

         \[\leadsto \color{blue}{\frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}}} \]

      2. *-commutative 89.0%

         \[\leadsto \frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \color{blue}{\left(\frac{B}{C} \cdot -0.5\right)}}} \]

      3. associate-*l/ 89.0%

         \[\leadsto \frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \color{blue}{\left(\frac{B \cdot -0.5}{C}\right)}}} \]

      4. associate-*r/ 89.0%

         \[\leadsto \frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \color{blue}{\left(B \cdot \frac{-0.5}{C}\right)}}} \]

   10. Simplified 89.0%

       \[\leadsto \color{blue}{\frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 5.1 \cdot 10^{+159}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{0.005555555555555556 \cdot \frac{\pi}{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -3.1 \cdot 10^{-26}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.32 \cdot 10^{+76} \lor \neg \left(C \leq 1.15 \cdot 10^{+103}\right) \land C \leq 2.3 \cdot 10^{+159}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -3.1e-26)
   (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
   (if (or (<= C 1.32e+76) (and (not (<= C 1.15e+103)) (<= C 2.3e+159)))
     (* (/ 180.0 PI) (atan (- 1.0 (/ A B))))
     (* 180.0 (/ (atan (* B (/ -0.5 C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.1e-26) {
		tmp = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	} else if ((C <= 1.32e+76) || (!(C <= 1.15e+103) && (C <= 2.3e+159))) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 - (A / B)));
	} else {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -3.1e-26) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else if ((C <= 1.32e+76) || (!(C <= 1.15e+103) && (C <= 2.3e+159))) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 - (A / B)));
	} else {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -3.1e-26:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	elif (C <= 1.32e+76) or (not (C <= 1.15e+103) and (C <= 2.3e+159)):
		tmp = (180.0 / math.pi) * math.atan((1.0 - (A / B)))
	else:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -3.1e-26)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	elseif ((C <= 1.32e+76) || (!(C <= 1.15e+103) && (C <= 2.3e+159)))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - Float64(A / B))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -3.1e-26)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	elseif ((C <= 1.32e+76) || (~((C <= 1.15e+103)) && (C <= 2.3e+159)))
		tmp = (180.0 / pi) * atan((1.0 - (A / B)));
	else
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -3.1e-26], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[C, 1.32e+76], And[N[Not[LessEqual[C, 1.15e+103]], $MachinePrecision], LessEqual[C, 2.3e+159]]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -3.09999999999999983e-26

   1. Initial program 77.8%

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

   3. Taylor expanded in C around -inf 73.6%

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

      1. associate-*r/ 73.6%

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

   5. Simplified 73.6%

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

   if -3.09999999999999983e-26 < C < 1.31999999999999999e76 or 1.15000000000000004e103 < C < 2.29999999999999995e159

   1. Initial program 53.7%

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

      1. associate-*l/ 53.7%

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

      2. *-lft-identity 53.7%

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

      3. +-commutative 53.7%

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

      4. unpow2 53.7%

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

      5. unpow2 53.7%

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

      6. hypot-define 80.6%

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

   3. Simplified 80.6%

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

      1. clear-num 80.6%

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

      2. un-div-inv 80.6%

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

      3. hypot-undefine 53.7%

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

      4. unpow2 53.7%

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

      5. unpow2 53.7%

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

      6. +-commutative 53.7%

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

      7. unpow2 53.7%

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

      8. unpow2 53.7%

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

      9. hypot-define 80.6%

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

   6. Applied egg-rr 80.6%

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

      1. associate-/r/ 80.6%

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

      2. sub-neg 80.6%

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

      3. associate-+l- 74.3%

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

      4. sub-neg 74.3%

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

      5. remove-double-neg 74.3%

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

      6. hypot-undefine 52.5%

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

      7. unpow2 52.5%

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

      8. unpow2 52.5%

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

      9. +-commutative 52.5%

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

      10. unpow2 52.5%

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

      11. unpow2 52.5%

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

      12. hypot-undefine 74.3%

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

   8. Simplified 74.3%

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

   9. Taylor expanded in C around 0 50.4%

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

       1. mul-1-neg 50.4%

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

       2. distribute-neg-in 50.4%

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

       3. unsub-neg 50.4%

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

       4. unpow2 50.4%

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

       5. unpow2 50.4%

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

       6. hypot-define 77.5%

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

   11. Simplified 77.5%

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

   12. Taylor expanded in B around -inf 55.0%

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

       1. mul-1-neg 55.0%

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

       2. unsub-neg 55.0%

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

   14. Simplified 55.0%

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

   if 1.31999999999999999e76 < C < 1.15000000000000004e103 or 2.29999999999999995e159 < C

   1. Initial program 10.9%

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

   3. Taylor expanded in C around inf 86.1%

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

   4. Taylor expanded in A around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-/l* 86.1%

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

   6. Simplified 86.1%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -3.1 \cdot 10^{-26}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.32 \cdot 10^{+76} \lor \neg \left(C \leq 1.15 \cdot 10^{+103}\right) \land C \leq 2.3 \cdot 10^{+159}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -7 \cdot 10^{-76}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq 2.75 \cdot 10^{+76} \lor \neg \left(C \leq 6.6 \cdot 10^{+102}\right) \land C \leq 1.8 \cdot 10^{+159}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -7e-76)
   (* (/ 180.0 PI) (atan (/ (- C B) B)))
   (if (or (<= C 2.75e+76) (and (not (<= C 6.6e+102)) (<= C 1.8e+159)))
     (* (/ 180.0 PI) (atan (- 1.0 (/ A B))))
     (* 180.0 (/ (atan (* B (/ -0.5 C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -7e-76) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	} else if ((C <= 2.75e+76) || (!(C <= 6.6e+102) && (C <= 1.8e+159))) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 - (A / B)));
	} else {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -7e-76) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	} else if ((C <= 2.75e+76) || (!(C <= 6.6e+102) && (C <= 1.8e+159))) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 - (A / B)));
	} else {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -7e-76:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	elif (C <= 2.75e+76) or (not (C <= 6.6e+102) and (C <= 1.8e+159)):
		tmp = (180.0 / math.pi) * math.atan((1.0 - (A / B)))
	else:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -7e-76)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	elseif ((C <= 2.75e+76) || (!(C <= 6.6e+102) && (C <= 1.8e+159)))
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - Float64(A / B))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -7e-76)
		tmp = (180.0 / pi) * atan(((C - B) / B));
	elseif ((C <= 2.75e+76) || (~((C <= 6.6e+102)) && (C <= 1.8e+159)))
		tmp = (180.0 / pi) * atan((1.0 - (A / B)));
	else
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -7e-76], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[C, 2.75e+76], And[N[Not[LessEqual[C, 6.6e+102]], $MachinePrecision], LessEqual[C, 1.8e+159]]], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -6.99999999999999995e-76

   1. Initial program 74.4%

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

      1. associate-*l/ 74.4%

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

      2. *-lft-identity 74.4%

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

      3. +-commutative 74.4%

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

      4. unpow2 74.4%

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

      5. unpow2 74.4%

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

      6. hypot-define 88.0%

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

   3. Simplified 88.0%

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

      1. clear-num 88.0%

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

      2. un-div-inv 88.0%

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

      3. hypot-undefine 74.4%

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

      4. unpow2 74.4%

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

      5. unpow2 74.4%

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

      6. +-commutative 74.4%

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

      7. unpow2 74.4%

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

      8. unpow2 74.4%

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

      9. hypot-define 88.0%

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

   6. Applied egg-rr 88.0%

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

      1. associate-/r/ 88.0%

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

      2. sub-neg 88.0%

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

      3. associate-+l- 84.6%

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

      4. sub-neg 84.6%

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

      5. remove-double-neg 84.6%

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

      6. hypot-undefine 73.6%

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

      7. unpow2 73.6%

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

      8. unpow2 73.6%

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

      9. +-commutative 73.6%

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

      10. unpow2 73.6%

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

      11. unpow2 73.6%

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

      12. hypot-undefine 84.6%

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

   8. Simplified 84.6%

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

   9. Taylor expanded in C around 0 73.3%

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

       1. +-commutative 73.3%

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

       2. unpow2 73.3%

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

       3. unpow2 73.3%

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

       4. hypot-define 84.3%

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

   11. Simplified 84.3%

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

   12. Taylor expanded in A around 0 74.8%

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

   if -6.99999999999999995e-76 < C < 2.75e76 or 6.59999999999999997e102 < C < 1.80000000000000018e159

   1. Initial program 53.4%

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

      1. associate-*l/ 53.4%

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

      2. *-lft-identity 53.4%

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

      3. +-commutative 53.4%

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

      4. unpow2 53.4%

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

      5. unpow2 53.4%

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

      6. hypot-define 81.0%

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

   3. Simplified 81.0%

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

      1. clear-num 81.0%

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

      2. un-div-inv 81.0%

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

      3. hypot-undefine 53.4%

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

      4. unpow2 53.4%

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

      5. unpow2 53.4%

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

      6. +-commutative 53.4%

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

      7. unpow2 53.4%

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

      8. unpow2 53.4%

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

      9. hypot-define 81.0%

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

   6. Applied egg-rr 81.0%

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

      1. associate-/r/ 81.0%

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

      2. sub-neg 81.0%

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

      3. associate-+l- 74.7%

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

      4. sub-neg 74.7%

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

      5. remove-double-neg 74.7%

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

      6. hypot-undefine 52.6%

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

      7. unpow2 52.6%

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

      8. unpow2 52.6%

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

      9. +-commutative 52.6%

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

      10. unpow2 52.6%

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

      11. unpow2 52.6%

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

      12. hypot-undefine 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in C around 0 50.5%

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

       1. mul-1-neg 50.5%

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

       2. distribute-neg-in 50.5%

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

       3. unsub-neg 50.5%

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

       4. unpow2 50.5%

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

       5. unpow2 50.5%

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

       6. hypot-define 78.4%

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

   11. Simplified 78.4%

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

   12. Taylor expanded in B around -inf 57.1%

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

       1. mul-1-neg 57.1%

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

       2. unsub-neg 57.1%

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

   14. Simplified 57.1%

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

   if 2.75e76 < C < 6.59999999999999997e102 or 1.80000000000000018e159 < C

   1. Initial program 10.9%

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

   3. Taylor expanded in C around inf 86.1%

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

   4. Taylor expanded in A around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-/l* 86.1%

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

   6. Simplified 86.1%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -7 \cdot 10^{-76}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq 2.75 \cdot 10^{+76} \lor \neg \left(C \leq 6.6 \cdot 10^{+102}\right) \land C \leq 1.8 \cdot 10^{+159}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{if}\;C \leq -1.05 \cdot 10^{-75}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq 3.25 \cdot 10^{+78}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;C \leq 3.65 \cdot 10^{+102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.8 \cdot 10^{+159}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ 180.0 PI) (atan (- 1.0 (/ A B))))))
   (if (<= C -1.05e-75)
     (* (/ 180.0 PI) (atan (/ (- C B) B)))
     (if (<= C 3.25e+78)
       t_0
       (if (<= C 3.65e+102)
         (* 180.0 (/ (atan (* B (/ -0.5 C))) PI))
         (if (<= C 1.8e+159) t_0 (/ (* 180.0 (atan (* -0.5 (/ B C)))) PI)))))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 / ((double) M_PI)) * atan((1.0 - (A / B)));
	double tmp;
	if (C <= -1.05e-75) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	} else if (C <= 3.25e+78) {
		tmp = t_0;
	} else if (C <= 3.65e+102) {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	} else if (C <= 1.8e+159) {
		tmp = t_0;
	} else {
		tmp = (180.0 * atan((-0.5 * (B / C)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 / Math.PI) * Math.atan((1.0 - (A / B)));
	double tmp;
	if (C <= -1.05e-75) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	} else if (C <= 3.25e+78) {
		tmp = t_0;
	} else if (C <= 3.65e+102) {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	} else if (C <= 1.8e+159) {
		tmp = t_0;
	} else {
		tmp = (180.0 * Math.atan((-0.5 * (B / C)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 / math.pi) * math.atan((1.0 - (A / B)))
	tmp = 0
	if C <= -1.05e-75:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	elif C <= 3.25e+78:
		tmp = t_0
	elif C <= 3.65e+102:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	elif C <= 1.8e+159:
		tmp = t_0
	else:
		tmp = (180.0 * math.atan((-0.5 * (B / C)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - Float64(A / B))))
	tmp = 0.0
	if (C <= -1.05e-75)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	elseif (C <= 3.25e+78)
		tmp = t_0;
	elseif (C <= 3.65e+102)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	elseif (C <= 1.8e+159)
		tmp = t_0;
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / C)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 / pi) * atan((1.0 - (A / B)));
	tmp = 0.0;
	if (C <= -1.05e-75)
		tmp = (180.0 / pi) * atan(((C - B) / B));
	elseif (C <= 3.25e+78)
		tmp = t_0;
	elseif (C <= 3.65e+102)
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	elseif (C <= 1.8e+159)
		tmp = t_0;
	else
		tmp = (180.0 * atan((-0.5 * (B / C)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[C, -1.05e-75], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.25e+78], t$95$0, If[LessEqual[C, 3.65e+102], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.8e+159], t$95$0, N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if C < -1.0500000000000001e-75

   1. Initial program 74.4%

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

      1. associate-*l/ 74.4%

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

      2. *-lft-identity 74.4%

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

      3. +-commutative 74.4%

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

      4. unpow2 74.4%

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

      5. unpow2 74.4%

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

      6. hypot-define 88.0%

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

   3. Simplified 88.0%

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

      1. clear-num 88.0%

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

      2. un-div-inv 88.0%

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

      3. hypot-undefine 74.4%

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

      4. unpow2 74.4%

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

      5. unpow2 74.4%

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

      6. +-commutative 74.4%

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

      7. unpow2 74.4%

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

      8. unpow2 74.4%

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

      9. hypot-define 88.0%

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

   6. Applied egg-rr 88.0%

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

      1. associate-/r/ 88.0%

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

      2. sub-neg 88.0%

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

      3. associate-+l- 84.6%

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

      4. sub-neg 84.6%

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

      5. remove-double-neg 84.6%

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

      6. hypot-undefine 73.6%

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

      7. unpow2 73.6%

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

      8. unpow2 73.6%

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

      9. +-commutative 73.6%

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

      10. unpow2 73.6%

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

      11. unpow2 73.6%

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

      12. hypot-undefine 84.6%

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

   8. Simplified 84.6%

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

   9. Taylor expanded in C around 0 73.3%

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

       1. +-commutative 73.3%

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

       2. unpow2 73.3%

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

       3. unpow2 73.3%

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

       4. hypot-define 84.3%

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

   11. Simplified 84.3%

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

   12. Taylor expanded in A around 0 74.8%

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

   if -1.0500000000000001e-75 < C < 3.25000000000000018e78 or 3.64999999999999995e102 < C < 1.80000000000000018e159

   1. Initial program 53.4%

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

      1. associate-*l/ 53.4%

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

      2. *-lft-identity 53.4%

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

      3. +-commutative 53.4%

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

      4. unpow2 53.4%

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

      5. unpow2 53.4%

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

      6. hypot-define 81.0%

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

   3. Simplified 81.0%

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

      1. clear-num 81.0%

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

      2. un-div-inv 81.0%

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

      3. hypot-undefine 53.4%

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

      4. unpow2 53.4%

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

      5. unpow2 53.4%

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

      6. +-commutative 53.4%

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

      7. unpow2 53.4%

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

      8. unpow2 53.4%

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

      9. hypot-define 81.0%

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

   6. Applied egg-rr 81.0%

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

      1. associate-/r/ 81.0%

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

      2. sub-neg 81.0%

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

      3. associate-+l- 74.7%

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

      4. sub-neg 74.7%

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

      5. remove-double-neg 74.7%

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

      6. hypot-undefine 52.6%

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

      7. unpow2 52.6%

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

      8. unpow2 52.6%

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

      9. +-commutative 52.6%

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

      10. unpow2 52.6%

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

      11. unpow2 52.6%

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

      12. hypot-undefine 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in C around 0 50.5%

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

       1. mul-1-neg 50.5%

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

       2. distribute-neg-in 50.5%

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

       3. unsub-neg 50.5%

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

       4. unpow2 50.5%

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

       5. unpow2 50.5%

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

       6. hypot-define 78.4%

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

   11. Simplified 78.4%

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

   12. Taylor expanded in B around -inf 57.1%

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

       1. mul-1-neg 57.1%

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

       2. unsub-neg 57.1%

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

   14. Simplified 57.1%

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

   if 3.25000000000000018e78 < C < 3.64999999999999995e102

   1. Initial program 20.0%

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

   3. Taylor expanded in C around inf 75.2%

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

   4. Taylor expanded in A around inf 75.2%

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

      1. associate-*r/ 75.2%

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

      2. *-commutative 75.2%

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

      3. associate-/l* 75.2%

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

   6. Simplified 75.2%

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

   if 1.80000000000000018e159 < C

   1. Initial program 8.7%

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

   3. Taylor expanded in C around inf 88.8%

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

   4. Taylor expanded in A around inf 88.8%

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

      1. associate-*r/ 88.9%

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

   6. Simplified 88.9%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -1.05 \cdot 10^{-75}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq 3.25 \cdot 10^{+78}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{elif}\;C \leq 3.65 \cdot 10^{+102}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.8 \cdot 10^{+159}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -4.4 \cdot 10^{+25}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;C \leq -5.5 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -4.4e+25)
   (* (/ 180.0 PI) (atan (/ C B)))
   (if (<= C -5.5e-203)
     (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
     (if (<= C 4e-85)
       (* 180.0 (/ (atan 1.0) PI))
       (* 180.0 (/ (atan (* B (/ -0.5 C))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.4e+25) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / B));
	} else if (C <= -5.5e-203) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (C <= 4e-85) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.4e+25) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else if (C <= -5.5e-203) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (C <= 4e-85) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -4.4e+25:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	elif C <= -5.5e-203:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif C <= 4e-85:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -4.4e+25)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / B)));
	elseif (C <= -5.5e-203)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (C <= 4e-85)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -4.4e+25)
		tmp = (180.0 / pi) * atan((C / B));
	elseif (C <= -5.5e-203)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (C <= 4e-85)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -4.4e+25], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -5.5e-203], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 4e-85], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -4.4000000000000001e25

   1. Initial program 83.6%

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

      1. associate-*l/ 83.6%

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

      2. *-lft-identity 83.6%

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

      3. +-commutative 83.6%

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

      4. unpow2 83.6%

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

      5. unpow2 83.6%

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

      6. hypot-define 95.2%

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

   3. Simplified 95.2%

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

      1. clear-num 95.2%

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

      2. un-div-inv 95.2%

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

      3. hypot-undefine 83.6%

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

      4. unpow2 83.6%

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

      5. unpow2 83.6%

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

      6. +-commutative 83.6%

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

      7. unpow2 83.6%

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

      8. unpow2 83.6%

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

      9. hypot-define 95.2%

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

   6. Applied egg-rr 95.2%

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

      1. associate-/r/ 95.2%

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

      2. sub-neg 95.2%

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

      3. associate-+l- 91.8%

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

      4. sub-neg 91.8%

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

      5. remove-double-neg 91.8%

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

      6. hypot-undefine 83.6%

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

      7. unpow2 83.6%

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

      8. unpow2 83.6%

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

      9. +-commutative 83.6%

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

      10. unpow2 83.6%

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

      11. unpow2 83.6%

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

      12. hypot-undefine 91.8%

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

   8. Simplified 91.8%

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

   9. Taylor expanded in C around 0 83.2%

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

       1. +-commutative 83.2%

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

       2. unpow2 83.2%

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

       3. unpow2 83.2%

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

       4. hypot-define 91.4%

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

   11. Simplified 91.4%

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

   12. Taylor expanded in C around inf 80.8%

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

   if -4.4000000000000001e25 < C < -5.5000000000000002e-203

   1. Initial program 59.7%

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

   3. Taylor expanded in A around -inf 38.9%

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

      1. associate-*r/ 38.9%

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

   5. Simplified 38.9%

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

   if -5.5000000000000002e-203 < C < 3.9999999999999999e-85

   1. Initial program 48.1%

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

   3. Taylor expanded in B around -inf 42.0%

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

   if 3.9999999999999999e-85 < C

   1. Initial program 32.6%

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

   3. Taylor expanded in C around inf 60.2%

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

   4. Taylor expanded in A around inf 60.2%

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

      1. associate-*r/ 60.2%

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

      2. *-commutative 60.2%

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

      3. associate-/l* 60.2%

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

   6. Simplified 60.2%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -4.4 \cdot 10^{+25}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;C \leq -5.5 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -5.5 \cdot 10^{+24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -7 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.8 \cdot 10^{-83}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -5.5e+24)
   (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
   (if (<= C -7e-203)
     (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
     (if (<= C 3.8e-83)
       (* 180.0 (/ (atan 1.0) PI))
       (* 180.0 (/ (atan (* B (/ -0.5 C))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -5.5e+24) {
		tmp = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	} else if (C <= -7e-203) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (C <= 3.8e-83) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -5.5e+24) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else if (C <= -7e-203) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (C <= 3.8e-83) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -5.5e+24:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	elif C <= -7e-203:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif C <= 3.8e-83:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -5.5e+24)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	elseif (C <= -7e-203)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (C <= 3.8e-83)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -5.5e+24)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	elseif (C <= -7e-203)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (C <= 3.8e-83)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -5.5e+24], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -7e-203], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.8e-83], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -5.5000000000000002e24

   1. Initial program 83.6%

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

   3. Taylor expanded in C around -inf 80.8%

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

      1. associate-*r/ 80.8%

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

   5. Simplified 80.8%

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

   if -5.5000000000000002e24 < C < -7.0000000000000003e-203

   1. Initial program 59.7%

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

   3. Taylor expanded in A around -inf 38.9%

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

      1. associate-*r/ 38.9%

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

   5. Simplified 38.9%

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

   if -7.0000000000000003e-203 < C < 3.79999999999999977e-83

   1. Initial program 48.1%

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

   3. Taylor expanded in B around -inf 42.0%

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

   if 3.79999999999999977e-83 < C

   1. Initial program 32.6%

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

   3. Taylor expanded in C around inf 60.2%

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

   4. Taylor expanded in A around inf 60.2%

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

      1. associate-*r/ 60.2%

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

      2. *-commutative 60.2%

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

      3. associate-/l* 60.2%

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

   6. Simplified 60.2%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -5.5 \cdot 10^{+24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -7 \cdot 10^{-203}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;C \leq 3.8 \cdot 10^{-83}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.0% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -4.4 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -6.4 \cdot 10^{-203}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;C \leq 2.5 \cdot 10^{-84}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -4.4e+25)
   (* 180.0 (/ (atan (/ (* C 2.0) B)) PI))
   (if (<= C -6.4e-203)
     (* (/ 180.0 PI) (atan (* 0.5 (/ B A))))
     (if (<= C 2.5e-84)
       (* 180.0 (/ (atan 1.0) PI))
       (* 180.0 (/ (atan (* B (/ -0.5 C))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.4e+25) {
		tmp = 180.0 * (atan(((C * 2.0) / B)) / ((double) M_PI));
	} else if (C <= -6.4e-203) {
		tmp = (180.0 / ((double) M_PI)) * atan((0.5 * (B / A)));
	} else if (C <= 2.5e-84) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.4e+25) {
		tmp = 180.0 * (Math.atan(((C * 2.0) / B)) / Math.PI);
	} else if (C <= -6.4e-203) {
		tmp = (180.0 / Math.PI) * Math.atan((0.5 * (B / A)));
	} else if (C <= 2.5e-84) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -4.4e+25:
		tmp = 180.0 * (math.atan(((C * 2.0) / B)) / math.pi)
	elif C <= -6.4e-203:
		tmp = (180.0 / math.pi) * math.atan((0.5 * (B / A)))
	elif C <= 2.5e-84:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -4.4e+25)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C * 2.0) / B)) / pi));
	elseif (C <= -6.4e-203)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(0.5 * Float64(B / A))));
	elseif (C <= 2.5e-84)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -4.4e+25)
		tmp = 180.0 * (atan(((C * 2.0) / B)) / pi);
	elseif (C <= -6.4e-203)
		tmp = (180.0 / pi) * atan((0.5 * (B / A)));
	elseif (C <= 2.5e-84)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -4.4e+25], N[(180.0 * N[(N[ArcTan[N[(N[(C * 2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -6.4e-203], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.5e-84], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -4.4000000000000001e25

   1. Initial program 83.6%

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

   3. Taylor expanded in C around -inf 80.8%

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

      1. associate-*r/ 80.8%

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

   5. Simplified 80.8%

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

   if -4.4000000000000001e25 < C < -6.40000000000000001e-203

   1. Initial program 59.7%

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

      1. associate-*l/ 59.7%

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

      2. *-lft-identity 59.7%

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

      3. +-commutative 59.7%

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

      4. unpow2 59.7%

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

      5. unpow2 59.7%

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

      6. hypot-define 75.6%

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

   3. Simplified 75.6%

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

      1. clear-num 75.6%

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

      2. un-div-inv 75.6%

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

      3. hypot-undefine 59.7%

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

      4. unpow2 59.7%

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

      5. unpow2 59.7%

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

      6. +-commutative 59.7%

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

      7. unpow2 59.7%

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

      8. unpow2 59.7%

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

      9. hypot-define 75.6%

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

   6. Applied egg-rr 75.6%

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

      1. associate-/r/ 75.6%

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

      2. sub-neg 75.6%

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

      3. associate-+l- 68.3%

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

      4. sub-neg 68.3%

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

      5. remove-double-neg 68.3%

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

      6. hypot-undefine 56.4%

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

      7. unpow2 56.4%

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

      8. unpow2 56.4%

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

      9. +-commutative 56.4%

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

      10. unpow2 56.4%

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

      11. unpow2 56.4%

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

      12. hypot-undefine 68.3%

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

   8. Simplified 68.3%

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

   9. Taylor expanded in C around 0 52.0%

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

       1. mul-1-neg 52.0%

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

       2. distribute-neg-in 52.0%

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

       3. unsub-neg 52.0%

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

       4. unpow2 52.0%

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

       5. unpow2 52.0%

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

       6. hypot-define 68.2%

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

   11. Simplified 68.2%

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

   12. Taylor expanded in A around -inf 39.0%

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

   if -6.40000000000000001e-203 < C < 2.5000000000000001e-84

   1. Initial program 48.1%

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

   3. Taylor expanded in B around -inf 42.0%

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

   if 2.5000000000000001e-84 < C

   1. Initial program 32.6%

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

   3. Taylor expanded in C around inf 60.2%

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

   4. Taylor expanded in A around inf 60.2%

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

      1. associate-*r/ 60.2%

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

      2. *-commutative 60.2%

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

      3. associate-/l* 60.2%

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

   6. Simplified 60.2%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -4.4 \cdot 10^{+25}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C \cdot 2}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -6.4 \cdot 10^{-203}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{elif}\;C \leq 2.5 \cdot 10^{-84}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -4.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 6.6 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -4.2e-26)
   (* (/ 180.0 PI) (atan (/ C B)))
   (if (<= C 6.6e-85)
     (* 180.0 (/ (atan 1.0) PI))
     (* 180.0 (/ (atan (* B (/ -0.5 C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.2e-26) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / B));
	} else if (C <= 6.6e-85) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.2e-26) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else if (C <= 6.6e-85) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -4.2e-26:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	elif C <= 6.6e-85:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -4.2e-26)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / B)));
	elseif (C <= 6.6e-85)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -4.2e-26)
		tmp = (180.0 / pi) * atan((C / B));
	elseif (C <= 6.6e-85)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -4.2e-26], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.6e-85], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -4.20000000000000016e-26

   1. Initial program 77.8%

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

      1. associate-*l/ 77.8%

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

      2. *-lft-identity 77.8%

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

      3. +-commutative 77.8%

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

      4. unpow2 77.8%

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

      5. unpow2 77.8%

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

      6. hypot-define 90.3%

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

   3. Simplified 90.3%

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

      1. clear-num 90.3%

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

      2. un-div-inv 90.3%

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

      3. hypot-undefine 77.8%

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

      4. unpow2 77.8%

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

      5. unpow2 77.8%

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

      6. +-commutative 77.8%

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

      7. unpow2 77.8%

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

      8. unpow2 77.8%

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

      9. hypot-define 90.3%

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

   6. Applied egg-rr 90.3%

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

      1. associate-/r/ 90.3%

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

      2. sub-neg 90.3%

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

      3. associate-+l- 87.3%

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

      4. sub-neg 87.3%

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

      5. remove-double-neg 87.3%

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

      6. hypot-undefine 77.8%

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

      7. unpow2 77.8%

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

      8. unpow2 77.8%

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

      9. +-commutative 77.8%

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

      10. unpow2 77.8%

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

      11. unpow2 77.8%

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

      12. hypot-undefine 87.3%

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

   8. Simplified 87.3%

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

   9. Taylor expanded in C around 0 77.4%

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

       1. +-commutative 77.4%

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

       2. unpow2 77.4%

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

       3. unpow2 77.4%

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

       4. hypot-define 87.0%

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

   11. Simplified 87.0%

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

   12. Taylor expanded in C around inf 73.6%

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

   if -4.20000000000000016e-26 < C < 6.59999999999999945e-85

   1. Initial program 53.5%

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

   3. Taylor expanded in B around -inf 38.1%

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

   if 6.59999999999999945e-85 < C

   1. Initial program 32.6%

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

   3. Taylor expanded in C around inf 60.2%

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

   4. Taylor expanded in A around inf 60.2%

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

      1. associate-*r/ 60.2%

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

      2. *-commutative 60.2%

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

      3. associate-/l* 60.2%

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

   6. Simplified 60.2%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -4.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{elif}\;C \leq 6.6 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 45.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.32 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-118}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.32e-145)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 9.5e-118)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.32e-145) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 9.5e-118) {
		tmp = 180.0 * (atan((0.0 / 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 <= -1.32e-145) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 9.5e-118) {
		tmp = 180.0 * (Math.atan((0.0 / 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 <= -1.32e-145:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 9.5e-118:
		tmp = 180.0 * (math.atan((0.0 / 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 <= -1.32e-145)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 9.5e-118)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / 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 <= -1.32e-145)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 9.5e-118)
		tmp = 180.0 * (atan((0.0 / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.32e-145], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.5e-118], N[(180.0 * N[(N[ArcTan[N[(0.0 / 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 < -1.32e-145

   1. Initial program 51.2%

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

   3. Taylor expanded in B around -inf 53.5%

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

   if -1.32e-145 < B < 9.49999999999999931e-118

   1. Initial program 55.2%

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

   3. Taylor expanded in C around inf 31.7%

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

      1. associate-*r/ 31.7%

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

      2. distribute-rgt1-in 31.7%

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

      3. metadata-eval 31.7%

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

      4. mul0-lft 31.7%

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

      5. metadata-eval 31.7%

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

   5. Simplified 31.7%

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

   if 9.49999999999999931e-118 < B

   1. Initial program 57.8%

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

   3. Taylor expanded in B around inf 49.1%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.32 \cdot 10^{-145}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-118}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 47.5% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.1 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{+22}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.1e-17)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.4e+22)
     (* (/ 180.0 PI) (atan (/ C B)))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.1e-17) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.4e+22) {
		tmp = (180.0 / ((double) M_PI)) * atan((C / B));
	} 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 <= -2.1e-17) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.4e+22) {
		tmp = (180.0 / Math.PI) * Math.atan((C / B));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.1e-17:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.4e+22:
		tmp = (180.0 / math.pi) * math.atan((C / B))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.1e-17)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.4e+22)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(C / B)));
	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 <= -2.1e-17)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.4e+22)
		tmp = (180.0 / pi) * atan((C / B));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.1e-17], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.4e+22], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.09999999999999992e-17

   1. Initial program 46.8%

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

   3. Taylor expanded in B around -inf 67.1%

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

   if -2.09999999999999992e-17 < B < 1.4e22

   1. Initial program 58.0%

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

      1. associate-*l/ 58.0%

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

      2. *-lft-identity 58.0%

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

      3. +-commutative 58.0%

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

      4. unpow2 58.0%

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

      5. unpow2 58.0%

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

      6. hypot-define 75.5%

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

   3. Simplified 75.5%

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

      1. clear-num 75.5%

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

      2. un-div-inv 75.5%

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

      3. hypot-undefine 58.0%

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

      4. unpow2 58.0%

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

      5. unpow2 58.0%

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

      6. +-commutative 58.0%

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

      7. unpow2 58.0%

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

      8. unpow2 58.0%

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

      9. hypot-define 75.5%

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

   6. Applied egg-rr 75.5%

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

      1. associate-/r/ 75.5%

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

      2. sub-neg 75.5%

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

      3. associate-+l- 64.8%

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

      4. sub-neg 64.8%

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

      5. remove-double-neg 64.8%

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

      6. hypot-undefine 56.8%

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

      7. unpow2 56.8%

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

      8. unpow2 56.8%

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

      9. +-commutative 56.8%

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

      10. unpow2 56.8%

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

      11. unpow2 56.8%

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

      12. hypot-undefine 64.8%

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

   8. Simplified 64.8%

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

   9. Taylor expanded in C around 0 55.8%

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

       1. +-commutative 55.8%

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

       2. unpow2 55.8%

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

       3. unpow2 55.8%

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

       4. hypot-define 56.5%

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

   11. Simplified 56.5%

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

   12. Taylor expanded in C around inf 33.8%

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

   if 1.4e22 < B

   1. Initial program 54.6%

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

   3. Taylor expanded in B around inf 62.0%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.1 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{+22}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.3% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.3 \cdot 10^{-212}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.3e-212)
   (* (/ 180.0 PI) (atan (- 1.0 (/ A B))))
   (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.3e-212) {
		tmp = (180.0 / ((double) M_PI)) * atan((1.0 - (A / B)));
	} else {
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.3e-212) {
		tmp = (180.0 / Math.PI) * Math.atan((1.0 - (A / B)));
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + B)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.3e-212:
		tmp = (180.0 / math.pi) * math.atan((1.0 - (A / B)))
	else:
		tmp = 180.0 * (math.atan(((C - (A + B)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.3e-212)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(1.0 - Float64(A / B))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + B)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.3e-212)
		tmp = (180.0 / pi) * atan((1.0 - (A / B)));
	else
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.3e-212], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.3e-212

   1. Initial program 49.2%

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

      1. associate-*l/ 49.2%

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

      2. *-lft-identity 49.2%

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

      3. +-commutative 49.2%

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

      4. unpow2 49.2%

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

      5. unpow2 49.2%

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

      6. hypot-define 76.8%

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

   3. Simplified 76.8%

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

      1. clear-num 76.8%

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

      2. un-div-inv 76.8%

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

      3. hypot-undefine 49.2%

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

      4. unpow2 49.2%

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

      5. unpow2 49.2%

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

      6. +-commutative 49.2%

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

      7. unpow2 49.2%

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

      8. unpow2 49.2%

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

      9. hypot-define 76.8%

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

   6. Applied egg-rr 76.8%

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

      1. associate-/r/ 76.8%

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

      2. sub-neg 76.8%

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

      3. associate-+l- 73.5%

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

      4. sub-neg 73.5%

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

      5. remove-double-neg 73.5%

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

      6. hypot-undefine 49.2%

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

      7. unpow2 49.2%

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

      8. unpow2 49.2%

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

      9. +-commutative 49.2%

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

      10. unpow2 49.2%

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

      11. unpow2 49.2%

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

      12. hypot-undefine 73.5%

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

   8. Simplified 73.5%

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

   9. Taylor expanded in C around 0 40.4%

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

       1. mul-1-neg 40.4%

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

       2. distribute-neg-in 40.4%

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

       3. unsub-neg 40.4%

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

       4. unpow2 40.4%

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

       5. unpow2 40.4%

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

       6. hypot-define 65.7%

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

   11. Simplified 65.7%

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

   12. Taylor expanded in B around -inf 61.0%

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

       1. mul-1-neg 61.0%

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

       2. unsub-neg 61.0%

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

   14. Simplified 61.0%

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

   if -1.3e-212 < B

   1. Initial program 58.6%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in B around inf 66.0%

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

      1. +-commutative 66.0%

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

   7. Simplified 66.0%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.3 \cdot 10^{-212}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(1 - \frac{A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 66.4% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 10^{-198}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1e-198)
   (* 180.0 (/ (atan (/ (+ C (- B A)) B)) PI))
   (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1e-198) {
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 1e-198) {
		tmp = 180.0 * (Math.atan(((C + (B - A)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + B)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 1e-198:
		tmp = 180.0 * (math.atan(((C + (B - A)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - (A + B)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 1e-198)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C + Float64(B - A)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + B)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 1e-198)
		tmp = 180.0 * (atan(((C + (B - A)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 1e-198], N[(180.0 * N[(N[ArcTan[N[(N[(C + N[(B - A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 9.9999999999999991e-199

   1. Initial program 51.6%

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

   3. Simplified 70.1%

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

   5. Taylor expanded in B around -inf 64.1%

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

      1. neg-mul-1 64.1%

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

      2. unsub-neg 64.1%

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

   7. Simplified 64.1%

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

   if 9.9999999999999991e-199 < B

   1. Initial program 59.8%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in B around inf 75.6%

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

      1. +-commutative 75.6%

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

   7. Simplified 75.6%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 10^{-198}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + \left(B - A\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 66.3% accurate, 3.6× speedup

Math

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

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1e-176)
   (* (/ 180.0 PI) (atan (/ (- (+ C B) A) B)))
   (* 180.0 (/ (atan (/ (- C (+ A B)) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-176) {
		tmp = (180.0 / ((double) M_PI)) * atan((((C + B) - A) / B));
	} else {
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1e-176) {
		tmp = (180.0 / Math.PI) * Math.atan((((C + B) - A) / B));
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + B)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1e-176:
		tmp = (180.0 / math.pi) * math.atan((((C + B) - A) / B))
	else:
		tmp = 180.0 * (math.atan(((C - (A + B)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1e-176)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(C + B) - A) / B)));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + B)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1e-176)
		tmp = (180.0 / pi) * atan((((C + B) - A) / B));
	else
		tmp = 180.0 * (atan(((C - (A + B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1e-176], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(N[(C + B), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1e-176

   1. Initial program 49.9%

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

      1. associate-*l/ 49.9%

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

      2. *-lft-identity 49.9%

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

      3. +-commutative 49.9%

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

      4. unpow2 49.9%

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

      5. unpow2 49.9%

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

      6. hypot-define 77.3%

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

   3. Simplified 77.3%

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

      1. clear-num 77.3%

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

      2. un-div-inv 77.3%

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

      3. hypot-undefine 49.9%

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

      4. unpow2 49.9%

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

      5. unpow2 49.9%

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

      6. +-commutative 49.9%

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

      7. unpow2 49.9%

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

      8. unpow2 49.9%

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

      9. hypot-define 77.3%

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

   6. Applied egg-rr 77.3%

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

      1. associate-/r/ 77.3%

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

      2. sub-neg 77.3%

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

      3. associate-+l- 75.5%

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

      4. sub-neg 75.5%

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

      5. remove-double-neg 75.5%

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

      6. hypot-undefine 50.0%

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

      7. unpow2 50.0%

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

      8. unpow2 50.0%

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

      9. +-commutative 50.0%

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

      10. unpow2 50.0%

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

      11. unpow2 50.0%

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

      12. hypot-undefine 75.5%

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

   8. Simplified 75.5%

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

   9. Taylor expanded in B around -inf 71.8%

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

   if -1e-176 < B

   1. Initial program 57.6%

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

   3. Simplified 72.2%

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

   5. Taylor expanded in B around inf 64.7%

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

      1. +-commutative 64.7%

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

   7. Simplified 64.7%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1 \cdot 10^{-176}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 40.3% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7.5 \cdot 10^{-308}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7.5e-308)
   (* 180.0 (/ (atan 1.0) PI))
   (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.5e-308) {
		tmp = 180.0 * (atan(1.0) / ((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 <= -7.5e-308) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7.5e-308:
		tmp = 180.0 * (math.atan(1.0) / 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 <= -7.5e-308)
		tmp = Float64(180.0 * Float64(atan(1.0) / 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 <= -7.5e-308)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7.5e-308], N[(180.0 * N[(N[ArcTan[1.0], $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 < -7.4999999999999998e-308

   1. Initial program 51.9%

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

   3. Taylor expanded in B around -inf 44.6%

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

   if -7.4999999999999998e-308 < B

   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 34.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.5 \cdot 10^{-308}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 21.7% accurate, 4.0× 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 54.2%

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

3. Taylor expanded in B around inf 16.4%

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

4. Final simplification 16.4%

   \[\leadsto 180 \cdot \frac{\tan^{-1} -1}{\pi} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(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)))