ABCF->ab-angle angle

Percentage Accurate: 54.0% → 87.8%

Time: 19.4s

Alternatives: 20

Speedup: 3.6×

• Could not converge on a ground truth

  1. reg0 = (bf "-1.642490806432145456785249511592637625346e-304")
  2. reg1 = (bf #e1.119533517885233904088243899662316772968e65)
  3. reg2 = (bf #e-2.159298382034281526581538818962611773596e103)

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.0% 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: 87.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], N[(N[(180.0 * t$95$1), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] / N[(-2.0 * N[(C / A), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 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. Step-by-step derivation

      1. associate-*r/ 54.6%

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

   4. Applied egg-rr 91.0%

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

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

   1. Initial program 19.4%

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

      1. associate--l- 12.1%

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

      2. +-commutative 12.1%

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

      3. unpow2 12.1%

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

      4. unpow2 12.1%

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

      5. hypot-undefine 12.1%

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

      6. associate-/r/ 12.1%

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

      7. associate--r+ 19.4%

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

   4. Applied egg-rr 19.4%

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

   5. Taylor expanded in A around -inf 63.5%

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

      1. associate-*r* 63.5%

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

      2. mul-1-neg 63.5%

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

      3. associate-*r/ 63.5%

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

      4. metadata-eval 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in B around -inf 91.7%

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

      1. associate-/r* 91.8%

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

      2. +-commutative 91.8%

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

      3. fma-define 91.8%

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

   10. Simplified 91.8%

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

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

   1. Initial program 60.5%

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

      1. *-commutative 60.5%

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

      2. associate--l- 60.5%

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

      3. +-commutative 60.5%

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

      4. unpow2 60.5%

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

      5. unpow2 60.5%

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

      6. hypot-undefine 86.9%

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

      7. div-inv 86.9%

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

      8. clear-num 86.9%

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

      9. un-div-inv 86.9%

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

   4. Applied egg-rr 90.4%

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

Alternative 2: 78.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.55 \cdot 10^{-38}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\frac{-1}{A}}{\frac{C \cdot 2}{B \cdot A} - \frac{2}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-124}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.55e-38)
   (/ (* 180.0 (atan (/ (/ -1.0 A) (- (/ (* C 2.0) (* B A)) (/ 2.0 B))))) PI)
   (if (<= A 1.9e-124)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (* 180.0 (/ (atan (/ (+ A (hypot A B)) (- B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.55e-38) {
		tmp = (180.0 * atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / ((double) M_PI);
	} else if (A <= 1.9e-124) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A + hypot(A, B)) / -B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.55e-38) {
		tmp = (180.0 * Math.atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / Math.PI;
	} else if (A <= 1.9e-124) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A + Math.hypot(A, B)) / -B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.55e-38:
		tmp = (180.0 * math.atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / math.pi
	elif A <= 1.9e-124:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A + math.hypot(A, B)) / -B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.55e-38)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-1.0 / A) / Float64(Float64(Float64(C * 2.0) / Float64(B * A)) - Float64(2.0 / B))))) / pi);
	elseif (A <= 1.9e-124)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A + hypot(A, B)) / Float64(-B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.55e-38)
		tmp = (180.0 * atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / pi;
	elseif (A <= 1.9e-124)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = 180.0 * (atan(((A + hypot(A, B)) / -B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.55e-38], N[(N[(180.0 * N[ArcTan[N[(N[(-1.0 / A), $MachinePrecision] / N[(N[(N[(C * 2.0), $MachinePrecision] / N[(B * A), $MachinePrecision]), $MachinePrecision] - N[(2.0 / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.9e-124], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A + N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.54999999999999991e-38

   1. Initial program 29.3%

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

      1. associate--l- 24.4%

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

      2. +-commutative 24.4%

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

      3. unpow2 24.4%

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

      4. unpow2 24.4%

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

      5. hypot-undefine 36.0%

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

      6. associate-/r/ 36.0%

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

      7. associate--r+ 55.5%

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

   4. Applied egg-rr 55.5%

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

   5. Taylor expanded in A around -inf 72.5%

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

      1. associate-*r* 72.5%

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

      2. mul-1-neg 72.5%

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

      3. associate-*r/ 72.5%

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

      4. metadata-eval 72.5%

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

   7. Simplified 72.5%

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

      1. associate-*r/ 72.6%

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

      2. associate-/r* 72.6%

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

      3. associate-*r/ 72.6%

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

   9. Applied egg-rr 72.6%

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

   if -1.54999999999999991e-38 < A < 1.90000000000000006e-124

   1. Initial program 48.3%

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

   3. Taylor expanded in A around 0 47.2%

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

      1. +-commutative 47.2%

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

      2. unpow2 47.2%

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

      3. unpow2 47.2%

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

      4. hypot-define 76.3%

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

   5. Simplified 76.3%

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

   if 1.90000000000000006e-124 < A

   1. Initial program 69.9%

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

   3. Taylor expanded in C around 0 68.0%

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

      1. associate-*r/ 68.0%

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

      2. mul-1-neg 68.0%

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

      3. unpow2 68.0%

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

      4. unpow2 68.0%

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

      5. hypot-define 90.9%

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

   5. Simplified 90.9%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.55 \cdot 10^{-38}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\frac{-1}{A}}{\frac{C \cdot 2}{B \cdot A} - \frac{2}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-124}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A + \mathsf{hypot}\left(A, B\right)}{-B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.2 \cdot 10^{-35}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\frac{-1}{A}}{\frac{C \cdot 2}{B \cdot A} - \frac{2}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.02 \cdot 10^{+35}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.2e-35)
   (/ (* 180.0 (atan (/ (/ -1.0 A) (- (/ (* C 2.0) (* B A)) (/ 2.0 B))))) PI)
   (if (<= A 1.02e+35)
     (/ 180.0 (/ PI (atan (/ (- C (hypot C B)) B))))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.2e-35) {
		tmp = (180.0 * atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / ((double) M_PI);
	} else if (A <= 1.02e+35) {
		tmp = 180.0 / (((double) M_PI) / atan(((C - hypot(C, B)) / B)));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.2e-35) {
		tmp = (180.0 * Math.atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / Math.PI;
	} else if (A <= 1.02e+35) {
		tmp = 180.0 / (Math.PI / Math.atan(((C - Math.hypot(C, B)) / B)));
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.2e-35:
		tmp = (180.0 * math.atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / math.pi
	elif A <= 1.02e+35:
		tmp = 180.0 / (math.pi / math.atan(((C - math.hypot(C, B)) / B)))
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.2e-35)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-1.0 / A) / Float64(Float64(Float64(C * 2.0) / Float64(B * A)) - Float64(2.0 / B))))) / pi);
	elseif (A <= 1.02e+35)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(C - hypot(C, B)) / B))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.2e-35)
		tmp = (180.0 * atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / pi;
	elseif (A <= 1.02e+35)
		tmp = 180.0 / (pi / atan(((C - hypot(C, B)) / B)));
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.2e-35], N[(N[(180.0 * N[ArcTan[N[(N[(-1.0 / A), $MachinePrecision] / N[(N[(N[(C * 2.0), $MachinePrecision] / N[(B * A), $MachinePrecision]), $MachinePrecision] - N[(2.0 / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.02e+35], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.2000000000000001e-35

   1. Initial program 29.3%

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

      1. associate--l- 24.4%

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

      2. +-commutative 24.4%

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

      3. unpow2 24.4%

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

      4. unpow2 24.4%

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

      5. hypot-undefine 36.0%

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

      6. associate-/r/ 36.0%

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

      7. associate--r+ 55.5%

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

   4. Applied egg-rr 55.5%

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

   5. Taylor expanded in A around -inf 72.5%

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

      1. associate-*r* 72.5%

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

      2. mul-1-neg 72.5%

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

      3. associate-*r/ 72.5%

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

      4. metadata-eval 72.5%

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

   7. Simplified 72.5%

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

      1. associate-*r/ 72.6%

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

      2. associate-/r* 72.6%

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

      3. associate-*r/ 72.6%

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

   9. Applied egg-rr 72.6%

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

   if -1.2000000000000001e-35 < A < 1.02000000000000007e35

   1. Initial program 52.0%

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

      1. *-commutative 52.0%

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

      2. associate--l- 52.0%

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

      3. +-commutative 52.0%

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

      4. unpow2 52.0%

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

      5. unpow2 52.0%

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

      6. hypot-undefine 82.4%

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

      7. div-inv 82.4%

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

      8. clear-num 82.5%

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

      9. un-div-inv 82.5%

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

   4. Applied egg-rr 82.5%

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

   5. Taylor expanded in A around 0 46.1%

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

      1. +-commutative 46.1%

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

      2. unpow2 46.1%

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

      3. unpow2 46.1%

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

      4. hypot-define 76.2%

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

   7. Simplified 76.2%

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

   if 1.02000000000000007e35 < A

   1. Initial program 77.1%

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

   3. Taylor expanded in B around -inf 85.7%

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

      1. associate--l+ 85.7%

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

      2. div-sub 89.6%

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

   5. Simplified 89.6%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.2 \cdot 10^{-35}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\frac{-1}{A}}{\frac{C \cdot 2}{B \cdot A} - \frac{2}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.02 \cdot 10^{+35}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{-36}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\frac{-1}{A}}{\frac{C \cdot 2}{B \cdot A} - \frac{2}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{+34}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.35e-36)
   (/ (* 180.0 (atan (/ (/ -1.0 A) (- (/ (* C 2.0) (* B A)) (/ 2.0 B))))) PI)
   (if (<= A 2.6e+34)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e-36) {
		tmp = (180.0 * atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / ((double) M_PI);
	} else if (A <= 2.6e+34) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e-36) {
		tmp = (180.0 * Math.atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / Math.PI;
	} else if (A <= 2.6e+34) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.35e-36:
		tmp = (180.0 * math.atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / math.pi
	elif A <= 2.6e+34:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.35e-36)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-1.0 / A) / Float64(Float64(Float64(C * 2.0) / Float64(B * A)) - Float64(2.0 / B))))) / pi);
	elseif (A <= 2.6e+34)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.35e-36)
		tmp = (180.0 * atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / pi;
	elseif (A <= 2.6e+34)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / B)) / pi);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.35e-36], N[(N[(180.0 * N[ArcTan[N[(N[(-1.0 / A), $MachinePrecision] / N[(N[(N[(C * 2.0), $MachinePrecision] / N[(B * A), $MachinePrecision]), $MachinePrecision] - N[(2.0 / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 2.6e+34], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.35000000000000004e-36

   1. Initial program 29.3%

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

      1. associate--l- 24.4%

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

      2. +-commutative 24.4%

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

      3. unpow2 24.4%

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

      4. unpow2 24.4%

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

      5. hypot-undefine 36.0%

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

      6. associate-/r/ 36.0%

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

      7. associate--r+ 55.5%

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

   4. Applied egg-rr 55.5%

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

   5. Taylor expanded in A around -inf 72.5%

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

      1. associate-*r* 72.5%

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

      2. mul-1-neg 72.5%

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

      3. associate-*r/ 72.5%

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

      4. metadata-eval 72.5%

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

   7. Simplified 72.5%

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

      1. associate-*r/ 72.6%

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

      2. associate-/r* 72.6%

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

      3. associate-*r/ 72.6%

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

   9. Applied egg-rr 72.6%

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

   if -1.35000000000000004e-36 < A < 2.59999999999999997e34

   1. Initial program 52.0%

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

   3. Taylor expanded in A around 0 46.1%

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

      1. +-commutative 46.1%

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

      2. unpow2 46.1%

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

      3. unpow2 46.1%

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

      4. hypot-define 76.2%

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

   5. Simplified 76.2%

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

   if 2.59999999999999997e34 < A

   1. Initial program 77.1%

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

   3. Taylor expanded in B around -inf 85.7%

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

      1. associate--l+ 85.7%

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

      2. div-sub 89.6%

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

   5. Simplified 89.6%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{-36}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\frac{-1}{A}}{\frac{C \cdot 2}{B \cdot A} - \frac{2}{B}}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{+34}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{-36}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\frac{-1}{A}}{\frac{C \cdot 2}{B \cdot A} - \frac{2}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.35e-36)
   (/ (* 180.0 (atan (/ (/ -1.0 A) (- (/ (* C 2.0) (* B A)) (/ 2.0 B))))) PI)
   (/ 180.0 (/ PI (atan (/ (- (- C A) (hypot B (- A C))) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e-36) {
		tmp = (180.0 * atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / ((double) M_PI);
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((((C - A) - hypot(B, (A - C))) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e-36) {
		tmp = (180.0 * Math.atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / Math.PI;
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((((C - A) - Math.hypot(B, (A - C))) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.35e-36:
		tmp = (180.0 * math.atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / math.pi
	else:
		tmp = 180.0 / (math.pi / math.atan((((C - A) - math.hypot(B, (A - C))) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.35e-36)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-1.0 / A) / Float64(Float64(Float64(C * 2.0) / Float64(B * A)) - Float64(2.0 / B))))) / pi);
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.35e-36)
		tmp = (180.0 * atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / pi;
	else
		tmp = 180.0 / (pi / atan((((C - A) - hypot(B, (A - C))) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.35e-36], N[(N[(180.0 * N[ArcTan[N[(N[(-1.0 / A), $MachinePrecision] / N[(N[(N[(C * 2.0), $MachinePrecision] / N[(B * A), $MachinePrecision]), $MachinePrecision] - N[(2.0 / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.35000000000000004e-36

   1. Initial program 29.3%

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

      1. associate--l- 24.4%

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

      2. +-commutative 24.4%

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

      3. unpow2 24.4%

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

      4. unpow2 24.4%

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

      5. hypot-undefine 36.0%

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

      6. associate-/r/ 36.0%

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

      7. associate--r+ 55.5%

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

   4. Applied egg-rr 55.5%

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

   5. Taylor expanded in A around -inf 72.5%

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

      1. associate-*r* 72.5%

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

      2. mul-1-neg 72.5%

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

      3. associate-*r/ 72.5%

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

      4. metadata-eval 72.5%

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

   7. Simplified 72.5%

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

      1. associate-*r/ 72.6%

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

      2. associate-/r* 72.6%

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

      3. associate-*r/ 72.6%

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

   9. Applied egg-rr 72.6%

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

   if -1.35000000000000004e-36 < A

   1. Initial program 58.7%

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

      1. *-commutative 58.7%

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

      2. associate--l- 58.7%

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

      3. +-commutative 58.7%

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

      4. unpow2 58.7%

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

      5. unpow2 58.7%

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

      6. hypot-undefine 86.6%

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

      7. div-inv 86.6%

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

      8. clear-num 86.6%

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

      9. un-div-inv 86.6%

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

   4. Applied egg-rr 86.6%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{-36}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\frac{-1}{A}}{\frac{C \cdot 2}{B \cdot A} - \frac{2}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.2 \cdot 10^{-35}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\frac{-1}{A}}{\frac{C \cdot 2}{B \cdot A} - \frac{2}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.2e-35)
   (/ (* 180.0 (atan (/ (/ -1.0 A) (- (/ (* C 2.0) (* B A)) (/ 2.0 B))))) PI)
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.2e-35) {
		tmp = (180.0 * atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.2e-35) {
		tmp = (180.0 * Math.atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.2e-35:
		tmp = (180.0 * math.atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.2e-35)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-1.0 / A) / Float64(Float64(Float64(C * 2.0) / Float64(B * A)) - Float64(2.0 / B))))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.2e-35)
		tmp = (180.0 * atan(((-1.0 / A) / (((C * 2.0) / (B * A)) - (2.0 / B))))) / pi;
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.2e-35], N[(N[(180.0 * N[ArcTan[N[(N[(-1.0 / A), $MachinePrecision] / N[(N[(N[(C * 2.0), $MachinePrecision] / N[(B * A), $MachinePrecision]), $MachinePrecision] - N[(2.0 / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $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]]

Derivation

1. Split input into 2 regimes

2. if A < -1.2000000000000001e-35

   1. Initial program 29.3%

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

      1. associate--l- 24.4%

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

      2. +-commutative 24.4%

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

      3. unpow2 24.4%

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

      4. unpow2 24.4%

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

      5. hypot-undefine 36.0%

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

      6. associate-/r/ 36.0%

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

      7. associate--r+ 55.5%

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

   4. Applied egg-rr 55.5%

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

   5. Taylor expanded in A around -inf 72.5%

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

      1. associate-*r* 72.5%

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

      2. mul-1-neg 72.5%

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

      3. associate-*r/ 72.5%

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

      4. metadata-eval 72.5%

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

   7. Simplified 72.5%

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

      1. associate-*r/ 72.6%

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

      2. associate-/r* 72.6%

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

      3. associate-*r/ 72.6%

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

   9. Applied egg-rr 72.6%

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

   if -1.2000000000000001e-35 < A

   1. Initial program 58.7%

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

   3. Simplified 86.6%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.2 \cdot 10^{-35}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\frac{-1}{A}}{\frac{C \cdot 2}{B \cdot A} - \frac{2}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.9% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.72 \cdot 10^{-301}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot \left(\frac{C - A}{B} - -1\right)}{B}\right)}}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-185}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A \cdot \left(2 + \frac{C \cdot -2}{A}\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.72e-301)
   (/ 180.0 (/ PI (atan (/ (* B (- (/ (- C A) B) -1.0)) B))))
   (if (<= B 6.5e-185)
     (* 180.0 (/ (atan (/ B (* A (+ 2.0 (/ (* C -2.0) A))))) PI))
     (/ 180.0 (/ PI (atan (/ (* B (+ (/ C B) (- -1.0 (/ A B)))) B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.72e-301) {
		tmp = 180.0 / (((double) M_PI) / atan(((B * (((C - A) / B) - -1.0)) / B)));
	} else if (B <= 6.5e-185) {
		tmp = 180.0 * (atan((B / (A * (2.0 + ((C * -2.0) / A))))) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan(((B * ((C / B) + (-1.0 - (A / B)))) / B)));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.72e-301) {
		tmp = 180.0 / (Math.PI / Math.atan(((B * (((C - A) / B) - -1.0)) / B)));
	} else if (B <= 6.5e-185) {
		tmp = 180.0 * (Math.atan((B / (A * (2.0 + ((C * -2.0) / A))))) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan(((B * ((C / B) + (-1.0 - (A / B)))) / B)));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.72e-301:
		tmp = 180.0 / (math.pi / math.atan(((B * (((C - A) / B) - -1.0)) / B)))
	elif B <= 6.5e-185:
		tmp = 180.0 * (math.atan((B / (A * (2.0 + ((C * -2.0) / A))))) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan(((B * ((C / B) + (-1.0 - (A / B)))) / B)))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.72e-301)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(B * Float64(Float64(Float64(C - A) / B) - -1.0)) / B))));
	elseif (B <= 6.5e-185)
		tmp = Float64(180.0 * Float64(atan(Float64(B / Float64(A * Float64(2.0 + Float64(Float64(C * -2.0) / A))))) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(B * Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))) / B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.72e-301)
		tmp = 180.0 / (pi / atan(((B * (((C - A) / B) - -1.0)) / B)));
	elseif (B <= 6.5e-185)
		tmp = 180.0 * (atan((B / (A * (2.0 + ((C * -2.0) / A))))) / pi);
	else
		tmp = 180.0 / (pi / atan(((B * ((C / B) + (-1.0 - (A / B)))) / B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.72e-301], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(B * N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 6.5e-185], N[(180.0 * N[(N[ArcTan[N[(B / N[(A * N[(2.0 + N[(N[(C * -2.0), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(B * N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.72000000000000008e-301

   1. Initial program 52.4%

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

      1. *-commutative 52.4%

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

      2. associate--l- 52.3%

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

      3. +-commutative 52.3%

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

      4. unpow2 52.3%

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

      5. unpow2 52.3%

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

      6. hypot-undefine 73.6%

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

      7. div-inv 73.6%

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

      8. clear-num 73.6%

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

      9. un-div-inv 73.6%

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

   4. Applied egg-rr 76.7%

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

   5. Taylor expanded in B around -inf 70.0%

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

      1. mul-1-neg 70.0%

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

      2. *-commutative 70.0%

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

      3. distribute-rgt-neg-in 70.0%

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

      4. sub-neg 70.0%

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

      5. associate-*r/ 70.0%

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

      6. mul-1-neg 70.0%

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

      7. sub-neg 70.0%

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

      8. distribute-neg-in 70.0%

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

      9. remove-double-neg 70.0%

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

      10. +-commutative 70.0%

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

      11. sub-neg 70.0%

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

      12. metadata-eval 70.0%

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

   7. Simplified 70.0%

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

   if -1.72000000000000008e-301 < B < 6.49999999999999946e-185

   1. Initial program 60.1%

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

      1. associate--l- 47.8%

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

      2. +-commutative 47.8%

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

      3. unpow2 47.8%

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

      4. unpow2 47.8%

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

      5. hypot-undefine 55.0%

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

      6. associate-/r/ 55.0%

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

      7. associate--r+ 79.4%

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

   4. Applied egg-rr 79.4%

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

   5. Taylor expanded in A around -inf 47.7%

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

      1. associate-*r* 47.7%

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

      2. mul-1-neg 47.7%

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

      3. associate-*r/ 47.7%

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

      4. metadata-eval 47.7%

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

   7. Simplified 47.7%

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

   8. Taylor expanded in B around -inf 61.2%

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

      1. associate-*r/ 61.2%

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

   10. Simplified 61.2%

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

   if 6.49999999999999946e-185 < B

   1. Initial program 47.6%

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

      1. *-commutative 47.6%

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

      2. associate--l- 47.5%

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

      3. +-commutative 47.5%

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

      4. unpow2 47.5%

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

      5. unpow2 47.5%

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

      6. hypot-undefine 78.4%

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

      7. div-inv 78.4%

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

      8. clear-num 78.4%

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

      9. un-div-inv 78.4%

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

   4. Applied egg-rr 81.2%

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

   5. Taylor expanded in B around inf 72.3%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.72 \cdot 10^{-301}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot \left(\frac{C - A}{B} - -1\right)}{B}\right)}}\\ \mathbf{elif}\;B \leq 6.5 \cdot 10^{-185}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A \cdot \left(2 + \frac{C \cdot -2}{A}\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -6.4 \cdot 10^{-304}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot \left(\frac{C - A}{B} - -1\right)}{B}\right)}}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-187}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A \cdot \left(2 + \frac{C \cdot -2}{A}\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -6.4e-304)
   (/ 180.0 (/ PI (atan (/ (* B (- (/ (- C A) B) -1.0)) B))))
   (if (<= B 8e-187)
     (* 180.0 (/ (atan (/ B (* A (+ 2.0 (/ (* C -2.0) A))))) PI))
     (* 180.0 (/ (atan (+ (/ C B) (- -1.0 (/ A B)))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.4e-304) {
		tmp = 180.0 / (((double) M_PI) / atan(((B * (((C - A) / B) - -1.0)) / B)));
	} else if (B <= 8e-187) {
		tmp = 180.0 * (atan((B / (A * (2.0 + ((C * -2.0) / A))))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -6.4e-304) {
		tmp = 180.0 / (Math.PI / Math.atan(((B * (((C - A) / B) - -1.0)) / B)));
	} else if (B <= 8e-187) {
		tmp = 180.0 * (Math.atan((B / (A * (2.0 + ((C * -2.0) / A))))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C / B) + (-1.0 - (A / B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -6.4e-304:
		tmp = 180.0 / (math.pi / math.atan(((B * (((C - A) / B) - -1.0)) / B)))
	elif B <= 8e-187:
		tmp = 180.0 * (math.atan((B / (A * (2.0 + ((C * -2.0) / A))))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C / B) + (-1.0 - (A / B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -6.4e-304)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(B * Float64(Float64(Float64(C - A) / B) - -1.0)) / B))));
	elseif (B <= 8e-187)
		tmp = Float64(180.0 * Float64(atan(Float64(B / Float64(A * Float64(2.0 + Float64(Float64(C * -2.0) / A))))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -6.4e-304)
		tmp = 180.0 / (pi / atan(((B * (((C - A) / B) - -1.0)) / B)));
	elseif (B <= 8e-187)
		tmp = 180.0 * (atan((B / (A * (2.0 + ((C * -2.0) / A))))) / pi);
	else
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -6.4e-304], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(B * N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8e-187], N[(180.0 * N[(N[ArcTan[N[(B / N[(A * N[(2.0 + N[(N[(C * -2.0), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -6.39999999999999998e-304

   1. Initial program 52.4%

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

      1. *-commutative 52.4%

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

      2. associate--l- 52.3%

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

      3. +-commutative 52.3%

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

      4. unpow2 52.3%

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

      5. unpow2 52.3%

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

      6. hypot-undefine 73.6%

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

      7. div-inv 73.6%

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

      8. clear-num 73.6%

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

      9. un-div-inv 73.6%

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

   4. Applied egg-rr 76.7%

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

   5. Taylor expanded in B around -inf 70.0%

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

      1. mul-1-neg 70.0%

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

      2. *-commutative 70.0%

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

      3. distribute-rgt-neg-in 70.0%

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

      4. sub-neg 70.0%

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

      5. associate-*r/ 70.0%

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

      6. mul-1-neg 70.0%

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

      7. sub-neg 70.0%

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

      8. distribute-neg-in 70.0%

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

      9. remove-double-neg 70.0%

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

      10. +-commutative 70.0%

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

      11. sub-neg 70.0%

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

      12. metadata-eval 70.0%

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

   7. Simplified 70.0%

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

   if -6.39999999999999998e-304 < B < 8.0000000000000001e-187

   1. Initial program 60.1%

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

      1. associate--l- 47.8%

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

      2. +-commutative 47.8%

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

      3. unpow2 47.8%

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

      4. unpow2 47.8%

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

      5. hypot-undefine 55.0%

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

      6. associate-/r/ 55.0%

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

      7. associate--r+ 79.4%

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

   4. Applied egg-rr 79.4%

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

   5. Taylor expanded in A around -inf 47.7%

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

      1. associate-*r* 47.7%

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

      2. mul-1-neg 47.7%

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

      3. associate-*r/ 47.7%

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

      4. metadata-eval 47.7%

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

   7. Simplified 47.7%

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

   8. Taylor expanded in B around -inf 61.2%

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

      1. associate-*r/ 61.2%

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

   10. Simplified 61.2%

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

   if 8.0000000000000001e-187 < B

   1. Initial program 47.6%

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

   3. Taylor expanded in B around inf 72.2%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -6.4 \cdot 10^{-304}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{B \cdot \left(\frac{C - A}{B} - -1\right)}{B}\right)}}\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-187}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A \cdot \left(2 + \frac{C \cdot -2}{A}\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.0% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.5 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-187}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A \cdot \left(2 + \frac{C \cdot -2}{A}\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.5e-302)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= B 3.6e-187)
     (* 180.0 (/ (atan (/ B (* A (+ 2.0 (/ (* C -2.0) A))))) PI))
     (* 180.0 (/ (atan (+ (/ C B) (- -1.0 (/ A B)))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.5e-302) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= 3.6e-187) {
		tmp = 180.0 * (atan((B / (A * (2.0 + ((C * -2.0) / A))))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.5e-302) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= 3.6e-187) {
		tmp = 180.0 * (Math.atan((B / (A * (2.0 + ((C * -2.0) / A))))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C / B) + (-1.0 - (A / B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.5e-302:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= 3.6e-187:
		tmp = 180.0 * (math.atan((B / (A * (2.0 + ((C * -2.0) / A))))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C / B) + (-1.0 - (A / B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.5e-302)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= 3.6e-187)
		tmp = Float64(180.0 * Float64(atan(Float64(B / Float64(A * Float64(2.0 + Float64(Float64(C * -2.0) / A))))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.5e-302)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= 3.6e-187)
		tmp = 180.0 * (atan((B / (A * (2.0 + ((C * -2.0) / A))))) / pi);
	else
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.5e-302], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.6e-187], N[(180.0 * N[(N[ArcTan[N[(B / N[(A * N[(2.0 + N[(N[(C * -2.0), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.49999999999999994e-302

   1. Initial program 52.4%

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

   3. Taylor expanded in B around -inf 68.4%

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

      1. associate--l+ 68.4%

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

      2. div-sub 69.9%

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

   5. Simplified 69.9%

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

   if -1.49999999999999994e-302 < B < 3.59999999999999994e-187

   1. Initial program 60.1%

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

      1. associate--l- 47.8%

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

      2. +-commutative 47.8%

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

      3. unpow2 47.8%

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

      4. unpow2 47.8%

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

      5. hypot-undefine 55.0%

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

      6. associate-/r/ 55.0%

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

      7. associate--r+ 79.4%

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

   4. Applied egg-rr 79.4%

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

   5. Taylor expanded in A around -inf 47.7%

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

      1. associate-*r* 47.7%

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

      2. mul-1-neg 47.7%

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

      3. associate-*r/ 47.7%

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

      4. metadata-eval 47.7%

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

   7. Simplified 47.7%

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

   8. Taylor expanded in B around -inf 61.2%

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

      1. associate-*r/ 61.2%

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

   10. Simplified 61.2%

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

   if 3.59999999999999994e-187 < B

   1. Initial program 47.6%

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

   3. Taylor expanded in B around inf 72.2%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.5 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-187}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A \cdot \left(2 + \frac{C \cdot -2}{A}\right)}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.4% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -9.2 \cdot 10^{+21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-A}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -9.2e+21)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -7.2e-166)
     (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
     (if (<= B 3.5e+44)
       (/ 180.0 (/ PI (atan (/ (- A) B))))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -9.2e+21) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -7.2e-166) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (B <= 3.5e+44) {
		tmp = 180.0 / (((double) M_PI) / atan((-A / 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 <= -9.2e+21) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -7.2e-166) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (B <= 3.5e+44) {
		tmp = 180.0 / (Math.PI / Math.atan((-A / B)));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -9.2e+21:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -7.2e-166:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif B <= 3.5e+44:
		tmp = 180.0 / (math.pi / math.atan((-A / B)))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -9.2e+21)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -7.2e-166)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (B <= 3.5e+44)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(-A) / 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 <= -9.2e+21)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -7.2e-166)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (B <= 3.5e+44)
		tmp = 180.0 / (pi / atan((-A / B)));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -9.2e+21], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -7.2e-166], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.5e+44], N[(180.0 / N[(Pi / N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -9.2e21

   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. Add Preprocessing

   3. Taylor expanded in B around -inf 68.1%

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

   if -9.2e21 < B < -7.2000000000000002e-166

   1. Initial program 46.9%

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

   3. Taylor expanded in A around -inf 48.4%

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

      1. associate-*r/ 48.4%

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

   5. Simplified 48.4%

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

   if -7.2000000000000002e-166 < B < 3.4999999999999999e44

   1. Initial program 60.4%

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

      1. *-commutative 60.4%

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

      2. associate--l- 57.5%

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

      3. +-commutative 57.5%

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

      4. unpow2 57.5%

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

      5. unpow2 57.5%

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

      6. hypot-undefine 65.7%

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

      7. div-inv 65.7%

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

      8. clear-num 65.7%

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

      9. un-div-inv 65.7%

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

   4. Applied egg-rr 75.1%

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

   5. Taylor expanded in B around inf 53.1%

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

   6. Taylor expanded in A around inf 41.3%

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

      1. associate-*r/ 41.3%

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

      2. mul-1-neg 41.3%

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

   8. Simplified 41.3%

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

   if 3.4999999999999999e44 < B

   1. Initial program 38.1%

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

   3. Taylor expanded in B around inf 73.5%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9.2 \cdot 10^{+21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -7.2 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-A}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.55 \cdot 10^{+22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -3.4 \cdot 10^{-166}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.32 \cdot 10^{+39}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-A}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.55e+22)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -3.4e-166)
     (* 180.0 (/ (atan (* B (/ 0.5 A))) PI))
     (if (<= B 1.32e+39)
       (/ 180.0 (/ PI (atan (/ (- A) B))))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.55e+22) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -3.4e-166) {
		tmp = 180.0 * (atan((B * (0.5 / A))) / ((double) M_PI));
	} else if (B <= 1.32e+39) {
		tmp = 180.0 / (((double) M_PI) / atan((-A / 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 <= -1.55e+22) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -3.4e-166) {
		tmp = 180.0 * (Math.atan((B * (0.5 / A))) / Math.PI);
	} else if (B <= 1.32e+39) {
		tmp = 180.0 / (Math.PI / Math.atan((-A / B)));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.55e+22:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -3.4e-166:
		tmp = 180.0 * (math.atan((B * (0.5 / A))) / math.pi)
	elif B <= 1.32e+39:
		tmp = 180.0 / (math.pi / math.atan((-A / B)))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.55e+22)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -3.4e-166)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / A))) / pi));
	elseif (B <= 1.32e+39)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(-A) / 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 <= -1.55e+22)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -3.4e-166)
		tmp = 180.0 * (atan((B * (0.5 / A))) / pi);
	elseif (B <= 1.32e+39)
		tmp = 180.0 / (pi / atan((-A / B)));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.55e+22], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -3.4e-166], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.32e+39], N[(180.0 / N[(Pi / N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -1.5500000000000001e22

   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. Add Preprocessing

   3. Taylor expanded in B around -inf 68.1%

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

   if -1.5500000000000001e22 < B < -3.3999999999999997e-166

   1. Initial program 46.9%

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

      1. associate--l- 46.7%

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

      2. +-commutative 46.7%

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

      3. unpow2 46.7%

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

      4. unpow2 46.7%

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

      5. hypot-undefine 46.8%

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

      6. associate-/r/ 46.8%

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

      7. associate--r+ 57.1%

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

   4. Applied egg-rr 57.1%

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

   5. Taylor expanded in A around -inf 46.5%

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

      1. associate-*r* 46.5%

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

      2. mul-1-neg 46.5%

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

      3. associate-*r/ 46.5%

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

      4. metadata-eval 46.5%

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

   7. Simplified 46.5%

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

   8. Taylor expanded in A around inf 48.4%

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

      1. associate-*r/ 48.4%

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

      2. *-commutative 48.4%

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

      3. associate-/l* 48.3%

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

   10. Simplified 48.3%

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

   if -3.3999999999999997e-166 < B < 1.32e39

   1. Initial program 60.4%

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

      1. *-commutative 60.4%

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

      2. associate--l- 57.5%

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

      3. +-commutative 57.5%

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

      4. unpow2 57.5%

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

      5. unpow2 57.5%

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

      6. hypot-undefine 65.7%

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

      7. div-inv 65.7%

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

      8. clear-num 65.7%

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

      9. un-div-inv 65.7%

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

   4. Applied egg-rr 75.1%

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

   5. Taylor expanded in B around inf 53.1%

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

   6. Taylor expanded in A around inf 41.3%

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

      1. associate-*r/ 41.3%

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

      2. mul-1-neg 41.3%

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

   8. Simplified 41.3%

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

   if 1.32e39 < B

   1. Initial program 38.1%

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

   3. Taylor expanded in B around inf 73.5%

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

Alternative 12: 65.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 8 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-274}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 8e-302)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (if (<= B 1.7e-274)
     (* 180.0 (/ (atan (/ 1.0 (* 2.0 (/ A B)))) PI))
     (* 180.0 (/ (atan (+ (/ C B) (- -1.0 (/ A B)))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 8e-302) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else if (B <= 1.7e-274) {
		tmp = 180.0 * (atan((1.0 / (2.0 * (A / B)))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 8e-302) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else if (B <= 1.7e-274) {
		tmp = 180.0 * (Math.atan((1.0 / (2.0 * (A / B)))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C / B) + (-1.0 - (A / B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 8e-302:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	elif B <= 1.7e-274:
		tmp = 180.0 * (math.atan((1.0 / (2.0 * (A / B)))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C / B) + (-1.0 - (A / B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 8e-302)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	elseif (B <= 1.7e-274)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 / Float64(2.0 * Float64(A / B)))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) + Float64(-1.0 - Float64(A / B)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 8e-302)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	elseif (B <= 1.7e-274)
		tmp = 180.0 * (atan((1.0 / (2.0 * (A / B)))) / pi);
	else
		tmp = 180.0 * (atan(((C / B) + (-1.0 - (A / B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 8e-302], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.7e-274], N[(180.0 * N[(N[ArcTan[N[(1.0 / N[(2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < 7.9999999999999997e-302

   1. Initial program 53.1%

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

   3. Taylor expanded in B around -inf 67.9%

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

      1. associate--l+ 67.9%

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

      2. div-sub 69.4%

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

   5. Simplified 69.4%

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

   if 7.9999999999999997e-302 < B < 1.6999999999999999e-274

   1. Initial program 36.5%

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

      1. associate--l- 19.1%

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

      2. +-commutative 19.1%

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

      3. unpow2 19.1%

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

      4. unpow2 19.1%

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

      5. hypot-undefine 31.7%

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

      6. associate-/r/ 31.7%

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

      7. associate--r+ 65.2%

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

   4. Applied egg-rr 65.2%

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

   5. Taylor expanded in A around -inf 90.6%

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

   if 1.6999999999999999e-274 < B

   1. Initial program 49.8%

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

   3. Taylor expanded in B around inf 69.7%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 8 \cdot 10^{-302}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-274}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{2 \cdot \frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + \left(-1 - \frac{A}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.8% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{-94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 8.4 \cdot 10^{-153}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 + \frac{C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 - \frac{A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.9e-94)
   (* 180.0 (/ (atan (* B (/ 0.5 A))) PI))
   (if (<= A 8.4e-153)
     (/ 180.0 (/ PI (atan (+ -1.0 (/ C B)))))
     (/ 180.0 (/ PI (atan (- -1.0 (/ A B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e-94) {
		tmp = 180.0 * (atan((B * (0.5 / A))) / ((double) M_PI));
	} else if (A <= 8.4e-153) {
		tmp = 180.0 / (((double) M_PI) / atan((-1.0 + (C / B))));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((-1.0 - (A / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.9e-94) {
		tmp = 180.0 * (Math.atan((B * (0.5 / A))) / Math.PI);
	} else if (A <= 8.4e-153) {
		tmp = 180.0 / (Math.PI / Math.atan((-1.0 + (C / B))));
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((-1.0 - (A / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.9e-94:
		tmp = 180.0 * (math.atan((B * (0.5 / A))) / math.pi)
	elif A <= 8.4e-153:
		tmp = 180.0 / (math.pi / math.atan((-1.0 + (C / B))))
	else:
		tmp = 180.0 / (math.pi / math.atan((-1.0 - (A / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.9e-94)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / A))) / pi));
	elseif (A <= 8.4e-153)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-1.0 + Float64(C / B)))));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-1.0 - Float64(A / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.9e-94)
		tmp = 180.0 * (atan((B * (0.5 / A))) / pi);
	elseif (A <= 8.4e-153)
		tmp = 180.0 / (pi / atan((-1.0 + (C / B))));
	else
		tmp = 180.0 / (pi / atan((-1.0 - (A / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.9e-94], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 8.4e-153], N[(180.0 / N[(Pi / N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.89999999999999995e-94

   1. Initial program 30.4%

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

      1. associate--l- 26.2%

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

      2. +-commutative 26.2%

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

      3. unpow2 26.2%

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

      4. unpow2 26.2%

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

      5. hypot-undefine 39.5%

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

      6. associate-/r/ 39.5%

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

      7. associate--r+ 56.3%

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

   4. Applied egg-rr 56.3%

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

   5. Taylor expanded in A around -inf 66.8%

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

      1. associate-*r* 66.8%

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

      2. mul-1-neg 66.8%

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

      3. associate-*r/ 66.8%

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

      4. metadata-eval 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in A around inf 67.8%

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

      1. associate-*r/ 67.8%

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

      2. *-commutative 67.8%

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

      3. associate-/l* 67.8%

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

   10. Simplified 67.8%

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

   if -2.89999999999999995e-94 < A < 8.40000000000000017e-153

   1. Initial program 51.7%

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

      1. *-commutative 51.7%

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

      2. associate--l- 51.7%

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

      3. +-commutative 51.7%

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

      4. unpow2 51.7%

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

      5. unpow2 51.7%

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

      6. hypot-undefine 80.5%

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

      7. div-inv 80.5%

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

      8. clear-num 80.5%

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

      9. un-div-inv 80.5%

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

   4. Applied egg-rr 80.5%

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

   5. Taylor expanded in B around inf 53.4%

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

   6. Taylor expanded in A around 0 53.5%

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

   if 8.40000000000000017e-153 < A

   1. Initial program 66.7%

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

      1. *-commutative 66.7%

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

      2. associate--l- 66.7%

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

      3. +-commutative 66.7%

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

      4. unpow2 66.7%

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

      5. unpow2 66.7%

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

      6. hypot-undefine 94.2%

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

      7. div-inv 94.2%

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

      8. clear-num 94.2%

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

      9. un-div-inv 94.2%

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

   4. Applied egg-rr 94.2%

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

   5. Taylor expanded in B around inf 65.1%

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

   6. Taylor expanded in C around 0 66.5%

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

      1. neg-mul-1 66.5%

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

      2. distribute-neg-in 66.5%

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

      3. metadata-eval 66.5%

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

      4. unsub-neg 66.5%

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

   8. Simplified 66.5%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.9 \cdot 10^{-94}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 8.4 \cdot 10^{-153}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 + \frac{C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 - \frac{A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.75 \cdot 10^{+21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -5.6 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 - \frac{A}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.75e+21)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -5.6e-168)
     (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
     (/ 180.0 (/ PI (atan (- -1.0 (/ A B))))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.75e+21) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -5.6e-168) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((-1.0 - (A / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.75e+21) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -5.6e-168) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((-1.0 - (A / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.75e+21:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -5.6e-168:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((-1.0 - (A / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.75e+21)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -5.6e-168)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-1.0 - Float64(A / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.75e+21)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -5.6e-168)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	else
		tmp = 180.0 / (pi / atan((-1.0 - (A / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.75e+21], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -5.6e-168], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.75e21

   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. Add Preprocessing

   3. Taylor expanded in B around -inf 68.1%

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

   if -1.75e21 < B < -5.6000000000000005e-168

   1. Initial program 46.9%

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

   3. Taylor expanded in A around -inf 48.4%

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

      1. associate-*r/ 48.4%

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

   5. Simplified 48.4%

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

   if -5.6000000000000005e-168 < B

   1. Initial program 52.6%

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

      1. *-commutative 52.6%

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

      2. associate--l- 50.7%

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

      3. +-commutative 50.7%

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

      4. unpow2 50.7%

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

      5. unpow2 50.7%

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

      6. hypot-undefine 73.1%

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

      7. div-inv 73.1%

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

      8. clear-num 73.1%

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

      9. un-div-inv 73.1%

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

   4. Applied egg-rr 79.1%

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

   5. Taylor expanded in B around inf 63.6%

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

   6. Taylor expanded in C around 0 56.6%

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

      1. neg-mul-1 56.6%

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

      2. distribute-neg-in 56.6%

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

      3. metadata-eval 56.6%

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

      4. unsub-neg 56.6%

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

   8. Simplified 56.6%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.75 \cdot 10^{+21}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -5.6 \cdot 10^{-168}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 - \frac{A}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.8% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.5 \cdot 10^{-142}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{+40}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-A}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.5e-142)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 8.5e+40)
     (/ 180.0 (/ PI (atan (/ (- A) B))))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.5e-142) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 8.5e+40) {
		tmp = 180.0 / (((double) M_PI) / atan((-A / 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 <= -4.5e-142) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 8.5e+40) {
		tmp = 180.0 / (Math.PI / Math.atan((-A / B)));
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4.5e-142:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 8.5e+40:
		tmp = 180.0 / (math.pi / math.atan((-A / B)))
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -4.5e-142)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 8.5e+40)
		tmp = Float64(180.0 / Float64(pi / atan(Float64(Float64(-A) / 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 <= -4.5e-142)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 8.5e+40)
		tmp = 180.0 / (pi / atan((-A / B)));
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.5e-142], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.5e+40], N[(180.0 / N[(Pi / N[ArcTan[N[((-A) / B), $MachinePrecision]], $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 < -4.50000000000000019e-142

   1. Initial program 47.8%

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

   3. Taylor expanded in B around -inf 55.9%

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

   if -4.50000000000000019e-142 < B < 8.49999999999999996e40

   1. Initial program 61.0%

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

      1. *-commutative 61.0%

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

      2. associate--l- 58.1%

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

      3. +-commutative 58.1%

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

      4. unpow2 58.1%

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

      5. unpow2 58.1%

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

      6. hypot-undefine 66.0%

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

      7. div-inv 66.0%

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

      8. clear-num 66.1%

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

      9. un-div-inv 66.1%

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

   4. Applied egg-rr 76.0%

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

   5. Taylor expanded in B around inf 53.0%

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

   6. Taylor expanded in A around inf 40.8%

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

      1. associate-*r/ 40.8%

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

      2. mul-1-neg 40.8%

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

   8. Simplified 40.8%

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

   if 8.49999999999999996e40 < B

   1. Initial program 38.1%

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

   3. Taylor expanded in B around inf 73.5%

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

Alternative 16: 45.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.8 \cdot 10^{-8}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.15 \cdot 10^{+65}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{C}{B}\right)}}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.8e-8)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.15e+65)
     (/ 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 <= -2.8e-8) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.15e+65) {
		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 <= -2.8e-8) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.15e+65) {
		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 <= -2.8e-8:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.15e+65:
		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 <= -2.8e-8)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.15e+65)
		tmp = Float64(180.0 / Float64(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 <= -2.8e-8)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.15e+65)
		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, -2.8e-8], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.15e+65], N[(180.0 / N[(Pi / N[ArcTan[N[(C / B), $MachinePrecision]], $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 < -2.7999999999999999e-8

   1. Initial program 47.4%

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

   3. Taylor expanded in B around -inf 64.1%

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

   if -2.7999999999999999e-8 < B < 1.15e65

   1. Initial program 59.1%

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

      1. *-commutative 59.1%

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

      2. associate--l- 56.7%

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

      3. +-commutative 56.7%

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

      4. unpow2 56.7%

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

      5. unpow2 56.7%

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

      6. hypot-undefine 63.2%

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

      7. div-inv 63.2%

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

      8. clear-num 63.2%

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

      9. un-div-inv 63.2%

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

   4. Applied egg-rr 72.9%

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

   5. Taylor expanded in B around inf 50.0%

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

   6. Taylor expanded in C around inf 33.6%

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

   if 1.15e65 < B

   1. Initial program 37.0%

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

   3. Taylor expanded in B around inf 78.2%

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

Alternative 17: 62.7% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.55 \cdot 10^{-96}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 + \frac{C}{B}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.55e-96)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))
   (/ 180.0 (/ PI (atan (+ -1.0 (/ C B)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.55e-96) {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 / (((double) M_PI) / atan((-1.0 + (C / B))));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.55e-96) {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	} else {
		tmp = 180.0 / (Math.PI / Math.atan((-1.0 + (C / B))));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 1.55e-96:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	else:
		tmp = 180.0 / (math.pi / math.atan((-1.0 + (C / B))))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 1.55e-96)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	else
		tmp = Float64(180.0 / Float64(pi / atan(Float64(-1.0 + Float64(C / B)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 1.55e-96)
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	else
		tmp = 180.0 / (pi / atan((-1.0 + (C / B))));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 1.55e-96], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 1.55e-96

   1. Initial program 54.7%

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

   3. Taylor expanded in B around -inf 62.9%

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

      1. associate--l+ 62.9%

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

      2. div-sub 64.6%

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

   5. Simplified 64.6%

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

   if 1.55e-96 < B

   1. Initial program 43.0%

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

      1. *-commutative 43.0%

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

      2. associate--l- 42.9%

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

      3. +-commutative 42.9%

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

      4. unpow2 42.9%

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

      5. unpow2 42.9%

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

      6. hypot-undefine 80.2%

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

      7. div-inv 80.2%

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

      8. clear-num 80.2%

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

      9. un-div-inv 80.2%

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

   4. Applied egg-rr 80.1%

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

   5. Taylor expanded in B around inf 76.0%

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

   6. Taylor expanded in A around 0 71.6%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.55 \cdot 10^{-96}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\frac{\pi}{\tan^{-1} \left(-1 + \frac{C}{B}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 44.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.7 \cdot 10^{-154}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.9 \cdot 10^{-104}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.7e-154)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.9e-104)
     (* 180.0 (/ (atan 0.0) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.7e-154) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.9e-104) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.7e-154) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.9e-104) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.7e-154:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.9e-104:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.7e-154)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.9e-104)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.7e-154)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.9e-104)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.7e-154], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.9e-104], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.69999999999999989e-154

   1. Initial program 48.9%

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

   3. Taylor expanded in B around -inf 55.1%

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

   if -2.69999999999999989e-154 < B < 4.9000000000000003e-104

   1. Initial program 60.6%

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

   3. Taylor expanded in C around inf 30.4%

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

   4. Taylor expanded in B around 0 26.3%

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

      1. associate-*r/ 26.3%

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

      2. *-commutative 26.3%

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

      3. distribute-rgt1-in 26.3%

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

      4. metadata-eval 26.3%

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

      5. mul0-lft 26.3%

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

      6. metadata-eval 26.3%

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

      7. div0 26.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   6. Simplified 26.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   if 4.9000000000000003e-104 < B

   1. Initial program 43.7%

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

   3. Taylor expanded in B around inf 60.7%

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

Alternative 19: 28.7% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 2.05 \cdot 10^{-108}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 2.05e-108)
   (* 180.0 (/ (atan 0.0) PI))
   (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 2.05e-108) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 2.05e-108) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 2.05e-108:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 2.05e-108)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 2.05e-108)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 2.05e-108], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 2.05000000000000018e-108

   1. Initial program 54.5%

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

   3. Taylor expanded in C around inf 24.3%

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

   4. Taylor expanded in B around 0 15.3%

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

      1. associate-*r/ 15.3%

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

      2. *-commutative 15.3%

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

      3. distribute-rgt1-in 15.3%

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

      4. metadata-eval 15.3%

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

      5. mul0-lft 15.3%

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

      6. metadata-eval 15.3%

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

      7. div0 15.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   6. Simplified 15.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{0}}{\pi} \]

   if 2.05000000000000018e-108 < B

   1. Initial program 43.7%

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

   3. Taylor expanded in B around inf 60.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 20.3% 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 51.3%

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

3. Taylor expanded in B around inf 21.6%

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

Reproduce

herbie shell --seed 2024146 
(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)))