ABCF->ab-angle angle

Percentage Accurate: 53.6% → 81.9%

Time: 6.2s

Alternatives: 11

Speedup: 2.2×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-A\right) + C\\ \mathbf{if}\;A \leq -1.7 \cdot 10^{+125}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C - A} \cdot -0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{t\_0 - \mathsf{hypot}\left(t\_0, B\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (+ (- A) C)))
   (if (<= A -1.7e+125)
     (/ (* 180.0 (atan (* (/ B (- C A)) -0.5))) PI)
     (* 180.0 (/ (atan (/ (- t_0 (hypot t_0 B)) B)) PI)))))

C

double code(double A, double B, double C) {
	double t_0 = -A + C;
	double tmp;
	if (A <= -1.7e+125) {
		tmp = (180.0 * atan(((B / (C - A)) * -0.5))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((t_0 - hypot(t_0, B)) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = -A + C;
	double tmp;
	if (A <= -1.7e+125) {
		tmp = (180.0 * Math.atan(((B / (C - A)) * -0.5))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((t_0 - Math.hypot(t_0, B)) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = -A + C
	tmp = 0
	if A <= -1.7e+125:
		tmp = (180.0 * math.atan(((B / (C - A)) * -0.5))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((t_0 - math.hypot(t_0, B)) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(-A) + C)
	tmp = 0.0
	if (A <= -1.7e+125)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / Float64(C - A)) * -0.5))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(t_0 - hypot(t_0, B)) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = -A + C;
	tmp = 0.0;
	if (A <= -1.7e+125)
		tmp = (180.0 * atan(((B / (C - A)) * -0.5))) / pi;
	else
		tmp = 180.0 * (atan(((t_0 - hypot(t_0, B)) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[((-A) + C), $MachinePrecision]}, If[LessEqual[A, -1.7e+125], N[(N[(180.0 * N[ArcTan[N[(N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(t$95$0 - N[Sqrt[t$95$0 ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if A < -1.6999999999999999e125

   1. Initial program 53.6%

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

   2. Taylor expanded in A around -inf

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

      1. lower-atan.f64 N/A

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

      2. lower-/.f64 N/A

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

   4. Applied rewrites 77.3%

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

   5. Taylor expanded in B around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 38.1

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

   7. Applied rewrites 38.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 38.1%

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

   if -1.6999999999999999e125 < A

   1. Initial program 53.6%

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

   2. Taylor expanded in A around -inf

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

      1. lower-atan.f64 N/A

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

      2. lower-/.f64 N/A

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

   4. Applied rewrites 77.3%

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

Alternative 2: 74.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.7 \cdot 10^{+125}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C - A} \cdot -0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 3.6 \cdot 10^{-80}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(\frac{C}{B} - 1\right) - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.7e+125)
   (/ (* 180.0 (atan (* (/ B (- C A)) -0.5))) PI)
   (if (<= A 3.6e-80)
     (* 180.0 (/ (atan (/ (- C (hypot C B)) B)) PI))
     (* 180.0 (/ (atan (- (- (/ C B) 1.0) (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.7e+125) {
		tmp = (180.0 * atan(((B / (C - A)) * -0.5))) / ((double) M_PI);
	} else if (A <= 3.6e-80) {
		tmp = 180.0 * (atan(((C - hypot(C, B)) / 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 (A <= -1.7e+125) {
		tmp = (180.0 * Math.atan(((B / (C - A)) * -0.5))) / Math.PI;
	} else if (A <= 3.6e-80) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B)) / 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 A <= -1.7e+125:
		tmp = (180.0 * math.atan(((B / (C - A)) * -0.5))) / math.pi
	elif A <= 3.6e-80:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B)) / 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 (A <= -1.7e+125)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / Float64(C - A)) * -0.5))) / pi);
	elseif (A <= 3.6e-80)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C / B) - 1.0) - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.7e+125)
		tmp = (180.0 * atan(((B / (C - A)) * -0.5))) / pi;
	elseif (A <= 3.6e-80)
		tmp = 180.0 * (atan(((C - hypot(C, B)) / 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[A, -1.7e+125], N[(N[(180.0 * N[ArcTan[N[(N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 3.6e-80], 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[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision] - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.6999999999999999e125

   1. Initial program 53.6%

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

   2. Taylor expanded in A around -inf

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

      1. lower-atan.f64 N/A

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

      2. lower-/.f64 N/A

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

   4. Applied rewrites 77.3%

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

   5. Taylor expanded in B around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 38.1

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

   7. Applied rewrites 38.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 38.1%

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

   if -1.6999999999999999e125 < A < 3.6e-80

   1. Initial program 53.6%

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

   2. Taylor expanded in A around -inf

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

      1. lower-atan.f64 N/A

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

      2. lower-/.f64 N/A

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

   4. Applied rewrites 77.3%

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

   5. Taylor expanded in A around 0

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

   7. Applied rewrites 71.2%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 62.6%

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

   if 3.6e-80 < A

   1. Initial program 53.6%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 49.0

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

   4. Applied rewrites 49.0%

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

Alternative 3: 61.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.9 \cdot 10^{+118}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C - A} \cdot -0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(\frac{C}{B} - 1\right) - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.9e+118)
   (/ (* 180.0 (atan (* (/ B (- C A)) -0.5))) PI)
   (* 180.0 (/ (atan (- (- (/ C B) 1.0) (/ A B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.9e+118) {
		tmp = (180.0 * atan(((B / (C - A)) * -0.5))) / ((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 (A <= -4.9e+118) {
		tmp = (180.0 * Math.atan(((B / (C - A)) * -0.5))) / 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 A <= -4.9e+118:
		tmp = (180.0 * math.atan(((B / (C - A)) * -0.5))) / 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 (A <= -4.9e+118)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / Float64(C - A)) * -0.5))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C / B) - 1.0) - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.9e+118)
		tmp = (180.0 * atan(((B / (C - A)) * -0.5))) / 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[A, -4.9e+118], N[(N[(180.0 * N[ArcTan[N[(N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision] - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -4.9000000000000003e118

   1. Initial program 53.6%

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

   2. Taylor expanded in A around -inf

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

      1. lower-atan.f64 N/A

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

      2. lower-/.f64 N/A

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

   4. Applied rewrites 77.3%

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

   5. Taylor expanded in B around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 38.1

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

   7. Applied rewrites 38.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 38.1%

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

   if -4.9000000000000003e118 < A

   1. Initial program 53.6%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 49.0

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

   4. Applied rewrites 49.0%

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

Alternative 4: 60.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{+54}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{C - A} \cdot -0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.42 \cdot 10^{-93}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.35e+54)
   (/ (* 180.0 (atan (* (/ B (- C A)) -0.5))) PI)
   (if (<= A 1.42e-93)
     (* 180.0 (/ (atan (- (/ C B) 1.0)) PI))
     (/ (* 180.0 (atan (/ (- (- A) B) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e+54) {
		tmp = (180.0 * atan(((B / (C - A)) * -0.5))) / ((double) M_PI);
	} else if (A <= 1.42e-93) {
		tmp = 180.0 * (atan(((C / B) - 1.0)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((-A - B) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e+54) {
		tmp = (180.0 * Math.atan(((B / (C - A)) * -0.5))) / Math.PI;
	} else if (A <= 1.42e-93) {
		tmp = 180.0 * (Math.atan(((C / B) - 1.0)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((-A - B) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.35e+54:
		tmp = (180.0 * math.atan(((B / (C - A)) * -0.5))) / math.pi
	elif A <= 1.42e-93:
		tmp = 180.0 * (math.atan(((C / B) - 1.0)) / math.pi)
	else:
		tmp = (180.0 * math.atan(((-A - B) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.35e+54)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / Float64(C - A)) * -0.5))) / pi);
	elseif (A <= 1.42e-93)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) - 1.0)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(-A) - B) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.35e+54)
		tmp = (180.0 * atan(((B / (C - A)) * -0.5))) / pi;
	elseif (A <= 1.42e-93)
		tmp = 180.0 * (atan(((C / B) - 1.0)) / pi);
	else
		tmp = (180.0 * atan(((-A - B) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.35e+54], N[(N[(180.0 * N[ArcTan[N[(N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.42e-93], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[((-A) - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.35000000000000005e54

   1. Initial program 53.6%

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

   2. Taylor expanded in A around -inf

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

      1. lower-atan.f64 N/A

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

      2. lower-/.f64 N/A

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

   4. Applied rewrites 77.3%

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

   5. Taylor expanded in B around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 38.1

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

   7. Applied rewrites 38.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 38.1%

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

   if -1.35000000000000005e54 < A < 1.4199999999999999e-93

   1. Initial program 53.6%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 49.0

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

   4. Applied rewrites 49.0%

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

   5. Taylor expanded in A around 0

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 38.5

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

   7. Applied rewrites 38.5%

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

   if 1.4199999999999999e-93 < A

   1. Initial program 53.6%

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

   2. Taylor expanded in C around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-fma.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 44.7

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

   4. Applied rewrites 44.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 44.7

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

   6. Applied rewrites 44.7%

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

   7. Taylor expanded in A around 0

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

      1. mul-1-neg N/A

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

      2. lower--.f64 N/A

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

      3. lower-neg.f64 39.1

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

   9. Applied rewrites 39.1%

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

Alternative 5: 60.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.05 \cdot 10^{+54}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.42 \cdot 10^{-93}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.05e+54)
   (/ (* 180.0 (atan (* (/ B A) 0.5))) PI)
   (if (<= A 1.42e-93)
     (* 180.0 (/ (atan (- (/ C B) 1.0)) PI))
     (/ (* 180.0 (atan (/ (- (- A) B) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.05e+54) {
		tmp = (180.0 * atan(((B / A) * 0.5))) / ((double) M_PI);
	} else if (A <= 1.42e-93) {
		tmp = 180.0 * (atan(((C / B) - 1.0)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((-A - B) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.05e+54) {
		tmp = (180.0 * Math.atan(((B / A) * 0.5))) / Math.PI;
	} else if (A <= 1.42e-93) {
		tmp = 180.0 * (Math.atan(((C / B) - 1.0)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((-A - B) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.05e+54:
		tmp = (180.0 * math.atan(((B / A) * 0.5))) / math.pi
	elif A <= 1.42e-93:
		tmp = 180.0 * (math.atan(((C / B) - 1.0)) / math.pi)
	else:
		tmp = (180.0 * math.atan(((-A - B) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.05e+54)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	elseif (A <= 1.42e-93)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) - 1.0)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(-A) - B) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.05e+54)
		tmp = (180.0 * atan(((B / A) * 0.5))) / pi;
	elseif (A <= 1.42e-93)
		tmp = 180.0 * (atan(((C / B) - 1.0)) / pi);
	else
		tmp = (180.0 * atan(((-A - B) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.05e+54], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.42e-93], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[((-A) - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.04999999999999984e54

   1. Initial program 53.6%

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

   2. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 26.5

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

   4. Applied rewrites 26.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 26.5

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

   6. Applied rewrites 26.5%

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

   if -2.04999999999999984e54 < A < 1.4199999999999999e-93

   1. Initial program 53.6%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 49.0

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

   4. Applied rewrites 49.0%

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

   5. Taylor expanded in A around 0

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 38.5

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

   7. Applied rewrites 38.5%

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

   if 1.4199999999999999e-93 < A

   1. Initial program 53.6%

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

   2. Taylor expanded in C around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-fma.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 44.7

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

   4. Applied rewrites 44.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 44.7

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

   6. Applied rewrites 44.7%

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

   7. Taylor expanded in A around 0

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

      1. mul-1-neg N/A

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

      2. lower--.f64 N/A

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

      3. lower-neg.f64 39.1

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

   9. Applied rewrites 39.1%

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

Alternative 6: 57.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.05 \cdot 10^{+54}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.05e+54)
   (/ (* 180.0 (atan (* (/ B A) 0.5))) PI)
   (if (<= A 5e+72)
     (* 180.0 (/ (atan (- (/ C B) 1.0)) PI))
     (* (/ (atan (* (/ A B) -2.0)) PI) 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.05e+54) {
		tmp = (180.0 * atan(((B / A) * 0.5))) / ((double) M_PI);
	} else if (A <= 5e+72) {
		tmp = 180.0 * (atan(((C / B) - 1.0)) / ((double) M_PI));
	} else {
		tmp = (atan(((A / B) * -2.0)) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.05e+54) {
		tmp = (180.0 * Math.atan(((B / A) * 0.5))) / Math.PI;
	} else if (A <= 5e+72) {
		tmp = 180.0 * (Math.atan(((C / B) - 1.0)) / Math.PI);
	} else {
		tmp = (Math.atan(((A / B) * -2.0)) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.05e+54:
		tmp = (180.0 * math.atan(((B / A) * 0.5))) / math.pi
	elif A <= 5e+72:
		tmp = 180.0 * (math.atan(((C / B) - 1.0)) / math.pi)
	else:
		tmp = (math.atan(((A / B) * -2.0)) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.05e+54)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B / A) * 0.5))) / pi);
	elseif (A <= 5e+72)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) - 1.0)) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(A / B) * -2.0)) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.05e+54)
		tmp = (180.0 * atan(((B / A) * 0.5))) / pi;
	elseif (A <= 5e+72)
		tmp = 180.0 * (atan(((C / B) - 1.0)) / pi);
	else
		tmp = (atan(((A / B) * -2.0)) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.05e+54], N[(N[(180.0 * N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 5e+72], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.04999999999999984e54

   1. Initial program 53.6%

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

   2. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 26.5

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

   4. Applied rewrites 26.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 26.5

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

   6. Applied rewrites 26.5%

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

   if -2.04999999999999984e54 < A < 4.99999999999999992e72

   1. Initial program 53.6%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 49.0

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

   4. Applied rewrites 49.0%

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

   5. Taylor expanded in A around 0

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 38.5

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

   7. Applied rewrites 38.5%

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

   if 4.99999999999999992e72 < A

   1. Initial program 53.6%

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

   2. Taylor expanded in A around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 23.6

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

   4. Applied rewrites 23.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 23.6

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

   6. Applied rewrites 23.6%

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

Alternative 7: 57.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.05 \cdot 10^{+54}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi} \cdot 180\\ \mathbf{elif}\;A \leq 5 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.05e+54)
   (* (/ (atan (* (/ B A) 0.5)) PI) 180.0)
   (if (<= A 5e+72)
     (* 180.0 (/ (atan (- (/ C B) 1.0)) PI))
     (* (/ (atan (* (/ A B) -2.0)) PI) 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.05e+54) {
		tmp = (atan(((B / A) * 0.5)) / ((double) M_PI)) * 180.0;
	} else if (A <= 5e+72) {
		tmp = 180.0 * (atan(((C / B) - 1.0)) / ((double) M_PI));
	} else {
		tmp = (atan(((A / B) * -2.0)) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.05e+54) {
		tmp = (Math.atan(((B / A) * 0.5)) / Math.PI) * 180.0;
	} else if (A <= 5e+72) {
		tmp = 180.0 * (Math.atan(((C / B) - 1.0)) / Math.PI);
	} else {
		tmp = (Math.atan(((A / B) * -2.0)) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.05e+54:
		tmp = (math.atan(((B / A) * 0.5)) / math.pi) * 180.0
	elif A <= 5e+72:
		tmp = 180.0 * (math.atan(((C / B) - 1.0)) / math.pi)
	else:
		tmp = (math.atan(((A / B) * -2.0)) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.05e+54)
		tmp = Float64(Float64(atan(Float64(Float64(B / A) * 0.5)) / pi) * 180.0);
	elseif (A <= 5e+72)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) - 1.0)) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(A / B) * -2.0)) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.05e+54)
		tmp = (atan(((B / A) * 0.5)) / pi) * 180.0;
	elseif (A <= 5e+72)
		tmp = 180.0 * (atan(((C / B) - 1.0)) / pi);
	else
		tmp = (atan(((A / B) * -2.0)) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.05e+54], N[(N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[A, 5e+72], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.04999999999999984e54

   1. Initial program 53.6%

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

   2. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 26.5

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

   4. Applied rewrites 26.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 26.5

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

   6. Applied rewrites 26.5%

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

   if -2.04999999999999984e54 < A < 4.99999999999999992e72

   1. Initial program 53.6%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 49.0

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

   4. Applied rewrites 49.0%

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

   5. Taylor expanded in A around 0

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 38.5

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

   7. Applied rewrites 38.5%

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

   if 4.99999999999999992e72 < A

   1. Initial program 53.6%

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

   2. Taylor expanded in A around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 23.6

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

   4. Applied rewrites 23.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 23.6

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

   6. Applied rewrites 23.6%

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

Alternative 8: 45.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq 5 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A 5e+72)
   (* 180.0 (/ (atan (- (/ C B) 1.0)) PI))
   (* (/ (atan (* (/ A B) -2.0)) PI) 180.0)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= 5e+72) {
		tmp = 180.0 * (atan(((C / B) - 1.0)) / ((double) M_PI));
	} else {
		tmp = (atan(((A / B) * -2.0)) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= 5e+72) {
		tmp = 180.0 * (Math.atan(((C / B) - 1.0)) / Math.PI);
	} else {
		tmp = (Math.atan(((A / B) * -2.0)) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= 5e+72:
		tmp = 180.0 * (math.atan(((C / B) - 1.0)) / math.pi)
	else:
		tmp = (math.atan(((A / B) * -2.0)) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= 5e+72)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) - 1.0)) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(A / B) * -2.0)) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= 5e+72)
		tmp = 180.0 * (atan(((C / B) - 1.0)) / pi);
	else
		tmp = (atan(((A / B) * -2.0)) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, 5e+72], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < 4.99999999999999992e72

   1. Initial program 53.6%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 49.0

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

   4. Applied rewrites 49.0%

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

   5. Taylor expanded in A around 0

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 38.5

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

   7. Applied rewrites 38.5%

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

   if 4.99999999999999992e72 < A

   1. Initial program 53.6%

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

   2. Taylor expanded in A around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 23.6

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

   4. Applied rewrites 23.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 23.6

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

   6. Applied rewrites 23.6%

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

Alternative 9: 45.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq 5 \cdot 10^{+72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A 5e+72)
   (* 180.0 (/ (atan (- (/ C B) 1.0)) PI))
   (* (/ (atan (/ (- A) B)) PI) 180.0)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= 5e+72) {
		tmp = 180.0 * (atan(((C / B) - 1.0)) / ((double) M_PI));
	} else {
		tmp = (atan((-A / B)) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= 5e+72) {
		tmp = 180.0 * (Math.atan(((C / B) - 1.0)) / Math.PI);
	} else {
		tmp = (Math.atan((-A / B)) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= 5e+72:
		tmp = 180.0 * (math.atan(((C / B) - 1.0)) / math.pi)
	else:
		tmp = (math.atan((-A / B)) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= 5e+72)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) - 1.0)) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(-A) / B)) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= 5e+72)
		tmp = 180.0 * (atan(((C / B) - 1.0)) / pi);
	else
		tmp = (atan((-A / B)) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, 5e+72], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < 4.99999999999999992e72

   1. Initial program 53.6%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 49.0

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

   4. Applied rewrites 49.0%

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

   5. Taylor expanded in A around 0

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 38.5

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

   7. Applied rewrites 38.5%

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

   if 4.99999999999999992e72 < A

   1. Initial program 53.6%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 49.0

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

   4. Applied rewrites 49.0%

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

   5. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 23.5

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

   7. Applied rewrites 23.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 23.5

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

   9. Applied rewrites 23.5%

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

Alternative 10: 33.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -7.5 \cdot 10^{-34}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -7.5e-34)
   (* 180.0 (/ (atan (/ C B)) PI))
   (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -7.5e-34) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -7.5e-34) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -7.5e-34:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -7.5e-34)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -7.5e-34)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -7.5e-34], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < -7.5000000000000004e-34

   1. Initial program 53.6%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 49.0

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

   4. Applied rewrites 49.0%

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

   5. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 23.5

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

   7. Applied rewrites 23.5%

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

   8. Taylor expanded in C around inf

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

      1. lower-/.f64 22.9

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

   10. Applied rewrites 22.9%

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

   if -7.5000000000000004e-34 < C

   1. Initial program 53.6%

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

   2. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
   3. Step-by-step derivation

   4. Applied rewrites 20.8%

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

Alternative 11: 20.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ 180 \cdot \frac{\tan^{-1} -1}{\pi} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 53.6%

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

2. Taylor expanded in B around inf

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\pi} \]
3. Step-by-step derivation

4. Applied rewrites 20.8%

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

Reproduce

herbie shell --seed 2025131 
(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)))