ABCF->ab-angle angle

Percentage Accurate: 53.6% → 79.4%

Time: 5.6s

Alternatives: 15

Speedup: 2.4×

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: 79.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.7 \cdot 10^{-19}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{-0.5 \cdot \left(B + B \cdot \frac{C}{A}\right)}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\left(\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)\right) \cdot {B}^{-1}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.7e-19)
   (* 180.0 (/ (atan (- (/ (* -0.5 (+ B (* B (/ C A)))) A))) PI))
   (/ (* 180.0 (atan (* (- (- C A) (hypot (- A C) B)) (pow B -1.0)))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.7e-19) {
		tmp = 180.0 * (atan(-((-0.5 * (B + (B * (C / A)))) / A)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) * pow(B, -1.0)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.7e-19) {
		tmp = 180.0 * (Math.atan(-((-0.5 * (B + (B * (C / A)))) / A)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((((C - A) - Math.hypot((A - C), B)) * Math.pow(B, -1.0)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.7e-19:
		tmp = 180.0 * (math.atan(-((-0.5 * (B + (B * (C / A)))) / A)) / math.pi)
	else:
		tmp = (180.0 * math.atan((((C - A) - math.hypot((A - C), B)) * math.pow(B, -1.0)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.7e-19)
		tmp = Float64(180.0 * Float64(atan(Float64(-Float64(Float64(-0.5 * Float64(B + Float64(B * Float64(C / A)))) / A))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) * (B ^ -1.0)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.7e-19)
		tmp = 180.0 * (atan(-((-0.5 * (B + (B * (C / A)))) / A)) / pi);
	else
		tmp = (180.0 * atan((((C - A) - hypot((A - C), B)) * (B ^ -1.0)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.7e-19], N[(180.0 * N[(N[ArcTan[(-N[(N[(-0.5 * N[(B + N[(B * N[(C / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision])], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] * N[Power[B, -1.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.7000000000000001e-19

   1. Initial program 25.9%

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

   2. Taylor expanded in A around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-lft-out N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 64.7

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

   4. Applied rewrites 64.7%

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

   if -1.7000000000000001e-19 < A

   1. Initial program 63.9%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 84.9%

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

Alternative 2: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-8}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - B\right)\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -1e-8)
     (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) B))) PI))
     (if (<= t_0 0.0)
       (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
       (/ (* 180.0 (atan (+ 1.0 (/ (- C A) B)))) PI)))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -1e-8) {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / ((double) M_PI));
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((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 t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_0 <= -1e-8) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - B))) / Math.PI);
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((1.0 + ((C - A) / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_0 <= -1e-8:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C - A) - B))) / math.pi)
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	else:
		tmp = (180.0 * math.atan((1.0 + ((C - A) / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_0 <= -1e-8)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - B))) / pi));
	elseif (t_0 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(Float64(C - A) / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -1e-8)
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / pi);
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	else
		tmp = (180.0 * atan((1.0 + ((C - A) / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-8], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $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)))))) < -1e-8

   1. Initial program 59.4%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 75.6%

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

   if -1e-8 < (*.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 17.8%

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

   2. 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 51.1

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

   4. Applied rewrites 51.1%

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

   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 59.0%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 87.3%

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

   4. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 76.7

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

   6. Applied rewrites 76.7%

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

Alternative 3: 75.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -6.1 \cdot 10^{+82}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - B\right)\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.8 \cdot 10^{+43}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-\frac{\mathsf{hypot}\left(B, A\right) + A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C} + A \cdot \frac{B}{C \cdot C}, \frac{0}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -6.1e+82)
   (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) B))) PI))
   (if (<= C 1.8e+43)
     (/ (* 180.0 (atan (- (/ (+ (hypot B A) A) B)))) PI)
     (/
      (* 180.0 (atan (fma -0.5 (+ (/ B C) (* A (/ B (* C C)))) (/ 0.0 B))))
      PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -6.1e+82) {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / ((double) M_PI));
	} else if (C <= 1.8e+43) {
		tmp = (180.0 * atan(-((hypot(B, A) + A) / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(fma(-0.5, ((B / C) + (A * (B / (C * C)))), (0.0 / B)))) / ((double) M_PI);
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -6.1e+82)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - B))) / pi));
	elseif (C <= 1.8e+43)
		tmp = Float64(Float64(180.0 * atan(Float64(-Float64(Float64(hypot(B, A) + A) / B)))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(fma(-0.5, Float64(Float64(B / C) + Float64(A * Float64(B / Float64(C * C)))), Float64(0.0 / B)))) / pi);
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -6.1e+82], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.8e+43], N[(N[(180.0 * N[ArcTan[(-N[(N[(N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision] + A), $MachinePrecision] / B), $MachinePrecision])], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(N[(B / C), $MachinePrecision] + N[(A * N[(B / N[(C * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0 / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -6.0999999999999999e82

   1. Initial program 79.6%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 82.8%

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

   if -6.0999999999999999e82 < C < 1.80000000000000005e43

   1. Initial program 57.0%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 80.1%

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

   4. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. pow2 N/A

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

      8. unpow2 N/A

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

      9. lower-hypot.f64 75.1

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

   6. Applied rewrites 75.1%

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

   if 1.80000000000000005e43 < C

   1. Initial program 22.5%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 55.8%

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

   4. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt1-in N/A

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

      5. metadata-eval N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \left(\frac{B}{C} + \frac{A \cdot B}{{C}^{2}}\right) + \left(\mathsf{neg}\left(\frac{0 \cdot A}{B}\right)\right)\right)}{\pi} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \left(\frac{B}{C} + \frac{A \cdot B}{{C}^{2}}\right) + \left(\mathsf{neg}\left(\frac{0 \cdot A}{B}\right)\right)\right)}{\pi} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \left(\frac{B}{C} + \frac{A \cdot B}{{C}^{2}}\right) + \left(\mathsf{neg}\left(\frac{0 \cdot A}{B}\right)\right)\right)}{\pi} \]

      8. lift-neg.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \left(\frac{B}{C} + \frac{A \cdot B}{{C}^{2}}\right) + \left(-\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      9. lower-fma.f64 N/A

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

   6. Applied rewrites 70.2%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\mathsf{fma}\left(-0.5, \frac{B}{C} + A \cdot \frac{B}{C \cdot C}, \frac{0}{B}\right)\right)}}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 75.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -6.1 \cdot 10^{+82}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - B\right)\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.8 \cdot 10^{+43}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-\frac{\mathsf{hypot}\left(A, B\right) + A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C} + A \cdot \frac{B}{C \cdot C}, \frac{0}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -6.1e+82)
   (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) B))) PI))
   (if (<= C 1.8e+43)
     (* 180.0 (/ (atan (- (/ (+ (hypot A B) A) B))) PI))
     (/
      (* 180.0 (atan (fma -0.5 (+ (/ B C) (* A (/ B (* C C)))) (/ 0.0 B))))
      PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -6.1e+82) {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / ((double) M_PI));
	} else if (C <= 1.8e+43) {
		tmp = 180.0 * (atan(-((hypot(A, B) + A) / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(fma(-0.5, ((B / C) + (A * (B / (C * C)))), (0.0 / B)))) / ((double) M_PI);
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -6.1e+82)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - B))) / pi));
	elseif (C <= 1.8e+43)
		tmp = Float64(180.0 * Float64(atan(Float64(-Float64(Float64(hypot(A, B) + A) / B))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(fma(-0.5, Float64(Float64(B / C) + Float64(A * Float64(B / Float64(C * C)))), Float64(0.0 / B)))) / pi);
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -6.1e+82], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.8e+43], N[(180.0 * N[(N[ArcTan[(-N[(N[(N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision] + A), $MachinePrecision] / B), $MachinePrecision])], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(N[(B / C), $MachinePrecision] + N[(A * N[(B / N[(C * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0 / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -6.0999999999999999e82

   1. Initial program 79.6%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 82.8%

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

   if -6.0999999999999999e82 < C < 1.80000000000000005e43

   1. Initial program 57.0%

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

   2. 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. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. unpow2 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 75.1

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

   4. Applied rewrites 75.1%

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

   if 1.80000000000000005e43 < C

   1. Initial program 22.5%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 55.8%

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

   4. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt1-in N/A

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

      5. metadata-eval N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \left(\frac{B}{C} + \frac{A \cdot B}{{C}^{2}}\right) + \left(\mathsf{neg}\left(\frac{0 \cdot A}{B}\right)\right)\right)}{\pi} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \left(\frac{B}{C} + \frac{A \cdot B}{{C}^{2}}\right) + \left(\mathsf{neg}\left(\frac{0 \cdot A}{B}\right)\right)\right)}{\pi} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \left(\frac{B}{C} + \frac{A \cdot B}{{C}^{2}}\right) + \left(\mathsf{neg}\left(\frac{0 \cdot A}{B}\right)\right)\right)}{\pi} \]

      8. lift-neg.f64 N/A

         \[\leadsto \frac{180 \cdot \tan^{-1} \left(\frac{-1}{2} \cdot \left(\frac{B}{C} + \frac{A \cdot B}{{C}^{2}}\right) + \left(-\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      9. lower-fma.f64 N/A

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

   6. Applied rewrites 70.2%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\mathsf{fma}\left(-0.5, \frac{B}{C} + A \cdot \frac{B}{C \cdot C}, \frac{0}{B}\right)\right)}}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 51.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -4.8 \cdot 10^{+82}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -8.2 \cdot 10^{-13}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;C \leq -3.5 \cdot 10^{-306}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.8 \cdot 10^{-115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -4.8e+82)
   (* 180.0 (/ (atan (/ C B)) PI))
   (if (<= C -8.2e-13)
     (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
     (if (<= C -3.5e-306)
       (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI)
       (if (<= C 4.8e-115)
         (* 180.0 (/ (atan 1.0) PI))
         (* 180.0 (/ (atan (* (/ B C) -0.5)) PI)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.8e+82) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (C <= -8.2e-13) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((double) M_PI));
	} else if (C <= -3.5e-306) {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	} else if (C <= 4.8e-115) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B / C) * -0.5)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.8e+82) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (C <= -8.2e-13) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else if (C <= -3.5e-306) {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	} else if (C <= 4.8e-115) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B / C) * -0.5)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -4.8e+82:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif C <= -8.2e-13:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	elif C <= -3.5e-306:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	elif C <= 4.8e-115:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B / C) * -0.5)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -4.8e+82)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (C <= -8.2e-13)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	elseif (C <= -3.5e-306)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	elseif (C <= 4.8e-115)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / C) * -0.5)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -4.8e+82)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (C <= -8.2e-13)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	elseif (C <= -3.5e-306)
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	elseif (C <= 4.8e-115)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(((B / C) * -0.5)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -4.8e+82], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -8.2e-13], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -3.5e-306], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 4.8e-115], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if C < -4.79999999999999996e82

   1. Initial program 79.7%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 95.4%

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

   4. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 80.2

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

   6. Applied rewrites 80.2%

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

   7. Taylor expanded in C around inf

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

      1. lift-/.f64 75.1

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

   9. Applied rewrites 75.1%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 75.1

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

   11. Applied rewrites 75.1%

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

   if -4.79999999999999996e82 < C < -8.2000000000000004e-13

   1. Initial program 65.8%

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

   2. 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 28.0

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

   4. Applied rewrites 28.0%

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

   if -8.2000000000000004e-13 < C < -3.50000000000000018e-306

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 83.5%

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

   4. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 53.8

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

   6. Applied rewrites 53.8%

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

   7. Taylor expanded in B around inf

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

   9. Applied rewrites 48.6%

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

   if -3.50000000000000018e-306 < C < 4.80000000000000042e-115

   1. Initial program 56.5%

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

   2. Taylor expanded in B around -inf

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

   4. Applied rewrites 29.5%

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

   if 4.80000000000000042e-115 < C

   1. Initial program 31.6%

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

   2. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 56.2

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   4. Applied rewrites 56.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}}{\pi} \]

   5. Taylor expanded in A around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 56.2

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

   7. Applied rewrites 56.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{B}{C} \cdot \color{blue}{-0.5}\right)}{\pi} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 6: 52.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -5 \cdot 10^{-73}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;C \leq -3.5 \cdot 10^{-306}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.8 \cdot 10^{-115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -5e-73)
   (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
   (if (<= C -3.5e-306)
     (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI)
     (if (<= C 4.8e-115)
       (* 180.0 (/ (atan 1.0) PI))
       (/ (* 180.0 (atan (* -0.5 (/ B C)))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -5e-73) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	} else if (C <= -3.5e-306) {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	} else if (C <= 4.8e-115) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((-0.5 * (B / C)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -5e-73) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else if (C <= -3.5e-306) {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	} else if (C <= 4.8e-115) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((-0.5 * (B / C)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -5e-73:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	elif C <= -3.5e-306:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	elif C <= 4.8e-115:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = (180.0 * math.atan((-0.5 * (B / C)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -5e-73)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	elseif (C <= -3.5e-306)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	elseif (C <= 4.8e-115)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-0.5 * Float64(B / C)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -5e-73)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	elseif (C <= -3.5e-306)
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	elseif (C <= 4.8e-115)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = (180.0 * atan((-0.5 * (B / C)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -5e-73], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -3.5e-306], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 4.8e-115], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -4.9999999999999998e-73

   1. Initial program 73.9%

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

   2. Taylor expanded in C around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 61.2

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

   4. Applied rewrites 61.2%

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

   if -4.9999999999999998e-73 < C < -3.50000000000000018e-306

   1. Initial program 59.3%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 83.1%

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

   4. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 52.1

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

   6. Applied rewrites 52.1%

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

   7. Taylor expanded in B around inf

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

   9. Applied rewrites 49.0%

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

   if -3.50000000000000018e-306 < C < 4.80000000000000042e-115

   1. Initial program 56.5%

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

   2. Taylor expanded in B around -inf

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

   4. Applied rewrites 29.5%

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

   if 4.80000000000000042e-115 < C

   1. Initial program 31.6%

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

   2. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 56.2

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   4. Applied rewrites 56.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}}{\pi} \]

   5. Taylor expanded in A around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 56.2

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

   7. Applied rewrites 56.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 56.2%

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

Alternative 7: 52.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -5 \cdot 10^{-73}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} \cdot 2\right)}{\pi}\\ \mathbf{elif}\;C \leq -3.5 \cdot 10^{-306}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.8 \cdot 10^{-115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -5e-73)
   (* 180.0 (/ (atan (* (/ C B) 2.0)) PI))
   (if (<= C -3.5e-306)
     (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI)
     (if (<= C 4.8e-115)
       (* 180.0 (/ (atan 1.0) PI))
       (* 180.0 (/ (atan (* (/ B C) -0.5)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -5e-73) {
		tmp = 180.0 * (atan(((C / B) * 2.0)) / ((double) M_PI));
	} else if (C <= -3.5e-306) {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	} else if (C <= 4.8e-115) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B / C) * -0.5)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -5e-73) {
		tmp = 180.0 * (Math.atan(((C / B) * 2.0)) / Math.PI);
	} else if (C <= -3.5e-306) {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	} else if (C <= 4.8e-115) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B / C) * -0.5)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -5e-73:
		tmp = 180.0 * (math.atan(((C / B) * 2.0)) / math.pi)
	elif C <= -3.5e-306:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	elif C <= 4.8e-115:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B / C) * -0.5)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -5e-73)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) * 2.0)) / pi));
	elseif (C <= -3.5e-306)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	elseif (C <= 4.8e-115)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / C) * -0.5)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -5e-73)
		tmp = 180.0 * (atan(((C / B) * 2.0)) / pi);
	elseif (C <= -3.5e-306)
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	elseif (C <= 4.8e-115)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(((B / C) * -0.5)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -5e-73], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] * 2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -3.5e-306], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 4.8e-115], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -4.9999999999999998e-73

   1. Initial program 73.9%

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

   2. Taylor expanded in C around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 61.2

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

   4. Applied rewrites 61.2%

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

   if -4.9999999999999998e-73 < C < -3.50000000000000018e-306

   1. Initial program 59.3%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 83.1%

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

   4. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 52.1

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

   6. Applied rewrites 52.1%

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

   7. Taylor expanded in B around inf

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

   9. Applied rewrites 49.0%

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

   if -3.50000000000000018e-306 < C < 4.80000000000000042e-115

   1. Initial program 56.5%

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

   2. Taylor expanded in B around -inf

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

   4. Applied rewrites 29.5%

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

   if 4.80000000000000042e-115 < C

   1. Initial program 31.6%

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

   2. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 56.2

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   4. Applied rewrites 56.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}}{\pi} \]

   5. Taylor expanded in A around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 56.2

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

   7. Applied rewrites 56.2%

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

Alternative 8: 52.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -5 \cdot 10^{-73}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq -3.5 \cdot 10^{-306}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.8 \cdot 10^{-115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -5e-73)
   (* 180.0 (/ (atan (/ C B)) PI))
   (if (<= C -3.5e-306)
     (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI)
     (if (<= C 4.8e-115)
       (* 180.0 (/ (atan 1.0) PI))
       (* 180.0 (/ (atan (* (/ B C) -0.5)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -5e-73) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (C <= -3.5e-306) {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	} else if (C <= 4.8e-115) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B / C) * -0.5)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -5e-73) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (C <= -3.5e-306) {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	} else if (C <= 4.8e-115) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B / C) * -0.5)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -5e-73:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif C <= -3.5e-306:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	elif C <= 4.8e-115:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B / C) * -0.5)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -5e-73)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (C <= -3.5e-306)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	elseif (C <= 4.8e-115)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / C) * -0.5)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -5e-73)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (C <= -3.5e-306)
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	elseif (C <= 4.8e-115)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(((B / C) * -0.5)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -5e-73], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, -3.5e-306], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 4.8e-115], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -4.9999999999999998e-73

   1. Initial program 73.9%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 92.2%

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

   4. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 73.0

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

   6. Applied rewrites 73.0%

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

   7. Taylor expanded in C around inf

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

      1. lift-/.f64 60.8

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

   9. Applied rewrites 60.8%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 60.8

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

   11. Applied rewrites 60.8%

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

   if -4.9999999999999998e-73 < C < -3.50000000000000018e-306

   1. Initial program 59.3%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 83.1%

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

   4. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 52.1

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

   6. Applied rewrites 52.1%

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

   7. Taylor expanded in B around inf

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

   9. Applied rewrites 49.0%

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

   if -3.50000000000000018e-306 < C < 4.80000000000000042e-115

   1. Initial program 56.5%

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

   2. Taylor expanded in B around -inf

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

   4. Applied rewrites 29.5%

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

   if 4.80000000000000042e-115 < C

   1. Initial program 31.6%

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

   2. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 56.2

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   4. Applied rewrites 56.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}}{\pi} \]

   5. Taylor expanded in A around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 56.2

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

   7. Applied rewrites 56.2%

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

Alternative 9: 46.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.2 \cdot 10^{-23}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.75 \cdot 10^{-283}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-123}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.2e-23)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -1.75e-283)
     (* 180.0 (/ (atan (/ C B)) PI))
     (if (<= B 2.9e-123)
       (/ (* 180.0 (atan (/ 0.0 B))) PI)
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.2e-23) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -1.75e-283) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else if (B <= 2.9e-123) {
		tmp = (180.0 * atan((0.0 / B))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.2e-23) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -1.75e-283) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else if (B <= 2.9e-123) {
		tmp = (180.0 * Math.atan((0.0 / B))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.2e-23:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -1.75e-283:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	elif B <= 2.9e-123:
		tmp = (180.0 * math.atan((0.0 / B))) / math.pi
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.2e-23)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -1.75e-283)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	elseif (B <= 2.9e-123)
		tmp = Float64(Float64(180.0 * atan(Float64(0.0 / B))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.2e-23)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -1.75e-283)
		tmp = 180.0 * (atan((C / B)) / pi);
	elseif (B <= 2.9e-123)
		tmp = (180.0 * atan((0.0 / B))) / pi;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.2e-23], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.75e-283], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.9e-123], N[(N[(180.0 * N[ArcTan[N[(0.0 / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -3.19999999999999976e-23

   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. Taylor expanded in B around -inf

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

   4. Applied rewrites 61.7%

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

   if -3.19999999999999976e-23 < B < -1.7499999999999999e-283

   1. Initial program 57.9%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 74.8%

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

   4. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 45.2

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

   6. Applied rewrites 45.2%

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

   7. Taylor expanded in C around inf

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

      1. lift-/.f64 31.4

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

   9. Applied rewrites 31.4%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 31.4

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

   11. Applied rewrites 31.4%

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

   if -1.7499999999999999e-283 < B < 2.90000000000000004e-123

   1. Initial program 59.1%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 81.3%

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

   4. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lift-*.f64 N/A

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

      6. mul0-lft N/A

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

      7. metadata-eval N/A

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

      8. mul0-lft N/A

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

      9. lift-*.f64 N/A

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

      10. lift-/.f64 30.9

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

      11. lift-*.f64 N/A

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

      12. mul0-lft 30.9

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

   6. Applied rewrites 30.9%

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

   if 2.90000000000000004e-123 < B

   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. Taylor expanded in B around inf

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

   4. Applied rewrites 50.3%

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

Alternative 10: 60.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-123}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.1e-18)
   (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
   (if (<= A -8.5e-123)
     (* 180.0 (/ (atan (* (/ B C) -0.5)) PI))
     (/ (* 180.0 (atan (+ 1.0 (/ (- C A) B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.1e-18) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((double) M_PI));
	} else if (A <= -8.5e-123) {
		tmp = 180.0 * (atan(((B / C) * -0.5)) / ((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 <= -2.1e-18) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else if (A <= -8.5e-123) {
		tmp = 180.0 * (Math.atan(((B / C) * -0.5)) / 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 <= -2.1e-18:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	elif A <= -8.5e-123:
		tmp = 180.0 * (math.atan(((B / C) * -0.5)) / 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 <= -2.1e-18)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	elseif (A <= -8.5e-123)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / C) * -0.5)) / pi));
	else
		tmp = Float64(Float64(180.0 * 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 <= -2.1e-18)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	elseif (A <= -8.5e-123)
		tmp = 180.0 * (atan(((B / C) * -0.5)) / 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, -2.1e-18], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -8.5e-123], N[(180.0 * N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.1e-18

   1. Initial program 25.8%

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

   2. 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 63.7

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

   4. Applied rewrites 63.7%

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

   if -2.1e-18 < A < -8.4999999999999995e-123

   1. Initial program 47.0%

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

   2. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 27.2

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   4. Applied rewrites 27.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}}{\pi} \]

   5. Taylor expanded in A around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 27.2

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

   7. Applied rewrites 27.2%

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

   if -8.4999999999999995e-123 < A

   1. Initial program 66.0%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 87.0%

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

   4. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 63.0

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

   6. Applied rewrites 63.0%

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

Alternative 11: 60.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.1 \cdot 10^{-18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.5 \cdot 10^{-123}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.1e-18)
   (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
   (if (<= A -8.5e-123)
     (* 180.0 (/ (atan (* (/ B C) -0.5)) PI))
     (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.1e-18) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((double) M_PI));
	} else if (A <= -8.5e-123) {
		tmp = 180.0 * (atan(((B / C) * -0.5)) / ((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 <= -2.1e-18) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else if (A <= -8.5e-123) {
		tmp = 180.0 * (Math.atan(((B / C) * -0.5)) / 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 <= -2.1e-18:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	elif A <= -8.5e-123:
		tmp = 180.0 * (math.atan(((B / C) * -0.5)) / 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 <= -2.1e-18)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	elseif (A <= -8.5e-123)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / C) * -0.5)) / 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 <= -2.1e-18)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	elseif (A <= -8.5e-123)
		tmp = 180.0 * (atan(((B / C) * -0.5)) / 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, -2.1e-18], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, -8.5e-123], N[(180.0 * N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $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 < -2.1e-18

   1. Initial program 25.8%

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

   2. 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 63.7

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

   4. Applied rewrites 63.7%

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

   if -2.1e-18 < A < -8.4999999999999995e-123

   1. Initial program 47.0%

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

   2. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

      10. lower-*.f64 27.2

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}{\pi} \]

   4. Applied rewrites 27.2%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(\frac{B}{C}, -0.5, -\frac{0 \cdot A}{B}\right)\right)}}{\pi} \]

   5. Taylor expanded in A around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 27.2

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

   7. Applied rewrites 27.2%

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

   if -8.4999999999999995e-123 < A

   1. Initial program 66.0%

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

   2. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 63.0

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

   4. Applied rewrites 63.0%

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

Alternative 12: 51.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.2 \cdot 10^{-23}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-256}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.2e-23)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 8.2e-256)
     (* 180.0 (/ (atan (/ C B)) PI))
     (/ (* 180.0 (atan (- -1.0 (/ A B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.2e-23) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 8.2e-256) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((-1.0 - (A / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.2e-23) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 8.2e-256) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan((-1.0 - (A / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.2e-23:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 8.2e-256:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = (180.0 * math.atan((-1.0 - (A / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.2e-23)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 8.2e-256)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.2e-23)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 8.2e-256)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = (180.0 * atan((-1.0 - (A / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.2e-23], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 8.2e-256], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.19999999999999976e-23

   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. Taylor expanded in B around -inf

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

   4. Applied rewrites 61.7%

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

   if -3.19999999999999976e-23 < B < 8.2e-256

   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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 76.6%

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

   4. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 45.1

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

   6. Applied rewrites 45.1%

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

   7. Taylor expanded in C around inf

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

      1. lift-/.f64 32.5

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

   9. Applied rewrites 32.5%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 32.5

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

   11. Applied rewrites 32.5%

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

   if 8.2e-256 < B

   1. Initial program 52.8%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 76.3%

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

   4. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 66.6

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

   6. Applied rewrites 66.6%

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

   7. Taylor expanded in B around inf

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

   9. Applied rewrites 57.1%

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

Alternative 13: 46.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.2 \cdot 10^{-23}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 4.8 \cdot 10^{-22}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.2e-23)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 4.8e-22)
     (* 180.0 (/ (atan (/ C B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.2e-23) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 4.8e-22) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.2e-23) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 4.8e-22) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.2e-23:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 4.8e-22:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.2e-23)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 4.8e-22)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.2e-23)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 4.8e-22)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.2e-23], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.8e-22], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.19999999999999976e-23

   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. Taylor expanded in B around -inf

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

   4. Applied rewrites 61.7%

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

   if -3.19999999999999976e-23 < B < 4.80000000000000005e-22

   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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

   3. Applied rewrites 75.9%

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

   4. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lower-/.f64 49.0

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

   6. Applied rewrites 49.0%

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

   7. Taylor expanded in C around inf

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

      1. lift-/.f64 31.8

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

   9. Applied rewrites 31.8%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 31.8

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

   11. Applied rewrites 31.8%

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

   if 4.80000000000000005e-22 < B

   1. Initial program 48.8%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 58.0%

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

Alternative 14: 40.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -1.999999999999994e-310

   1. Initial program 53.7%

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

   2. Taylor expanded in B around -inf

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

   4. Applied rewrites 41.1%

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

   if -1.999999999999994e-310 < B

   1. Initial program 53.5%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 39.5%

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

Alternative 15: 20.7% accurate, 3.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 20.7%

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

Reproduce

herbie shell --seed 2025095 
(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)))