ABCF->ab-angle angle

Percentage Accurate: 53.4% → 80.2%

Time: 6.0s

Alternatives: 7

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.4% accurate, 1.0× speedup

Math

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

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: 80.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;C \leq 1.22 \cdot 10^{+17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 1.22e+17)
   (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (hypot (- C A) B)))) PI))
   (* (atan (* -0.5 (/ B C))) (/ 180.0 PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.22e+17) {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((C - A), B)))) / ((double) M_PI));
	} else {
		tmp = atan((-0.5 * (B / C))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.22e+17) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.hypot((C - A), B)))) / Math.PI);
	} else {
		tmp = Math.atan((-0.5 * (B / C))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 1.22e+17:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.hypot((C - A), B)))) / math.pi)
	else:
		tmp = math.atan((-0.5 * (B / C))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 1.22e+17)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - hypot(Float64(C - A), B)))) / pi));
	else
		tmp = Float64(atan(Float64(-0.5 * Float64(B / C))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 1.22e+17)
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((C - A), B)))) / pi);
	else
		tmp = atan((-0.5 * (B / C))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 1.22e+17], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 1.22e17

   1. Initial program 53.4%

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

      1. lift-sqrt.f64 N/A

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

      2. sqrt-fabs-rev N/A

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

      3. lift-sqrt.f64 N/A

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

      4. rem-sqrt-square-rev N/A

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

      5. lift-sqrt.f64 N/A

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

      6. lift-sqrt.f64 N/A

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

      7. rem-square-sqrt N/A

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

      8. lift-+.f64 N/A

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

      9. lift-pow.f64 N/A

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

      10. unpow2 N/A

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

      11. lift-pow.f64 N/A

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

      12. unpow2 N/A

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

      13. sqr-neg-rev N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lift--.f64 N/A

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

      17. lift--.f64 N/A

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

      18. sub-negate-rev N/A

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

      19. lift--.f64 N/A

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

   3. Applied rewrites 77.4%

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

   if 1.22e17 < C

   1. Initial program 53.4%

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

   2. 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. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 26.0%

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

   4. Applied rewrites 26.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 26.0%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, \frac{0}{B}\right)\right) \cdot 180}{\pi}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

   8. Applied rewrites 26.0%

      \[\leadsto \color{blue}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 74.8% accurate, 1.9× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;C \leq 1.22 \cdot 10^{+17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{\left|B\right|} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{\left|B\right|}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= C 1.22e+17)
    (* 180.0 (/ (atan (- (/ (- C A) (fabs B)) 1.0)) PI))
    (* (atan (* -0.5 (/ (fabs B) C))) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.22e+17) {
		tmp = 180.0 * (atan((((C - A) / fabs(B)) - 1.0)) / ((double) M_PI));
	} else {
		tmp = atan((-0.5 * (fabs(B) / C))) * (180.0 / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.22e+17) {
		tmp = 180.0 * (Math.atan((((C - A) / Math.abs(B)) - 1.0)) / Math.PI);
	} else {
		tmp = Math.atan((-0.5 * (Math.abs(B) / C))) * (180.0 / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 1.22e+17:
		tmp = 180.0 * (math.atan((((C - A) / math.fabs(B)) - 1.0)) / math.pi)
	else:
		tmp = math.atan((-0.5 * (math.fabs(B) / C))) * (180.0 / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 1.22e+17)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / abs(B)) - 1.0)) / pi));
	else
		tmp = Float64(atan(Float64(-0.5 * Float64(abs(B) / C))) * Float64(180.0 / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 1.22e+17)
		tmp = 180.0 * (atan((((C - A) / abs(B)) - 1.0)) / pi);
	else
		tmp = atan((-0.5 * (abs(B) / C))) * (180.0 / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[C, 1.22e+17], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(-0.5 * N[(N[Abs[B], $MachinePrecision] / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < 1.22e17

   1. Initial program 53.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip-rev N/A

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

      5. lift--.f64 N/A

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

      6. div-sub N/A

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

      7. mult-flip-rev N/A

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

      8. lift-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. mult-flip-rev N/A

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

      12. lower-/.f64 N/A

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

      13. lower-/.f64 51.2%

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

   3. Applied rewrites 51.2%

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

   4. Taylor expanded in B around inf

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

   6. Applied rewrites 50.4%

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

   if 1.22e17 < C

   1. Initial program 53.4%

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

   2. 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. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 26.0%

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

   4. Applied rewrites 26.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 26.0%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, \frac{0}{B}\right)\right) \cdot 180}{\pi}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

   8. Applied rewrites 26.0%

      \[\leadsto \color{blue}{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 59.2% accurate, 1.8× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq -2100000000000:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\left|B\right|}{A} \cdot 0.5\right)}{\pi} \cdot 180\\ \mathbf{elif}\;A \leq 1.2 \cdot 10^{+57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(-2 \cdot \frac{A}{\left|B\right|}\right)}{\pi} \cdot 180\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= A -2100000000000.0)
    (* (/ (atan (* (/ (fabs B) A) 0.5)) PI) 180.0)
    (if (<= A 1.2e+57)
      (* 180.0 (/ (atan -1.0) PI))
      (* (/ (atan (* -2.0 (/ A (fabs B)))) PI) 180.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2100000000000.0) {
		tmp = (atan(((fabs(B) / A) * 0.5)) / ((double) M_PI)) * 180.0;
	} else if (A <= 1.2e+57) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = (atan((-2.0 * (A / fabs(B)))) / ((double) M_PI)) * 180.0;
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2100000000000.0) {
		tmp = (Math.atan(((Math.abs(B) / A) * 0.5)) / Math.PI) * 180.0;
	} else if (A <= 1.2e+57) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = (Math.atan((-2.0 * (A / Math.abs(B)))) / Math.PI) * 180.0;
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2100000000000.0:
		tmp = (math.atan(((math.fabs(B) / A) * 0.5)) / math.pi) * 180.0
	elif A <= 1.2e+57:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = (math.atan((-2.0 * (A / math.fabs(B)))) / math.pi) * 180.0
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2100000000000.0)
		tmp = Float64(Float64(atan(Float64(Float64(abs(B) / A) * 0.5)) / pi) * 180.0);
	elseif (A <= 1.2e+57)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(Float64(atan(Float64(-2.0 * Float64(A / abs(B)))) / pi) * 180.0);
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2100000000000.0)
		tmp = (atan(((abs(B) / A) * 0.5)) / pi) * 180.0;
	elseif (A <= 1.2e+57)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = (atan((-2.0 * (A / abs(B)))) / pi) * 180.0;
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[A, -2100000000000.0], N[(N[(N[ArcTan[N[(N[(N[Abs[B], $MachinePrecision] / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[A, 1.2e+57], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(-2.0 * N[(A / N[Abs[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -2.1e12

   1. Initial program 53.4%

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

   2. 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. lower-*.f64 N/A

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

      2. lower-/.f64 26.7%

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

   4. Applied rewrites 26.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 26.7%

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 26.7%

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

   6. Applied rewrites 26.7%

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

   if -2.1e12 < A < 1.20000000000000002e57

   1. Initial program 53.4%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.1%

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

   if 1.20000000000000002e57 < A

   1. Initial program 53.4%

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

   2. 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. lower-*.f64 N/A

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

      2. lower-/.f64 23.5%

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

   4. Applied rewrites 23.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 23.5%

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. count-2-rev N/A

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

      9. lower-+.f64 23.5%

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

   6. Applied rewrites 23.5%

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

   7. Taylor expanded in A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 23.4%

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

   9. Applied rewrites 23.4%

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

Alternative 4: 58.8% accurate, 1.8× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;C \leq -1.45 \cdot 10^{+40}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{\left|B\right|}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.6 \cdot 10^{+16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{\left|B\right|}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= C -1.45e+40)
    (* 180.0 (/ (atan (/ (- C A) (fabs B))) PI))
    (if (<= C 2.6e+16)
      (* 180.0 (/ (atan -1.0) PI))
      (* (atan (* -0.5 (/ (fabs B) C))) (/ 180.0 PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.45e+40) {
		tmp = 180.0 * (atan(((C - A) / fabs(B))) / ((double) M_PI));
	} else if (C <= 2.6e+16) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = atan((-0.5 * (fabs(B) / C))) * (180.0 / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.45e+40) {
		tmp = 180.0 * (Math.atan(((C - A) / Math.abs(B))) / Math.PI);
	} else if (C <= 2.6e+16) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = Math.atan((-0.5 * (Math.abs(B) / C))) * (180.0 / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.45e+40:
		tmp = 180.0 * (math.atan(((C - A) / math.fabs(B))) / math.pi)
	elif C <= 2.6e+16:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = math.atan((-0.5 * (math.fabs(B) / C))) * (180.0 / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.45e+40)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / abs(B))) / pi));
	elseif (C <= 2.6e+16)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(atan(Float64(-0.5 * Float64(abs(B) / C))) * Float64(180.0 / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.45e+40)
		tmp = 180.0 * (atan(((C - A) / abs(B))) / pi);
	elseif (C <= 2.6e+16)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = atan((-0.5 * (abs(B) / C))) * (180.0 / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[C, -1.45e+40], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.6e+16], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(-0.5 * N[(N[Abs[B], $MachinePrecision] / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if C < -1.45000000000000009e40

   1. Initial program 53.4%

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

   2. 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. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 49.0%

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

   4. Applied rewrites 49.0%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 35.0%

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

   7. Applied rewrites 35.0%

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

   if -1.45000000000000009e40 < C < 2.6e16

   1. Initial program 53.4%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.1%

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

   if 2.6e16 < C

   1. Initial program 53.4%

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

   2. 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. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 26.0%

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

   4. Applied rewrites 26.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 26.0%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, \frac{0}{B}\right)\right) \cdot 180}{\pi}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

   8. Applied rewrites 26.0%

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

Alternative 5: 54.0% accurate, 1.9× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;\left|B\right| \leq 1.65 \cdot 10^{+51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{\left|B\right|}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= (fabs B) 1.65e+51)
    (* 180.0 (/ (atan (/ (- C A) (fabs B))) PI))
    (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (fabs(B) <= 1.65e+51) {
		tmp = 180.0 * (atan(((C - A) / fabs(B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (Math.abs(B) <= 1.65e+51) {
		tmp = 180.0 * (Math.atan(((C - A) / Math.abs(B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if math.fabs(B) <= 1.65e+51:
		tmp = 180.0 * (math.atan(((C - A) / math.fabs(B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (abs(B) <= 1.65e+51)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / abs(B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (abs(B) <= 1.65e+51)
		tmp = 180.0 * (atan(((C - A) / abs(B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[B], $MachinePrecision], 1.65e+51], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if B < 1.6499999999999999e51

   1. Initial program 53.4%

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

   2. 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. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 49.0%

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

   4. Applied rewrites 49.0%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 35.0%

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

   7. Applied rewrites 35.0%

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

   if 1.6499999999999999e51 < B

   1. Initial program 53.4%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.1%

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

Alternative 6: 48.1% accurate, 2.0× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq 3.4 \cdot 10^{+59}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{\left|B\right|}\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= A 3.4e+59)
    (* 180.0 (/ (atan -1.0) PI))
    (* 180.0 (/ (atan (- 1.0 (/ A (fabs B)))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= 3.4e+59) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / fabs(B)))) / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= 3.4e+59) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / Math.abs(B)))) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= 3.4e+59:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / math.fabs(B)))) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= 3.4e+59)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / abs(B)))) / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= 3.4e+59)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / abs(B)))) / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[A, 3.4e+59], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / N[Abs[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < 3.40000000000000006e59

   1. Initial program 53.4%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.1%

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

   if 3.40000000000000006e59 < A

   1. Initial program 53.4%

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

   2. 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. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 49.0%

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

   4. Applied rewrites 49.0%

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

   5. Taylor expanded in C around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 38.6%

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

   7. Applied rewrites 38.6%

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

Alternative 7: 39.8% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 53.4%

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

2. Taylor expanded in B around inf

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

4. Applied rewrites 21.1%

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

Reproduce

herbie shell --seed 2025189 
(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)))