ABCF->ab-angle angle

Percentage Accurate: 53.2% → 82.1%

Time: 5.1s

Alternatives: 9

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: 53.2% 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: 82.1% accurate, 0.6× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{\left|B\right|} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {\left(\left|B\right|\right)}^{2}}\right)\right)}{\pi} \leq -40:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(C - A, \left|B\right|\right)}{\left|B\right|}\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\mathsf{fma}\left(\frac{\left|B\right|}{C}, -0.5, \frac{0}{\left|B\right|}\right)\right) \cdot \left(\frac{1}{\pi} \cdot 180\right)\\ \end{array} \]

FPCore

(FPCore (A B C)
  :precision binary64
  (*
 (copysign 1.0 B)
 (if (<=
      (*
       180.0
       (/
        (atan
         (*
          (/ 1.0 (fabs B))
          (-
           (- C A)
           (sqrt (+ (pow (- A C) 2.0) (pow (fabs B) 2.0))))))
        PI))
      -40.0)
   (*
    (/ (atan (/ (- (- C A) (hypot (- C A) (fabs B))) (fabs B))) PI)
    180.0)
   (*
    (atan (fma (/ (fabs B) C) -0.5 (/ 0.0 (fabs B))))
    (* (/ 1.0 PI) 180.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if ((180.0 * (atan(((1.0 / fabs(B)) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(fabs(B), 2.0)))))) / ((double) M_PI))) <= -40.0) {
		tmp = (atan((((C - A) - hypot((C - A), fabs(B))) / fabs(B))) / ((double) M_PI)) * 180.0;
	} else {
		tmp = atan(fma((fabs(B) / C), -0.5, (0.0 / fabs(B)))) * ((1.0 / ((double) M_PI)) * 180.0);
	}
	return copysign(1.0, B) * tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (Float64(180.0 * Float64(atan(Float64(Float64(1.0 / abs(B)) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (abs(B) ^ 2.0)))))) / pi)) <= -40.0)
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) - hypot(Float64(C - A), abs(B))) / abs(B))) / pi) * 180.0);
	else
		tmp = Float64(atan(fma(Float64(abs(B) / C), -0.5, Float64(0.0 / abs(B)))) * Float64(Float64(1.0 / pi) * 180.0));
	end
	return Float64(copysign(1.0, B) * 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[(180.0 * N[(N[ArcTan[N[(N[(1.0 / N[Abs[B], $MachinePrecision]), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[Abs[B], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], -40.0], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + N[Abs[B], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[ArcTan[N[(N[(N[Abs[B], $MachinePrecision] / C), $MachinePrecision] * -0.5 + N[(0.0 / N[Abs[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[(1.0 / Pi), $MachinePrecision] * 180.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.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))))))) (PI.f64))) < -40

   1. Initial program 53.2%

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

      1. 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. *-commutative N/A

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

      3. lower-*.f64 53.2%

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

   3. Applied rewrites 53.2%

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

   4. Taylor expanded in A around 0

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

   6. Applied rewrites 51.7%

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

      1. lift-sqrt.f64 N/A

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

      2. pow1/2 N/A

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

      3. lift-fma.f64 N/A

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

      4. pow2 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. pow2 N/A

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

      8. pow1/2 N/A

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

      9. sqrt-fabs-rev N/A

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

      10. pow1/2 N/A

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

      11. lift--.f64 N/A

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

      12. pow2 N/A

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

      13. pow2 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-fma.f64 N/A

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

      16. pow1/2 N/A

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

      17. lift-sqrt.f64 N/A

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

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

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

   8. Applied rewrites 72.5%

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

   9. Taylor expanded in C around 0

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

       1. lower--.f64 78.2%

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

   11. Applied rewrites 78.2%

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

   if -40 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.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))))))) (PI.f64)))

   1. Initial program 53.2%

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

   2. 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 25.6%

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

   4. Applied rewrites 25.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(-1, \frac{A + -1 \cdot A}{B}, -0.5 \cdot \frac{B}{C}\right)\right)}}{\pi} \]
   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. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 25.6%

      \[\leadsto \color{blue}{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, \frac{0}{B}\right)\right) \cdot \left(\frac{1}{\pi} \cdot 180\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 80.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{+149}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{0.5 \cdot \mathsf{fma}\left(\frac{C}{A}, B, B\right)}{A}\right) \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C - A, B\right)}{B}\right)}{\pi} \cdot 180\\ \end{array} \]

FPCore

(FPCore (A B C)
  :precision binary64
  (if (<= A -3.1e+149)
  (/ (* (atan (/ (* 0.5 (fma (/ C A) B B)) A)) 180.0) PI)
  (* (/ (atan (/ (- C (hypot (- C A) B)) B)) PI) 180.0)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e+149) {
		tmp = (atan(((0.5 * fma((C / A), B, B)) / A)) * 180.0) / ((double) M_PI);
	} else {
		tmp = (atan(((C - hypot((C - A), B)) / B)) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.1e+149)
		tmp = Float64(Float64(atan(Float64(Float64(0.5 * fma(Float64(C / A), B, B)) / A)) * 180.0) / pi);
	else
		tmp = Float64(Float64(atan(Float64(Float64(C - hypot(Float64(C - A), B)) / B)) / pi) * 180.0);
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.1e+149], N[(N[(N[ArcTan[N[(N[(0.5 * N[(N[(C / A), $MachinePrecision] * B + B), $MachinePrecision]), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(C - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -3.0999999999999999e149

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 48.9%

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

   4. Applied rewrites 48.9%

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

   5. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 32.8%

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

   7. Applied rewrites 32.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 33.0%

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

   if -3.0999999999999999e149 < A

   1. Initial program 53.2%

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

      1. 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. *-commutative N/A

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

      3. lower-*.f64 53.2%

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

   3. Applied rewrites 53.2%

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

   4. Taylor expanded in A around 0

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

   6. Applied rewrites 51.7%

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

      1. lift-sqrt.f64 N/A

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

      2. pow1/2 N/A

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

      3. lift-fma.f64 N/A

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

      4. pow2 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. pow2 N/A

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

      8. pow1/2 N/A

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

      9. sqrt-fabs-rev N/A

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

      10. pow1/2 N/A

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

      11. lift--.f64 N/A

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

      12. pow2 N/A

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

      13. pow2 N/A

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

      14. lift-*.f64 N/A

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

      15. lift-fma.f64 N/A

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

      16. pow1/2 N/A

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

      17. lift-sqrt.f64 N/A

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

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

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

   8. Applied rewrites 72.5%

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

Alternative 3: 75.4% accurate, 1.4× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;C \leq 2.5 \cdot 10^{+64}:\\ \;\;\;\;\left(\tan^{-1} \left(\frac{\frac{C - \left(A + \left|B\right|\right)}{\left|B\right|} \cdot \left|B\right|}{\left|B\right|}\right) \cdot 180\right) \cdot \frac{1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot \left|B\right|}{C}\right)\\ \end{array} \]

FPCore

(FPCore (A B C)
  :precision binary64
  (*
 (copysign 1.0 B)
 (if (<= C 2.5e+64)
   (*
    (*
     (atan
      (/ (* (/ (- C (+ A (fabs B))) (fabs B)) (fabs B)) (fabs B)))
     180.0)
    (/ 1.0 PI))
   (* (/ 180.0 PI) (atan (/ (* -0.5 (fabs B)) C))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.5e+64) {
		tmp = (atan(((((C - (A + fabs(B))) / fabs(B)) * fabs(B)) / fabs(B))) * 180.0) * (1.0 / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((-0.5 * fabs(B)) / C));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.5e+64) {
		tmp = (Math.atan(((((C - (A + Math.abs(B))) / Math.abs(B)) * Math.abs(B)) / Math.abs(B))) * 180.0) * (1.0 / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((-0.5 * Math.abs(B)) / C));
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 2.5e+64:
		tmp = (math.atan(((((C - (A + math.fabs(B))) / math.fabs(B)) * math.fabs(B)) / math.fabs(B))) * 180.0) * (1.0 / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((-0.5 * math.fabs(B)) / C))
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 2.5e+64)
		tmp = Float64(Float64(atan(Float64(Float64(Float64(Float64(C - Float64(A + abs(B))) / abs(B)) * abs(B)) / abs(B))) * 180.0) * Float64(1.0 / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(-0.5 * abs(B)) / C)));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 2.5e+64)
		tmp = (atan(((((C - (A + abs(B))) / abs(B)) * abs(B)) / abs(B))) * 180.0) * (1.0 / pi);
	else
		tmp = (180.0 / pi) * atan(((-0.5 * abs(B)) / C));
	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, 2.5e+64], N[(N[(N[ArcTan[N[(N[(N[(N[(C - N[(A + N[Abs[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision] * N[Abs[B], $MachinePrecision]), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] * N[(1.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(-0.5 * N[Abs[B], $MachinePrecision]), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < 2.5e64

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 48.9%

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

   4. Applied rewrites 48.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. mult-flip N/A

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

      5. lower-*.f64 N/A

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

   6. Applied rewrites 50.2%

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

   if 2.5e64 < C

   1. Initial program 53.2%

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

   2. 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 25.6%

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

   4. Applied rewrites 25.6%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. mult-flip N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lift-/.f64 N/A

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

      12. distribute-neg-frac N/A

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

      13. lower-/.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. distribute-rgt1-in N/A

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

      17. metadata-eval N/A

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

      18. mul0-lft N/A

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

      19. metadata-eval 25.6%

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

   6. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   8. Applied rewrites 25.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 25.6%

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

   10. Applied rewrites 25.6%

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

Alternative 4: 74.6% accurate, 1.7× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;C \leq 8.5 \cdot 10^{+63}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{\left|B\right|} - \left(1 + \frac{A}{\left|B\right|}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{-0.5 \cdot \left|B\right|}{C}\right)\\ \end{array} \]

FPCore

(FPCore (A B C)
  :precision binary64
  (*
 (copysign 1.0 B)
 (if (<= C 8.5e+63)
   (* 180.0 (/ (atan (- (/ C (fabs B)) (+ 1.0 (/ A (fabs B))))) PI))
   (* (/ 180.0 PI) (atan (/ (* -0.5 (fabs B)) C))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 8.5e+63) {
		tmp = 180.0 * (atan(((C / fabs(B)) - (1.0 + (A / fabs(B))))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((-0.5 * fabs(B)) / C));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 8.5e+63) {
		tmp = 180.0 * (Math.atan(((C / Math.abs(B)) - (1.0 + (A / Math.abs(B))))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((-0.5 * Math.abs(B)) / C));
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 8.5e+63:
		tmp = 180.0 * (math.atan(((C / math.fabs(B)) - (1.0 + (A / math.fabs(B))))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((-0.5 * math.fabs(B)) / C))
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 8.5e+63)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / abs(B)) - Float64(1.0 + Float64(A / abs(B))))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(-0.5 * abs(B)) / C)));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 8.5e+63)
		tmp = 180.0 * (atan(((C / abs(B)) - (1.0 + (A / abs(B))))) / pi);
	else
		tmp = (180.0 / pi) * atan(((-0.5 * abs(B)) / C));
	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, 8.5e+63], N[(180.0 * N[(N[ArcTan[N[(N[(C / N[Abs[B], $MachinePrecision]), $MachinePrecision] - N[(1.0 + N[(A / N[Abs[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(-0.5 * N[Abs[B], $MachinePrecision]), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < 8.5000000000000004e63

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 48.9%

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

   4. Applied rewrites 48.9%

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

   if 8.5000000000000004e63 < C

   1. Initial program 53.2%

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

   2. 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 25.6%

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

   4. Applied rewrites 25.6%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. mult-flip N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lift-/.f64 N/A

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

      12. distribute-neg-frac N/A

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

      13. lower-/.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. distribute-rgt1-in N/A

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

      17. metadata-eval N/A

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

      18. mul0-lft N/A

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

      19. metadata-eval 25.6%

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

   6. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   8. Applied rewrites 25.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 25.6%

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

   10. Applied rewrites 25.6%

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

Alternative 5: 58.4% accurate, 1.9× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{+149}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\left|B\right|}{A} \cdot 0.5\right) \cdot 180}{\pi}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{+64}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{\left|B\right|}\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
  :precision binary64
  (*
 (copysign 1.0 B)
 (if (<= A -3.1e+149)
   (/ (* (atan (* (/ (fabs B) A) 0.5)) 180.0) PI)
   (if (<= A 2.6e+64)
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (* -2.0 (/ A (fabs B)))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e+149) {
		tmp = (atan(((fabs(B) / A) * 0.5)) * 180.0) / ((double) M_PI);
	} else if (A <= 2.6e+64) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-2.0 * (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 <= -3.1e+149) {
		tmp = (Math.atan(((Math.abs(B) / A) * 0.5)) * 180.0) / Math.PI;
	} else if (A <= 2.6e+64) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / Math.abs(B)))) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.1e+149:
		tmp = (math.atan(((math.fabs(B) / A) * 0.5)) * 180.0) / math.pi
	elif A <= 2.6e+64:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / math.fabs(B)))) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.1e+149)
		tmp = Float64(Float64(atan(Float64(Float64(abs(B) / A) * 0.5)) * 180.0) / pi);
	elseif (A <= 2.6e+64)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * 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 <= -3.1e+149)
		tmp = (atan(((abs(B) / A) * 0.5)) * 180.0) / pi;
	elseif (A <= 2.6e+64)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-2.0 * (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, -3.1e+149], N[(N[(N[ArcTan[N[(N[(N[Abs[B], $MachinePrecision] / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 2.6e+64], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / N[Abs[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -3.0999999999999999e149

   1. Initial program 53.2%

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

   2. 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 26.1%

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

   4. Applied rewrites 26.1%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(0.5 \cdot \frac{B}{A}\right)}}{\pi} \]
   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. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 26.1%

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

   if -3.0999999999999999e149 < A < 2.6e64

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.4%

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

   if 2.6e64 < A

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 48.9%

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

   4. Applied rewrites 48.9%

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

   5. Taylor expanded in A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 23.1%

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

   7. Applied rewrites 23.1%

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

Alternative 6: 58.4% accurate, 1.9× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{+149}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{\left|B\right|}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{+64}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{\left|B\right|}\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
  :precision binary64
  (*
 (copysign 1.0 B)
 (if (<= A -3.1e+149)
   (* 180.0 (/ (atan (* 0.5 (/ (fabs B) A))) PI))
   (if (<= A 2.6e+64)
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (* -2.0 (/ A (fabs B)))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e+149) {
		tmp = 180.0 * (atan((0.5 * (fabs(B) / A))) / ((double) M_PI));
	} else if (A <= 2.6e+64) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-2.0 * (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 <= -3.1e+149) {
		tmp = 180.0 * (Math.atan((0.5 * (Math.abs(B) / A))) / Math.PI);
	} else if (A <= 2.6e+64) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / Math.abs(B)))) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.1e+149:
		tmp = 180.0 * (math.atan((0.5 * (math.fabs(B) / A))) / math.pi)
	elif A <= 2.6e+64:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / math.fabs(B)))) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.1e+149)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(abs(B) / A))) / pi));
	elseif (A <= 2.6e+64)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * 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 <= -3.1e+149)
		tmp = 180.0 * (atan((0.5 * (abs(B) / A))) / pi);
	elseif (A <= 2.6e+64)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-2.0 * (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, -3.1e+149], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(N[Abs[B], $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.6e+64], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / N[Abs[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -3.0999999999999999e149

   1. Initial program 53.2%

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

   2. 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 26.1%

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

   4. Applied rewrites 26.1%

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

   if -3.0999999999999999e149 < A < 2.6e64

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.4%

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

   if 2.6e64 < A

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 48.9%

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

   4. Applied rewrites 48.9%

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

   5. Taylor expanded in A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 23.1%

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

   7. Applied rewrites 23.1%

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

Alternative 7: 56.2% accurate, 1.9× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;C \leq -4.3 \cdot 10^{+191}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + C}{\left|B\right|}\right)\\ \mathbf{elif}\;C \leq 6.5 \cdot 10^{+64}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{\left|B\right|}{C}\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
  :precision binary64
  (*
 (copysign 1.0 B)
 (if (<= C -4.3e+191)
   (* (/ 180.0 PI) (atan (/ (+ C C) (fabs B))))
   (if (<= C 6.5e+64)
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (* -0.5 (/ (fabs B) C))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.3e+191) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C + C) / fabs(B)));
	} else if (C <= 6.5e+64) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (fabs(B) / C))) / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.3e+191) {
		tmp = (180.0 / Math.PI) * Math.atan(((C + C) / Math.abs(B)));
	} else if (C <= 6.5e+64) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (Math.abs(B) / C))) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -4.3e+191:
		tmp = (180.0 / math.pi) * math.atan(((C + C) / math.fabs(B)))
	elif C <= 6.5e+64:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (math.fabs(B) / C))) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -4.3e+191)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + C) / abs(B))));
	elseif (C <= 6.5e+64)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(abs(B) / C))) / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -4.3e+191)
		tmp = (180.0 / pi) * atan(((C + C) / abs(B)));
	elseif (C <= 6.5e+64)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (abs(B) / C))) / 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, -4.3e+191], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C + C), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.5e+64], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(N[Abs[B], $MachinePrecision] / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if C < -4.2999999999999998e191

   1. Initial program 53.2%

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

   2. 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 22.6%

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

   4. Applied rewrites 22.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(2 \cdot \frac{C}{B}\right)}}{\pi} \]
   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. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 22.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 22.6%

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

   8. Applied rewrites 22.6%

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

   if -4.2999999999999998e191 < C < 6.5000000000000001e64

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.4%

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

   if 6.5000000000000001e64 < C

   1. Initial program 53.2%

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

   2. 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 25.6%

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

   4. Applied rewrites 25.6%

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

   5. 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. lower-*.f64 N/A

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

      2. lower-/.f64 25.6%

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

   7. Applied rewrites 25.6%

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

Alternative 8: 46.5% accurate, 2.1× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;C \leq -4.3 \cdot 10^{+191}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C + C}{\left|B\right|}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
  :precision binary64
  (*
 (copysign 1.0 B)
 (if (<= C -4.3e+191)
   (* (/ 180.0 PI) (atan (/ (+ C C) (fabs B))))
   (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -4.3e+191) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C + C) / fabs(B)));
	} 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 (C <= -4.3e+191) {
		tmp = (180.0 / Math.PI) * Math.atan(((C + C) / Math.abs(B)));
	} 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 C <= -4.3e+191:
		tmp = (180.0 / math.pi) * math.atan(((C + C) / math.fabs(B)))
	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 (C <= -4.3e+191)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C + C) / abs(B))));
	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 (C <= -4.3e+191)
		tmp = (180.0 / pi) * atan(((C + C) / abs(B)));
	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[C, -4.3e+191], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C + C), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < -4.2999999999999998e191

   1. Initial program 53.2%

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

   2. 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 22.6%

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

   4. Applied rewrites 22.6%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(2 \cdot \frac{C}{B}\right)}}{\pi} \]
   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. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 22.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 22.6%

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

   8. Applied rewrites 22.6%

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

   if -4.2999999999999998e191 < C

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.4%

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

Alternative 9: 41.0% accurate, 3.1× 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 53.2%

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

2. Taylor expanded in B around inf

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

4. Applied rewrites 21.4%

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

Reproduce

herbie shell --seed 2025212 
(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)))