ABCF->ab-angle angle

Percentage Accurate: 55.0% → 82.6%

Time: 4.9s

Alternatives: 16

Speedup: 2.4×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 55.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B\_m} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B\_m}^{2}}\right)\right)}{\pi} \leq -20:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B\_m} \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(A - C, B\_m\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B\_m}{C} + A \cdot \frac{B\_m}{C \cdot C}, \frac{0}{B\_m}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<=
       (*
        180.0
        (/
         (atan
          (*
           (/ 1.0 B_m)
           (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B_m 2.0))))))
         PI))
       -20.0)
    (* 180.0 (/ (atan (* (/ 1.0 B_m) (- (- C A) (hypot (- A C) B_m)))) PI))
    (*
     180.0
     (/
      (atan (fma -0.5 (+ (/ B_m C) (* A (/ B_m (* C C)))) (/ 0.0 B_m)))
      PI)))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if ((180.0 * (atan(((1.0 / B_m) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B_m, 2.0)))))) / ((double) M_PI))) <= -20.0) {
		tmp = 180.0 * (atan(((1.0 / B_m) * ((C - A) - hypot((A - C), B_m)))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(fma(-0.5, ((B_m / C) + (A * (B_m / (C * C)))), (0.0 / B_m))) / ((double) M_PI));
	}
	return B_s * tmp;
}

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B_m) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B_m ^ 2.0)))))) / pi)) <= -20.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B_m) * Float64(Float64(C - A) - hypot(Float64(A - C), B_m)))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(fma(-0.5, Float64(Float64(B_m / C) + Float64(A * Float64(B_m / Float64(C * C)))), Float64(0.0 / B_m))) / pi));
	end
	return Float64(B_s * tmp)
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B$95$m), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B$95$m, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], -20.0], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B$95$m), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(N[(B$95$m / C), $MachinePrecision] + N[(A * N[(B$95$m / N[(C * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0 / B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $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))) < -20

   1. Initial program 61.0%

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

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-pow.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 N/A

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

      9. lift--.f64 88.2

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

   3. Applied rewrites 88.2%

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

   if -20 < (*.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 19.5%

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

      1. lift-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. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-pow.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 N/A

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

      9. lift--.f64 22.8

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

   3. Applied rewrites 22.8%

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

      1. lift-/.f64 N/A

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

      2. inv-pow N/A

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

      3. pow-to-exp N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 22.5

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

   5. Applied rewrites 22.5%

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

   6. Taylor expanded in C around inf

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

      1. exp-to-pow N/A

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

      2. inv-pow N/A

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

      3. pow2 N/A

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

      4. pow2 N/A

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

      5. +-commutative N/A

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

   8. Applied rewrites 48.9%

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

Alternative 2: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ \begin{array}{l} t_0 := \left(-A\right) + C\\ B\_s \cdot \begin{array}{l} \mathbf{if}\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B\_m} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B\_m}^{2}}\right)\right)}{\pi} \leq -20:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{t\_0 - \mathsf{hypot}\left(t\_0, B\_m\right)}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B\_m}{C} + A \cdot \frac{B\_m}{C \cdot C}, \frac{0}{B\_m}\right)\right)}{\pi}\\ \end{array} \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (let* ((t_0 (+ (- A) C)))
   (*
    B_s
    (if (<=
         (*
          180.0
          (/
           (atan
            (*
             (/ 1.0 B_m)
             (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B_m 2.0))))))
           PI))
         -20.0)
      (* 180.0 (/ (atan (/ (- t_0 (hypot t_0 B_m)) B_m)) PI))
      (*
       180.0
       (/
        (atan (fma -0.5 (+ (/ B_m C) (* A (/ B_m (* C C)))) (/ 0.0 B_m)))
        PI))))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double t_0 = -A + C;
	double tmp;
	if ((180.0 * (atan(((1.0 / B_m) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B_m, 2.0)))))) / ((double) M_PI))) <= -20.0) {
		tmp = 180.0 * (atan(((t_0 - hypot(t_0, B_m)) / B_m)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(fma(-0.5, ((B_m / C) + (A * (B_m / (C * C)))), (0.0 / B_m))) / ((double) M_PI));
	}
	return B_s * tmp;
}

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	t_0 = Float64(Float64(-A) + C)
	tmp = 0.0
	if (Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B_m) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B_m ^ 2.0)))))) / pi)) <= -20.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(t_0 - hypot(t_0, B_m)) / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(fma(-0.5, Float64(Float64(B_m / C) + Float64(A * Float64(B_m / Float64(C * C)))), Float64(0.0 / B_m))) / pi));
	end
	return Float64(B_s * tmp)
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := Block[{t$95$0 = N[((-A) + C), $MachinePrecision]}, N[(B$95$s * If[LessEqual[N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B$95$m), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B$95$m, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], -20.0], N[(180.0 * N[(N[ArcTan[N[(N[(t$95$0 - N[Sqrt[t$95$0 ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(N[(B$95$m / C), $MachinePrecision] + N[(A * N[(B$95$m / N[(C * C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0 / B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $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))) < -20

   1. Initial program 61.0%

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

   2. Taylor expanded in A around -inf

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

      1. lower-atan.f64 N/A

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

      2. lower-/.f64 N/A

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

   4. Applied rewrites 88.2%

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

   if -20 < (*.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 19.5%

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

      1. lift-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. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-pow.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 N/A

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

      9. lift--.f64 22.8

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

   3. Applied rewrites 22.8%

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

      1. lift-/.f64 N/A

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

      2. inv-pow N/A

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

      3. pow-to-exp N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 22.5

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

   5. Applied rewrites 22.5%

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

   6. Taylor expanded in C around inf

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

      1. exp-to-pow N/A

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

      2. inv-pow N/A

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

      3. pow2 N/A

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

      4. pow2 N/A

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

      5. +-commutative N/A

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

   8. Applied rewrites 48.9%

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

Alternative 3: 81.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -4.5 \cdot 10^{+89}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\mathsf{fma}\left(\frac{C}{A}, B\_m, B\_m\right) \cdot -0.5}{-A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B\_m} \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(-C, B\_m\right)\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A -4.5e+89)
    (/ (* 180.0 (atan (/ (* (fma (/ C A) B_m B_m) -0.5) (- A)))) PI)
    (* 180.0 (/ (atan (* (/ 1.0 B_m) (- (- C A) (hypot (- C) B_m)))) PI)))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -4.5e+89) {
		tmp = (180.0 * atan(((fma((C / A), B_m, B_m) * -0.5) / -A))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((1.0 / B_m) * ((C - A) - hypot(-C, B_m)))) / ((double) M_PI));
	}
	return B_s * tmp;
}

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= -4.5e+89)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(fma(Float64(C / A), B_m, B_m) * -0.5) / Float64(-A)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B_m) * Float64(Float64(C - A) - hypot(Float64(-C), B_m)))) / pi));
	end
	return Float64(B_s * tmp)
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, -4.5e+89], N[(N[(180.0 * N[ArcTan[N[(N[(N[(N[(C / A), $MachinePrecision] * B$95$m + B$95$m), $MachinePrecision] * -0.5), $MachinePrecision] / (-A)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B$95$m), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[(-C) ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < -4.5e89

   1. Initial program 19.5%

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

   2. Taylor expanded in A around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-lft-out N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 73.6

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

   4. Applied rewrites 73.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 73.7%

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

   if -4.5e89 < A

   1. Initial program 62.5%

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

      1. lift-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. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-pow.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 N/A

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

      9. lift--.f64 83.7

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

   3. Applied rewrites 83.7%

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

   4. Taylor expanded in A around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 82.5

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

   6. Applied rewrites 82.5%

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

Alternative 4: 80.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -4.5 \cdot 10^{+89}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\mathsf{fma}\left(\frac{C}{A}, B\_m, B\_m\right) \cdot -0.5}{-A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B\_m} \cdot \left(C - \mathsf{hypot}\left(A - C, B\_m\right)\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A -4.5e+89)
    (/ (* 180.0 (atan (/ (* (fma (/ C A) B_m B_m) -0.5) (- A)))) PI)
    (* 180.0 (/ (atan (* (/ 1.0 B_m) (- C (hypot (- A C) B_m)))) PI)))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -4.5e+89) {
		tmp = (180.0 * atan(((fma((C / A), B_m, B_m) * -0.5) / -A))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((1.0 / B_m) * (C - hypot((A - C), B_m)))) / ((double) M_PI));
	}
	return B_s * tmp;
}

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= -4.5e+89)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(fma(Float64(C / A), B_m, B_m) * -0.5) / Float64(-A)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B_m) * Float64(C - hypot(Float64(A - C), B_m)))) / pi));
	end
	return Float64(B_s * tmp)
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, -4.5e+89], N[(N[(180.0 * N[ArcTan[N[(N[(N[(N[(C / A), $MachinePrecision] * B$95$m + B$95$m), $MachinePrecision] * -0.5), $MachinePrecision] / (-A)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B$95$m), $MachinePrecision] * N[(C - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < -4.5e89

   1. Initial program 19.5%

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

   2. Taylor expanded in A around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-lft-out N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 73.6

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

   4. Applied rewrites 73.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 73.7%

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

   if -4.5e89 < A

   1. Initial program 62.5%

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

      1. lift-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. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-pow.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 N/A

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

      9. lift--.f64 83.7

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

   3. Applied rewrites 83.7%

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

   4. Taylor expanded in A around 0

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

   6. Applied rewrites 82.5%

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

Alternative 5: 79.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -4.6 \cdot 10^{+89}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\mathsf{fma}\left(\frac{C}{A}, B\_m, B\_m\right) \cdot -0.5}{-A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-117}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B\_m} \cdot \left(C - \mathsf{hypot}\left(-C, B\_m\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B\_m} \cdot \left(\left(C - A\right) - B\_m\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A -4.6e+89)
    (/ (* 180.0 (atan (/ (* (fma (/ C A) B_m B_m) -0.5) (- A)))) PI)
    (if (<= A 5e-117)
      (* 180.0 (/ (atan (* (/ 1.0 B_m) (- C (hypot (- C) B_m)))) PI))
      (* 180.0 (/ (atan (* (/ 1.0 B_m) (- (- C A) B_m))) PI))))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -4.6e+89) {
		tmp = (180.0 * atan(((fma((C / A), B_m, B_m) * -0.5) / -A))) / ((double) M_PI);
	} else if (A <= 5e-117) {
		tmp = 180.0 * (atan(((1.0 / B_m) * (C - hypot(-C, B_m)))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((1.0 / B_m) * ((C - A) - B_m))) / ((double) M_PI));
	}
	return B_s * tmp;
}

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= -4.6e+89)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(fma(Float64(C / A), B_m, B_m) * -0.5) / Float64(-A)))) / pi);
	elseif (A <= 5e-117)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B_m) * Float64(C - hypot(Float64(-C), B_m)))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B_m) * Float64(Float64(C - A) - B_m))) / pi));
	end
	return Float64(B_s * tmp)
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, -4.6e+89], N[(N[(180.0 * N[ArcTan[N[(N[(N[(N[(C / A), $MachinePrecision] * B$95$m + B$95$m), $MachinePrecision] * -0.5), $MachinePrecision] / (-A)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 5e-117], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B$95$m), $MachinePrecision] * N[(C - N[Sqrt[(-C) ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B$95$m), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -4.5999999999999998e89

   1. Initial program 19.5%

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

   2. Taylor expanded in A around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-lft-out N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 73.6

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

   4. Applied rewrites 73.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 73.7%

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

   if -4.5999999999999998e89 < A < 5e-117

   1. Initial program 54.3%

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

      1. lift-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. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-pow.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 N/A

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

      9. lift--.f64 77.3

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

   3. Applied rewrites 77.3%

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

   4. Taylor expanded in A around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 76.0

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

   6. Applied rewrites 76.0%

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

   7. Taylor expanded in A around 0

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

   9. Applied rewrites 75.9%

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

   if 5e-117 < A

   1. Initial program 73.4%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 86.1%

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

Alternative 6: 75.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq 88000000000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B\_m} \cdot \left(\left(C - A\right) - B\_m\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B\_m}{C} \cdot -0.5\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= C 88000000000000.0)
    (* 180.0 (/ (atan (* (/ 1.0 B_m) (- (- C A) B_m))) PI))
    (/ (* 180.0 (atan (* (/ B_m C) -0.5))) PI))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (C <= 88000000000000.0) {
		tmp = 180.0 * (atan(((1.0 / B_m) * ((C - A) - B_m))) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((B_m / C) * -0.5))) / ((double) M_PI);
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (C <= 88000000000000.0) {
		tmp = 180.0 * (Math.atan(((1.0 / B_m) * ((C - A) - B_m))) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((B_m / C) * -0.5))) / Math.PI;
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if C <= 88000000000000.0:
		tmp = 180.0 * (math.atan(((1.0 / B_m) * ((C - A) - B_m))) / math.pi)
	else:
		tmp = (180.0 * math.atan(((B_m / C) * -0.5))) / math.pi
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (C <= 88000000000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B_m) * Float64(Float64(C - A) - B_m))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B_m / C) * -0.5))) / pi);
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (C <= 88000000000000.0)
		tmp = 180.0 * (atan(((1.0 / B_m) * ((C - A) - B_m))) / pi);
	else
		tmp = (180.0 * atan(((B_m / C) * -0.5))) / pi;
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[C, 88000000000000.0], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B$95$m), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B$95$m / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < 8.8e13

   1. Initial program 64.2%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 78.8%

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

   if 8.8e13 < C

   1. Initial program 25.3%

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

   2. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

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

      10. lower-*.f64 66.4

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

   4. Applied rewrites 66.4%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 66.4%

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

   7. Taylor expanded in B around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 66.4

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

   9. Applied rewrites 66.4%

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

Alternative 7: 75.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq 88000000000000:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\left(\left(C - A\right) - B\_m\right) \cdot \frac{1}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B\_m}{C} \cdot -0.5\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= C 88000000000000.0)
    (/ (* 180.0 (atan (* (- (- C A) B_m) (/ 1.0 B_m)))) PI)
    (/ (* 180.0 (atan (* (/ B_m C) -0.5))) PI))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (C <= 88000000000000.0) {
		tmp = (180.0 * atan((((C - A) - B_m) * (1.0 / B_m)))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(((B_m / C) * -0.5))) / ((double) M_PI);
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (C <= 88000000000000.0) {
		tmp = (180.0 * Math.atan((((C - A) - B_m) * (1.0 / B_m)))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan(((B_m / C) * -0.5))) / Math.PI;
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if C <= 88000000000000.0:
		tmp = (180.0 * math.atan((((C - A) - B_m) * (1.0 / B_m)))) / math.pi
	else:
		tmp = (180.0 * math.atan(((B_m / C) * -0.5))) / math.pi
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (C <= 88000000000000.0)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - B_m) * Float64(1.0 / B_m)))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B_m / C) * -0.5))) / pi);
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (C <= 88000000000000.0)
		tmp = (180.0 * atan((((C - A) - B_m) * (1.0 / B_m)))) / pi;
	else
		tmp = (180.0 * atan(((B_m / C) * -0.5))) / pi;
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[C, 88000000000000.0], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - B$95$m), $MachinePrecision] * N[(1.0 / B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B$95$m / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < 8.8e13

   1. Initial program 64.2%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 78.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 78.8%

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

   if 8.8e13 < C

   1. Initial program 25.3%

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

   2. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

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

      10. lower-*.f64 66.4

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

   4. Applied rewrites 66.4%

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

      1. lift-*.f64 N/A

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

      2. lift-PI.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 66.4%

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

   7. Taylor expanded in B around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 66.4

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

   9. Applied rewrites 66.4%

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

Alternative 8: 69.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -4.2 \cdot 10^{+88}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B\_m}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.4 \cdot 10^{-9}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B\_m} \cdot \left(C - B\_m\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A -4.2e+88)
    (/ (* 180.0 (atan (* (/ B_m A) 0.5))) PI)
    (if (<= A 2.4e-9)
      (* 180.0 (/ (atan (* (/ 1.0 B_m) (- C B_m))) PI))
      (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B_m))) PI))))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -4.2e+88) {
		tmp = (180.0 * atan(((B_m / A) * 0.5))) / ((double) M_PI);
	} else if (A <= 2.4e-9) {
		tmp = 180.0 * (atan(((1.0 / B_m) * (C - B_m))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B_m))) / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -4.2e+88) {
		tmp = (180.0 * Math.atan(((B_m / A) * 0.5))) / Math.PI;
	} else if (A <= 2.4e-9) {
		tmp = 180.0 * (Math.atan(((1.0 / B_m) * (C - B_m))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B_m))) / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if A <= -4.2e+88:
		tmp = (180.0 * math.atan(((B_m / A) * 0.5))) / math.pi
	elif A <= 2.4e-9:
		tmp = 180.0 * (math.atan(((1.0 / B_m) * (C - B_m))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B_m))) / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= -4.2e+88)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B_m / A) * 0.5))) / pi);
	elseif (A <= 2.4e-9)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B_m) * Float64(C - B_m))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B_m))) / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (A <= -4.2e+88)
		tmp = (180.0 * atan(((B_m / A) * 0.5))) / pi;
	elseif (A <= 2.4e-9)
		tmp = 180.0 * (atan(((1.0 / B_m) * (C - B_m))) / pi);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B_m))) / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, -4.2e+88], N[(N[(180.0 * N[ArcTan[N[(N[(B$95$m / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 2.4e-9], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B$95$m), $MachinePrecision] * N[(C - B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -4.2e88

   1. Initial program 19.5%

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

   2. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 73.7

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

   4. Applied rewrites 73.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 73.7%

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

   if -4.2e88 < A < 2.4e-9

   1. Initial program 55.8%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 70.9%

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

   5. Taylor expanded in A around 0

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

   7. Applied rewrites 68.9%

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

   if 2.4e-9 < A

   1. Initial program 76.6%

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

   2. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 68.9

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

   4. Applied rewrites 68.9%

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

Alternative 9: 60.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -6.1 \cdot 10^{+41}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B\_m}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 5.6 \cdot 10^{-14}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A -6.1e+41)
    (/ (* 180.0 (atan (* (/ B_m A) 0.5))) PI)
    (if (<= A 5.6e-14)
      (* 180.0 (/ (atan -1.0) PI))
      (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B_m))) PI))))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -6.1e+41) {
		tmp = (180.0 * atan(((B_m / A) * 0.5))) / ((double) M_PI);
	} else if (A <= 5.6e-14) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B_m))) / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -6.1e+41) {
		tmp = (180.0 * Math.atan(((B_m / A) * 0.5))) / Math.PI;
	} else if (A <= 5.6e-14) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B_m))) / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if A <= -6.1e+41:
		tmp = (180.0 * math.atan(((B_m / A) * 0.5))) / math.pi
	elif A <= 5.6e-14:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B_m))) / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= -6.1e+41)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B_m / A) * 0.5))) / pi);
	elseif (A <= 5.6e-14)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B_m))) / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (A <= -6.1e+41)
		tmp = (180.0 * atan(((B_m / A) * 0.5))) / pi;
	elseif (A <= 5.6e-14)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B_m))) / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, -6.1e+41], N[(N[(180.0 * N[ArcTan[N[(N[(B$95$m / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 5.6e-14], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -6.09999999999999998e41

   1. Initial program 23.5%

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

   2. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 69.3

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

   4. Applied rewrites 69.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 69.4%

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

   if -6.09999999999999998e41 < A < 5.6000000000000001e-14

   1. Initial program 56.8%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 51.6%

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

   if 5.6000000000000001e-14 < A

   1. Initial program 76.6%

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

   2. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 68.8

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

   4. Applied rewrites 68.8%

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

Alternative 10: 59.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -6.1 \cdot 10^{+41}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B\_m}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-6}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A}{B\_m} \cdot -2\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A -6.1e+41)
    (/ (* 180.0 (atan (* (/ B_m A) 0.5))) PI)
    (if (<= A 1.9e-6)
      (* 180.0 (/ (atan -1.0) PI))
      (* 180.0 (/ (atan (* (/ A B_m) -2.0)) PI))))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -6.1e+41) {
		tmp = (180.0 * atan(((B_m / A) * 0.5))) / ((double) M_PI);
	} else if (A <= 1.9e-6) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A / B_m) * -2.0)) / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -6.1e+41) {
		tmp = (180.0 * Math.atan(((B_m / A) * 0.5))) / Math.PI;
	} else if (A <= 1.9e-6) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A / B_m) * -2.0)) / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if A <= -6.1e+41:
		tmp = (180.0 * math.atan(((B_m / A) * 0.5))) / math.pi
	elif A <= 1.9e-6:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A / B_m) * -2.0)) / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= -6.1e+41)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B_m / A) * 0.5))) / pi);
	elseif (A <= 1.9e-6)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A / B_m) * -2.0)) / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (A <= -6.1e+41)
		tmp = (180.0 * atan(((B_m / A) * 0.5))) / pi;
	elseif (A <= 1.9e-6)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan(((A / B_m) * -2.0)) / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, -6.1e+41], N[(N[(180.0 * N[ArcTan[N[(N[(B$95$m / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.9e-6], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A / B$95$m), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -6.09999999999999998e41

   1. Initial program 23.5%

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

   2. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 69.3

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

   4. Applied rewrites 69.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 69.4%

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

   if -6.09999999999999998e41 < A < 1.9e-6

   1. Initial program 56.9%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 51.6%

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

   if 1.9e-6 < A

   1. Initial program 76.8%

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

   2. Taylor expanded in A around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 68.6

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

   4. Applied rewrites 68.6%

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

Alternative 11: 59.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -6.1 \cdot 10^{+41}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B\_m}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-6}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A -6.1e+41)
    (/ (* 180.0 (atan (* (/ B_m A) 0.5))) PI)
    (if (<= A 1.9e-6)
      (* 180.0 (/ (atan -1.0) PI))
      (* 180.0 (/ (atan (/ (- A) B_m)) PI))))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -6.1e+41) {
		tmp = (180.0 * atan(((B_m / A) * 0.5))) / ((double) M_PI);
	} else if (A <= 1.9e-6) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-A / B_m)) / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -6.1e+41) {
		tmp = (180.0 * Math.atan(((B_m / A) * 0.5))) / Math.PI;
	} else if (A <= 1.9e-6) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-A / B_m)) / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if A <= -6.1e+41:
		tmp = (180.0 * math.atan(((B_m / A) * 0.5))) / math.pi
	elif A <= 1.9e-6:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-A / B_m)) / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= -6.1e+41)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B_m / A) * 0.5))) / pi);
	elseif (A <= 1.9e-6)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B_m)) / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (A <= -6.1e+41)
		tmp = (180.0 * atan(((B_m / A) * 0.5))) / pi;
	elseif (A <= 1.9e-6)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-A / B_m)) / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, -6.1e+41], N[(N[(180.0 * N[ArcTan[N[(N[(B$95$m / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.9e-6], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[((-A) / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -6.09999999999999998e41

   1. Initial program 23.5%

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

   2. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 69.3

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

   4. Applied rewrites 69.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 69.4%

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

   if -6.09999999999999998e41 < A < 1.9e-6

   1. Initial program 56.9%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 51.6%

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

   if 1.9e-6 < A

   1. Initial program 76.8%

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

   2. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 69.3

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

   4. Applied rewrites 69.3%

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

   5. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 68.1

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

   7. Applied rewrites 68.1%

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

Alternative 12: 59.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -6.1 \cdot 10^{+41}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B\_m}{A} \cdot 0.5\right)}{\pi} \cdot 180\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-6}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A -6.1e+41)
    (* (/ (atan (* (/ B_m A) 0.5)) PI) 180.0)
    (if (<= A 1.9e-6)
      (* 180.0 (/ (atan -1.0) PI))
      (* 180.0 (/ (atan (/ (- A) B_m)) PI))))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -6.1e+41) {
		tmp = (atan(((B_m / A) * 0.5)) / ((double) M_PI)) * 180.0;
	} else if (A <= 1.9e-6) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-A / B_m)) / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -6.1e+41) {
		tmp = (Math.atan(((B_m / A) * 0.5)) / Math.PI) * 180.0;
	} else if (A <= 1.9e-6) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-A / B_m)) / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if A <= -6.1e+41:
		tmp = (math.atan(((B_m / A) * 0.5)) / math.pi) * 180.0
	elif A <= 1.9e-6:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-A / B_m)) / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= -6.1e+41)
		tmp = Float64(Float64(atan(Float64(Float64(B_m / A) * 0.5)) / pi) * 180.0);
	elseif (A <= 1.9e-6)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B_m)) / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (A <= -6.1e+41)
		tmp = (atan(((B_m / A) * 0.5)) / pi) * 180.0;
	elseif (A <= 1.9e-6)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-A / B_m)) / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, -6.1e+41], N[(N[(N[ArcTan[N[(N[(B$95$m / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[A, 1.9e-6], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[((-A) / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -6.09999999999999998e41

   1. Initial program 23.5%

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

   2. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 69.3

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

   4. Applied rewrites 69.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 69.3

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

      4. pow2 69.3

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

      5. pow2 69.3

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

   6. Applied rewrites 69.3%

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

   if -6.09999999999999998e41 < A < 1.9e-6

   1. Initial program 56.9%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 51.6%

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

   if 1.9e-6 < A

   1. Initial program 76.8%

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

   2. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 69.3

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

   4. Applied rewrites 69.3%

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

   5. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 68.1

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

   7. Applied rewrites 68.1%

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

Alternative 13: 52.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -3.5 \cdot 10^{+195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B\_m}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-6}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A -3.5e+195)
    (* 180.0 (/ (atan (/ 0.0 B_m)) PI))
    (if (<= A 1.9e-6)
      (* 180.0 (/ (atan -1.0) PI))
      (* 180.0 (/ (atan (/ (- A) B_m)) PI))))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -3.5e+195) {
		tmp = 180.0 * (atan((0.0 / B_m)) / ((double) M_PI));
	} else if (A <= 1.9e-6) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-A / B_m)) / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -3.5e+195) {
		tmp = 180.0 * (Math.atan((0.0 / B_m)) / Math.PI);
	} else if (A <= 1.9e-6) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-A / B_m)) / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if A <= -3.5e+195:
		tmp = 180.0 * (math.atan((0.0 / B_m)) / math.pi)
	elif A <= 1.9e-6:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-A / B_m)) / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= -3.5e+195)
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B_m)) / pi));
	elseif (A <= 1.9e-6)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B_m)) / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (A <= -3.5e+195)
		tmp = 180.0 * (atan((0.0 / B_m)) / pi);
	elseif (A <= 1.9e-6)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-A / B_m)) / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, -3.5e+195], N[(180.0 * N[(N[ArcTan[N[(0.0 / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.9e-6], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[((-A) / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -3.5000000000000002e195

   1. Initial program 9.5%

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

      1. lift-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. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-pow.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 N/A

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

      9. lift--.f64 53.6

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

   3. Applied rewrites 53.6%

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

      1. lift-/.f64 N/A

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

      2. inv-pow N/A

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

      3. pow-to-exp N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 52.7

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

   5. Applied rewrites 52.7%

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

   6. Taylor expanded in C around inf

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

      1. exp-to-pow N/A

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

      2. inv-pow N/A

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

      3. pow2 N/A

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

      4. pow2 N/A

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

      5. associate-*r/ N/A

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

      6. *-commutative N/A

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

      7. distribute-rgt1-in N/A

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

      8. metadata-eval N/A

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

      9. mul0-lft N/A

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

      10. metadata-eval N/A

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

      11. mul0-lft N/A

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

      12. lift-/.f64 N/A

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

      13. mul0-lft 40.5

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

   8. Applied rewrites 40.5%

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

   if -3.5000000000000002e195 < A < 1.9e-6

   1. Initial program 52.4%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 47.6%

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

   if 1.9e-6 < A

   1. Initial program 76.8%

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

   2. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 69.3

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

   4. Applied rewrites 69.3%

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

   5. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 68.1

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

   7. Applied rewrites 68.1%

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

Alternative 14: 52.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq -2.4 \cdot 10^{+44}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B\_m}\right)}{\pi}\\ \mathbf{elif}\;C \leq 10^{+133}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= C -2.4e+44)
    (* 180.0 (/ (atan (/ C B_m)) PI))
    (if (<= C 1e+133)
      (* 180.0 (/ (atan -1.0) PI))
      (* 180.0 (/ (atan (/ 0.0 B_m)) PI))))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (C <= -2.4e+44) {
		tmp = 180.0 * (atan((C / B_m)) / ((double) M_PI));
	} else if (C <= 1e+133) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((0.0 / B_m)) / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (C <= -2.4e+44) {
		tmp = 180.0 * (Math.atan((C / B_m)) / Math.PI);
	} else if (C <= 1e+133) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((0.0 / B_m)) / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if C <= -2.4e+44:
		tmp = 180.0 * (math.atan((C / B_m)) / math.pi)
	elif C <= 1e+133:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((0.0 / B_m)) / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (C <= -2.4e+44)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B_m)) / pi));
	elseif (C <= 1e+133)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(0.0 / B_m)) / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (C <= -2.4e+44)
		tmp = 180.0 * (atan((C / B_m)) / pi);
	elseif (C <= 1e+133)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((0.0 / B_m)) / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[C, -2.4e+44], N[(180.0 * N[(N[ArcTan[N[(C / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1e+133], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(0.0 / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if C < -2.40000000000000013e44

   1. Initial program 78.5%

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

   2. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 72.4

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

   4. Applied rewrites 72.4%

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

   5. Taylor expanded in C around inf

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

      1. lower-/.f64 72.2

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

   7. Applied rewrites 72.2%

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

   if -2.40000000000000013e44 < C < 1e133

   1. Initial program 55.4%

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

   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 48.6%

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

   if 1e133 < C

   1. Initial program 15.9%

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

      1. lift-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. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. unpow2 N/A

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

      6. lift-pow.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 N/A

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

      9. lift--.f64 56.3

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

   3. Applied rewrites 56.3%

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

      1. lift-/.f64 N/A

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

      2. inv-pow N/A

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

      3. pow-to-exp N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 55.1

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

   5. Applied rewrites 55.1%

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

   6. Taylor expanded in C around inf

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

      1. exp-to-pow N/A

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

      2. inv-pow N/A

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

      3. pow2 N/A

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

      4. pow2 N/A

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

      5. associate-*r/ N/A

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

      6. *-commutative N/A

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

      7. distribute-rgt1-in N/A

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

      8. metadata-eval N/A

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

      9. mul0-lft N/A

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

      10. metadata-eval N/A

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

      11. mul0-lft N/A

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

      12. lift-/.f64 N/A

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

      13. mul0-lft 35.9

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

   8. Applied rewrites 35.9%

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

Alternative 15: 49.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq -2.4 \cdot 10^{+44}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= C -2.4e+44)
    (* 180.0 (/ (atan (/ C B_m)) PI))
    (* 180.0 (/ (atan -1.0) PI)))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (C <= -2.4e+44) {
		tmp = 180.0 * (atan((C / B_m)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (C <= -2.4e+44) {
		tmp = 180.0 * (Math.atan((C / B_m)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if C <= -2.4e+44:
		tmp = 180.0 * (math.atan((C / B_m)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (C <= -2.4e+44)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (C <= -2.4e+44)
		tmp = 180.0 * (atan((C / B_m)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[C, -2.4e+44], N[(180.0 * N[(N[ArcTan[N[(C / B$95$m), $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 C < -2.40000000000000013e44

   1. Initial program 78.5%

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

   2. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 72.4

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

   4. Applied rewrites 72.4%

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

   5. Taylor expanded in C around inf

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

      1. lower-/.f64 72.2

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

   7. Applied rewrites 72.2%

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

   if -2.40000000000000013e44 < C

   1. Initial program 48.5%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 43.0%

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

Alternative 16: 40.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \left(180 \cdot \frac{\tan^{-1} -1}{\pi}\right) \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C) :precision binary64 (* B_s (* 180.0 (/ (atan -1.0) PI))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	return B_s * (180.0 * (atan(-1.0) / ((double) M_PI)));
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	return B_s * (180.0 * (Math.atan(-1.0) / Math.PI));
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	return B_s * (180.0 * (math.atan(-1.0) / math.pi))

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	return Float64(B_s * Float64(180.0 * Float64(atan(-1.0) / pi)))
end

MATLAB

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

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 55.0%

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

2. Taylor expanded in B around inf

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

4. Applied rewrites 40.4%

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

Reproduce

herbie shell --seed 2025120 
(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)))