ABCF->ab-angle angle

Percentage Accurate: 54.0% → 82.2%

Time: 5.7s

Alternatives: 15

Speedup: 2.3×

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: 54.0% 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: 82.2% accurate, 0.6× speedup

Math

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

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 (/ B_m C) -0.5 (/ 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((B_m / C), -0.5, (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(Float64(180.0 * atan(fma(Float64(B_m / C), -0.5, 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[(N[(180.0 * N[ArcTan[N[(N[(B$95$m / C), $MachinePrecision] * -0.5 + N[(0.0 / B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $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 54.0%

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

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

      6. mul-1-neg N/A

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

      7. lift-pow.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-flip N/A

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

      10. unpow2 N/A

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

      11. sub-negate-rev N/A

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

      12. mul-1-neg N/A

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

      13. sub-negate-rev N/A

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

      14. mul-1-neg N/A

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

      15. unpow2 N/A

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

      16. lower-hypot.f64 N/A

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

      17. mul-1-neg N/A

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

      18. sub-negate-rev N/A

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

      19. lift--.f64 78.7

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

   3. Applied rewrites 78.7%

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

   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 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 66.7%

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

   10. Taylor expanded in C around inf

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

   12. Applied rewrites 25.1%

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

Alternative 2: 78.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq -1.3 \cdot 10^{-54}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - B\_m\right) - A}{B\_m}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8.2 \cdot 10^{+160}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-\left(\mathsf{hypot}\left(A, B\_m\right) + A\right)}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B\_m}{C} \cdot -0.5\right)}{\pi}\\ \end{array} \end{array} \]

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 -1.3e-54)
    (/ (* 180.0 (atan (/ (- (- C B_m) A) B_m))) PI)
    (if (<= C 8.2e+160)
      (* 180.0 (/ (atan (/ (- (+ (hypot A B_m) 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 <= -1.3e-54) {
		tmp = (180.0 * atan((((C - B_m) - A) / B_m))) / ((double) M_PI);
	} else if (C <= 8.2e+160) {
		tmp = 180.0 * (atan((-(hypot(A, B_m) + 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 <= -1.3e-54) {
		tmp = (180.0 * Math.atan((((C - B_m) - A) / B_m))) / Math.PI;
	} else if (C <= 8.2e+160) {
		tmp = 180.0 * (Math.atan((-(Math.hypot(A, B_m) + 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 <= -1.3e-54:
		tmp = (180.0 * math.atan((((C - B_m) - A) / B_m))) / math.pi
	elif C <= 8.2e+160:
		tmp = 180.0 * (math.atan((-(math.hypot(A, B_m) + 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 <= -1.3e-54)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - B_m) - A) / B_m))) / pi);
	elseif (C <= 8.2e+160)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-Float64(hypot(A, B_m) + A)) / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(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 <= -1.3e-54)
		tmp = (180.0 * atan((((C - B_m) - A) / B_m))) / pi;
	elseif (C <= 8.2e+160)
		tmp = 180.0 * (atan((-(hypot(A, B_m) + 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, -1.3e-54], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - B$95$m), $MachinePrecision] - A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 8.2e+160], N[(180.0 * N[(N[ArcTan[N[((-N[(N[Sqrt[A ^ 2 + B$95$m ^ 2], $MachinePrecision] + A), $MachinePrecision]) / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B$95$m / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if C < -1.30000000000000001e-54

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 66.7%

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

   if -1.30000000000000001e-54 < C < 8.19999999999999996e160

   1. Initial program 54.0%

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

   2. Taylor expanded in C around 0

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-fma.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 44.5

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

   4. Applied rewrites 44.5%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lower-hypot.f64 63.9

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

   6. Applied rewrites 63.9%

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

   if 8.19999999999999996e160 < C

   1. Initial program 54.0%

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

   2. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-sqrt.f64 N/A

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

      4. +-commutative N/A

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

      5. unpow2 N/A

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

      6. lower-fma.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 44.9

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

   4. Applied rewrites 44.9%

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

   5. Taylor expanded in C around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 25.1

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

   7. Applied rewrites 25.1%

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

Alternative 3: 75.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq 4.6 \cdot 10^{+55}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - B\_m\right) - A}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(\frac{B\_m}{C}, -0.5, \frac{0}{B\_m}\right)\right)}{\pi}\\ \end{array} \end{array} \]

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 (<= C 4.6e+55)
    (/ (* 180.0 (atan (/ (- (- C B_m) A) B_m))) PI)
    (/ (* 180.0 (atan (fma (/ B_m C) -0.5 (/ 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 <= 4.6e+55) {
		tmp = (180.0 * atan((((C - B_m) - A) / B_m))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(fma((B_m / C), -0.5, (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 (C <= 4.6e+55)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - B_m) - A) / B_m))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(fma(Float64(B_m / C), -0.5, 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[C, 4.6e+55], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - B$95$m), $MachinePrecision] - A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B$95$m / C), $MachinePrecision] * -0.5 + N[(0.0 / B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < 4.59999999999999975e55

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 66.7%

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

   if 4.59999999999999975e55 < C

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 66.7%

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

   10. Taylor expanded in C around inf

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

   12. Applied rewrites 25.1%

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

Alternative 4: 75.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq 4.6 \cdot 10^{+55}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - B\_m\right) - A}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B\_m}{C} \cdot -0.5\right)}{\pi}\\ \end{array} \end{array} \]

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 4.6e+55)
    (/ (* 180.0 (atan (/ (- (- C B_m) 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 <= 4.6e+55) {
		tmp = (180.0 * atan((((C - B_m) - 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 <= 4.6e+55) {
		tmp = (180.0 * Math.atan((((C - B_m) - 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 <= 4.6e+55:
		tmp = (180.0 * math.atan((((C - B_m) - 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 <= 4.6e+55)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - B_m) - A) / B_m))) / pi);
	else
		tmp = Float64(180.0 * Float64(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 <= 4.6e+55)
		tmp = (180.0 * atan((((C - B_m) - 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, 4.6e+55], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - B$95$m), $MachinePrecision] - A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B$95$m / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < 4.59999999999999975e55

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 66.7%

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

   if 4.59999999999999975e55 < C

   1. Initial program 54.0%

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

   2. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-sqrt.f64 N/A

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

      4. +-commutative N/A

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

      5. unpow2 N/A

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

      6. lower-fma.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 44.9

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

   4. Applied rewrites 44.9%

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

   5. Taylor expanded in C around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 25.1

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

   7. Applied rewrites 25.1%

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

Alternative 5: 74.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq -1.35 \cdot 10^{-54}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B\_m} - 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{+55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-\left(A + B\_m\right)}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B\_m}{C} \cdot -0.5\right)}{\pi}\\ \end{array} \end{array} \]

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 -1.35e-54)
    (/ (* 180.0 (atan (- (/ C B_m) 1.0))) PI)
    (if (<= C 4.6e+55)
      (* 180.0 (/ (atan (/ (- (+ A B_m)) 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 <= -1.35e-54) {
		tmp = (180.0 * atan(((C / B_m) - 1.0))) / ((double) M_PI);
	} else if (C <= 4.6e+55) {
		tmp = 180.0 * (atan((-(A + B_m) / 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 <= -1.35e-54) {
		tmp = (180.0 * Math.atan(((C / B_m) - 1.0))) / Math.PI;
	} else if (C <= 4.6e+55) {
		tmp = 180.0 * (Math.atan((-(A + B_m) / 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 <= -1.35e-54:
		tmp = (180.0 * math.atan(((C / B_m) - 1.0))) / math.pi
	elif C <= 4.6e+55:
		tmp = 180.0 * (math.atan((-(A + B_m) / 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 <= -1.35e-54)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B_m) - 1.0))) / pi);
	elseif (C <= 4.6e+55)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-Float64(A + B_m)) / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(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 <= -1.35e-54)
		tmp = (180.0 * atan(((C / B_m) - 1.0))) / pi;
	elseif (C <= 4.6e+55)
		tmp = 180.0 * (atan((-(A + B_m) / 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, -1.35e-54], N[(N[(180.0 * N[ArcTan[N[(N[(C / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 4.6e+55], N[(180.0 * N[(N[ArcTan[N[((-N[(A + B$95$m), $MachinePrecision]) / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B$95$m / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if C < -1.35000000000000013e-54

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 66.7%

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

   10. Taylor expanded in A around 0

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

       1. sub-flip N/A

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. add-to-fraction N/A

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

       5. mul-1-neg N/A

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

       6. +-commutative N/A

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

       7. sub-flip N/A

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

       8. sub-to-mult-rev N/A

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

       9. lift-/.f64 N/A

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

       10. lift--.f64 N/A

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

       11. lift-*.f64 N/A

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

       12. div-sub N/A

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

       13. lift-*.f64 N/A

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

       14. lift--.f64 N/A

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

       15. lift-/.f64 N/A

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

       16. lower--.f64 N/A

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

       17. lower-/.f64 56.1

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

   12. Applied rewrites 56.1%

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

   if -1.35000000000000013e-54 < C < 4.59999999999999975e55

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

   8. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-+.f64 55.7

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

   10. Applied rewrites 55.7%

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

   if 4.59999999999999975e55 < C

   1. Initial program 54.0%

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

   2. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-sqrt.f64 N/A

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

      4. +-commutative N/A

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

      5. unpow2 N/A

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

      6. lower-fma.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 44.9

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

   4. Applied rewrites 44.9%

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

   5. Taylor expanded in C around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 25.1

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

   7. Applied rewrites 25.1%

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

Alternative 6: 74.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq -1.35 \cdot 10^{-54}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B\_m} - 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{+55}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(-B\_m\right) - A}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B\_m}{C} \cdot -0.5\right)}{\pi}\\ \end{array} \end{array} \]

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 -1.35e-54)
    (/ (* 180.0 (atan (- (/ C B_m) 1.0))) PI)
    (if (<= C 4.6e+55)
      (/ (* 180.0 (atan (/ (- (- B_m) 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 <= -1.35e-54) {
		tmp = (180.0 * atan(((C / B_m) - 1.0))) / ((double) M_PI);
	} else if (C <= 4.6e+55) {
		tmp = (180.0 * atan(((-B_m - 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 <= -1.35e-54) {
		tmp = (180.0 * Math.atan(((C / B_m) - 1.0))) / Math.PI;
	} else if (C <= 4.6e+55) {
		tmp = (180.0 * Math.atan(((-B_m - 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 <= -1.35e-54:
		tmp = (180.0 * math.atan(((C / B_m) - 1.0))) / math.pi
	elif C <= 4.6e+55:
		tmp = (180.0 * math.atan(((-B_m - 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 <= -1.35e-54)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B_m) - 1.0))) / pi);
	elseif (C <= 4.6e+55)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(-B_m) - A) / B_m))) / pi);
	else
		tmp = Float64(180.0 * Float64(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 <= -1.35e-54)
		tmp = (180.0 * atan(((C / B_m) - 1.0))) / pi;
	elseif (C <= 4.6e+55)
		tmp = (180.0 * atan(((-B_m - 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, -1.35e-54], N[(N[(180.0 * N[ArcTan[N[(N[(C / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 4.6e+55], N[(N[(180.0 * N[ArcTan[N[(N[((-B$95$m) - A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B$95$m / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if C < -1.35000000000000013e-54

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 66.7%

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

   10. Taylor expanded in A around 0

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

       1. sub-flip N/A

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. add-to-fraction N/A

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

       5. mul-1-neg N/A

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

       6. +-commutative N/A

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

       7. sub-flip N/A

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

       8. sub-to-mult-rev N/A

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

       9. lift-/.f64 N/A

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

       10. lift--.f64 N/A

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

       11. lift-*.f64 N/A

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

       12. div-sub N/A

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

       13. lift-*.f64 N/A

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

       14. lift--.f64 N/A

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

       15. lift-/.f64 N/A

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

       16. lower--.f64 N/A

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

       17. lower-/.f64 56.1

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

   12. Applied rewrites 56.1%

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

   if -1.35000000000000013e-54 < C < 4.59999999999999975e55

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 66.7%

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

   10. Taylor expanded in C around 0

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

       1. sub-to-mult-rev N/A

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

       2. mul-1-neg N/A

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

       3. add-flip N/A

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

       4. mul-1-neg N/A

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

       5. sub-negate-rev N/A

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

       6. mul-1-neg N/A

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

       7. lower--.f64 N/A

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

       8. lower-neg.f64 55.7

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

   12. Applied rewrites 55.7%

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

   if 4.59999999999999975e55 < C

   1. Initial program 54.0%

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

   2. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-sqrt.f64 N/A

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

      4. +-commutative N/A

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

      5. unpow2 N/A

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

      6. lower-fma.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 44.9

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

   4. Applied rewrites 44.9%

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

   5. Taylor expanded in C around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 25.1

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

   7. Applied rewrites 25.1%

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

Alternative 7: 74.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq -1.35 \cdot 10^{-54}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B\_m} - 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 4.6 \cdot 10^{+55}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B\_m}{C} \cdot -0.5\right)}{\pi}\\ \end{array} \end{array} \]

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 -1.35e-54)
    (/ (* 180.0 (atan (- (/ C B_m) 1.0))) PI)
    (if (<= C 4.6e+55)
      (/ (* 180.0 (atan (- -1.0 (/ 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 <= -1.35e-54) {
		tmp = (180.0 * atan(((C / B_m) - 1.0))) / ((double) M_PI);
	} else if (C <= 4.6e+55) {
		tmp = (180.0 * atan((-1.0 - (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 <= -1.35e-54) {
		tmp = (180.0 * Math.atan(((C / B_m) - 1.0))) / Math.PI;
	} else if (C <= 4.6e+55) {
		tmp = (180.0 * Math.atan((-1.0 - (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 <= -1.35e-54:
		tmp = (180.0 * math.atan(((C / B_m) - 1.0))) / math.pi
	elif C <= 4.6e+55:
		tmp = (180.0 * math.atan((-1.0 - (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 <= -1.35e-54)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B_m) - 1.0))) / pi);
	elseif (C <= 4.6e+55)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B_m)))) / pi);
	else
		tmp = Float64(180.0 * Float64(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 <= -1.35e-54)
		tmp = (180.0 * atan(((C / B_m) - 1.0))) / pi;
	elseif (C <= 4.6e+55)
		tmp = (180.0 * atan((-1.0 - (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, -1.35e-54], N[(N[(180.0 * N[ArcTan[N[(N[(C / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 4.6e+55], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B$95$m / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if C < -1.35000000000000013e-54

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 66.7%

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

   10. Taylor expanded in A around 0

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

       1. sub-flip N/A

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. add-to-fraction N/A

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

       5. mul-1-neg N/A

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

       6. +-commutative N/A

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

       7. sub-flip N/A

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

       8. sub-to-mult-rev N/A

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

       9. lift-/.f64 N/A

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

       10. lift--.f64 N/A

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

       11. lift-*.f64 N/A

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

       12. div-sub N/A

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

       13. lift-*.f64 N/A

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

       14. lift--.f64 N/A

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

       15. lift-/.f64 N/A

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

       16. lower--.f64 N/A

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

       17. lower-/.f64 56.1

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

   12. Applied rewrites 56.1%

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

   if -1.35000000000000013e-54 < C < 4.59999999999999975e55

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 66.7%

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

   10. Taylor expanded in C around 0

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

   12. Applied rewrites 55.7%

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

   if 4.59999999999999975e55 < C

   1. Initial program 54.0%

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

   2. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-sqrt.f64 N/A

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

      4. +-commutative N/A

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

      5. unpow2 N/A

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

      6. lower-fma.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 44.9

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

   4. Applied rewrites 44.9%

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

   5. Taylor expanded in C around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 25.1

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

   7. Applied rewrites 25.1%

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

Alternative 8: 74.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -1.7 \cdot 10^{+90}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B\_m}{A} \cdot 0.5\right)}{\pi} \cdot 180\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-34}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B\_m} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

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 -1.7e+90)
    (* (/ (atan (* (/ B_m A) 0.5)) PI) 180.0)
    (if (<= A 5e-34)
      (/ (* 180.0 (atan (- (/ C B_m) 1.0))) PI)
      (/ (* 180.0 (atan (- -1.0 (/ 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 <= -1.7e+90) {
		tmp = (atan(((B_m / A) * 0.5)) / ((double) M_PI)) * 180.0;
	} else if (A <= 5e-34) {
		tmp = (180.0 * atan(((C / B_m) - 1.0))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((-1.0 - (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 <= -1.7e+90) {
		tmp = (Math.atan(((B_m / A) * 0.5)) / Math.PI) * 180.0;
	} else if (A <= 5e-34) {
		tmp = (180.0 * Math.atan(((C / B_m) - 1.0))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan((-1.0 - (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 <= -1.7e+90:
		tmp = (math.atan(((B_m / A) * 0.5)) / math.pi) * 180.0
	elif A <= 5e-34:
		tmp = (180.0 * math.atan(((C / B_m) - 1.0))) / math.pi
	else:
		tmp = (180.0 * math.atan((-1.0 - (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 <= -1.7e+90)
		tmp = Float64(Float64(atan(Float64(Float64(B_m / A) * 0.5)) / pi) * 180.0);
	elseif (A <= 5e-34)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B_m) - 1.0))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - 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 <= -1.7e+90)
		tmp = (atan(((B_m / A) * 0.5)) / pi) * 180.0;
	elseif (A <= 5e-34)
		tmp = (180.0 * atan(((C / B_m) - 1.0))) / pi;
	else
		tmp = (180.0 * atan((-1.0 - (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, -1.7e+90], N[(N[(N[ArcTan[N[(N[(B$95$m / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[A, 5e-34], N[(N[(180.0 * N[ArcTan[N[(N[(C / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -1.70000000000000009e90

   1. Initial program 54.0%

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

   2. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 26.9

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

   4. Applied rewrites 26.9%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lower-*.f64 N/A

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

      4. pow2 N/A

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

      5. pow2 N/A

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

      6. pow2 N/A

         \[\leadsto 180 \cdot \left(\tan^{-1} \left(\frac{B}{A} \cdot \frac{1}{2}\right) \cdot \mathsf{Rewrite=>}\left(lower-/.f64, \left(\frac{1}{\pi}\right)\right)\right) \]

   6. Applied rewrites 26.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 26.8

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. mult-flip-rev N/A

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

      7. lower-/.f64 26.9

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

   8. Applied rewrites 26.9%

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

   if -1.70000000000000009e90 < A < 5.0000000000000003e-34

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 66.7%

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

   10. Taylor expanded in A around 0

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

       1. sub-flip N/A

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. add-to-fraction N/A

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

       5. mul-1-neg N/A

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

       6. +-commutative N/A

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

       7. sub-flip N/A

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

       8. sub-to-mult-rev N/A

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

       9. lift-/.f64 N/A

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

       10. lift--.f64 N/A

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

       11. lift-*.f64 N/A

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

       12. div-sub N/A

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

       13. lift-*.f64 N/A

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

       14. lift--.f64 N/A

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

       15. lift-/.f64 N/A

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

       16. lower--.f64 N/A

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

       17. lower-/.f64 56.1

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

   12. Applied rewrites 56.1%

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

   if 5.0000000000000003e-34 < A

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 66.7%

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

   10. Taylor expanded in C around 0

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

   12. Applied rewrites 55.7%

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

Alternative 9: 67.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq -1.35 \cdot 10^{-54}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C}{B\_m} - 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.5 \cdot 10^{+167}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \end{array} \end{array} \]

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 -1.35e-54)
    (/ (* 180.0 (atan (- (/ C B_m) 1.0))) PI)
    (if (<= C 6.5e+167)
      (/ (* 180.0 (atan (- -1.0 (/ A B_m)))) PI)
      (* 180.0 (/ (atan 0.0) 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 <= -1.35e-54) {
		tmp = (180.0 * atan(((C / B_m) - 1.0))) / ((double) M_PI);
	} else if (C <= 6.5e+167) {
		tmp = (180.0 * atan((-1.0 - (A / B_m)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(0.0) / ((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 <= -1.35e-54) {
		tmp = (180.0 * Math.atan(((C / B_m) - 1.0))) / Math.PI;
	} else if (C <= 6.5e+167) {
		tmp = (180.0 * Math.atan((-1.0 - (A / B_m)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(0.0) / 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 <= -1.35e-54:
		tmp = (180.0 * math.atan(((C / B_m) - 1.0))) / math.pi
	elif C <= 6.5e+167:
		tmp = (180.0 * math.atan((-1.0 - (A / B_m)))) / math.pi
	else:
		tmp = 180.0 * (math.atan(0.0) / 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 <= -1.35e-54)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C / B_m) - 1.0))) / pi);
	elseif (C <= 6.5e+167)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B_m)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(0.0) / 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 <= -1.35e-54)
		tmp = (180.0 * atan(((C / B_m) - 1.0))) / pi;
	elseif (C <= 6.5e+167)
		tmp = (180.0 * atan((-1.0 - (A / B_m)))) / pi;
	else
		tmp = 180.0 * (atan(0.0) / 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, -1.35e-54], N[(N[(180.0 * N[ArcTan[N[(N[(C / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 6.5e+167], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if C < -1.35000000000000013e-54

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 66.7%

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

   10. Taylor expanded in A around 0

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

       1. sub-flip N/A

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. add-to-fraction N/A

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

       5. mul-1-neg N/A

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

       6. +-commutative N/A

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

       7. sub-flip N/A

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

       8. sub-to-mult-rev N/A

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

       9. lift-/.f64 N/A

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

       10. lift--.f64 N/A

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

       11. lift-*.f64 N/A

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

       12. div-sub N/A

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

       13. lift-*.f64 N/A

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

       14. lift--.f64 N/A

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

       15. lift-/.f64 N/A

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

       16. lower--.f64 N/A

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

       17. lower-/.f64 56.1

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

   12. Applied rewrites 56.1%

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

   if -1.35000000000000013e-54 < C < 6.5e167

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 66.7%

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

   10. Taylor expanded in C around 0

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

   12. Applied rewrites 55.7%

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

   if 6.5e167 < C

   1. Initial program 54.0%

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

   2. Taylor expanded in C around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-rgt1-in N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 13.5

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

   4. Applied rewrites 13.5%

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

   5. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]
   6. Step-by-step derivation

   7. Applied rewrites 13.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 67.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq -1.35 \cdot 10^{-54}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B\_m} - 1\right)}{\pi}\\ \mathbf{elif}\;C \leq 6.5 \cdot 10^{+167}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 - \frac{A}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \end{array} \end{array} \]

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 -1.35e-54)
    (* 180.0 (/ (atan (- (/ C B_m) 1.0)) PI))
    (if (<= C 6.5e+167)
      (/ (* 180.0 (atan (- -1.0 (/ A B_m)))) PI)
      (* 180.0 (/ (atan 0.0) 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 <= -1.35e-54) {
		tmp = 180.0 * (atan(((C / B_m) - 1.0)) / ((double) M_PI));
	} else if (C <= 6.5e+167) {
		tmp = (180.0 * atan((-1.0 - (A / B_m)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(0.0) / ((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 <= -1.35e-54) {
		tmp = 180.0 * (Math.atan(((C / B_m) - 1.0)) / Math.PI);
	} else if (C <= 6.5e+167) {
		tmp = (180.0 * Math.atan((-1.0 - (A / B_m)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(0.0) / 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 <= -1.35e-54:
		tmp = 180.0 * (math.atan(((C / B_m) - 1.0)) / math.pi)
	elif C <= 6.5e+167:
		tmp = (180.0 * math.atan((-1.0 - (A / B_m)))) / math.pi
	else:
		tmp = 180.0 * (math.atan(0.0) / 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 <= -1.35e-54)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B_m) - 1.0)) / pi));
	elseif (C <= 6.5e+167)
		tmp = Float64(Float64(180.0 * atan(Float64(-1.0 - Float64(A / B_m)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(0.0) / 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 <= -1.35e-54)
		tmp = 180.0 * (atan(((C / B_m) - 1.0)) / pi);
	elseif (C <= 6.5e+167)
		tmp = (180.0 * atan((-1.0 - (A / B_m)))) / pi;
	else
		tmp = 180.0 * (atan(0.0) / 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, -1.35e-54], N[(180.0 * N[(N[ArcTan[N[(N[(C / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 6.5e+167], N[(N[(180.0 * N[ArcTan[N[(-1.0 - N[(A / B$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if C < -1.35000000000000013e-54

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in A around 0

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 56.1

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

   7. Applied rewrites 56.1%

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

   if -1.35000000000000013e-54 < C < 6.5e167

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   9. Applied rewrites 66.7%

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

   10. Taylor expanded in C around 0

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

   12. Applied rewrites 55.7%

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

   if 6.5e167 < C

   1. Initial program 54.0%

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

   2. Taylor expanded in C around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-rgt1-in N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 13.5

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

   4. Applied rewrites 13.5%

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

   5. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]
   6. Step-by-step derivation

   7. Applied rewrites 13.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 63.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -3.9 \cdot 10^{+223}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;A \leq 5.4 \cdot 10^{+137}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B\_m} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

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 -3.9e+223)
    (* 180.0 (/ (atan 0.0) PI))
    (if (<= A 5.4e+137)
      (* 180.0 (/ (atan (- (/ C B_m) 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 <= -3.9e+223) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (A <= 5.4e+137) {
		tmp = 180.0 * (atan(((C / B_m) - 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 <= -3.9e+223) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (A <= 5.4e+137) {
		tmp = 180.0 * (Math.atan(((C / B_m) - 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 <= -3.9e+223:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif A <= 5.4e+137:
		tmp = 180.0 * (math.atan(((C / B_m) - 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 <= -3.9e+223)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (A <= 5.4e+137)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B_m) - 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 <= -3.9e+223)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (A <= 5.4e+137)
		tmp = 180.0 * (atan(((C / B_m) - 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, -3.9e+223], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.4e+137], N[(180.0 * N[(N[ArcTan[N[(N[(C / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $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 < -3.8999999999999999e223

   1. Initial program 54.0%

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

   2. Taylor expanded in C around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-rgt1-in N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 13.5

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

   4. Applied rewrites 13.5%

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

   5. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]
   6. Step-by-step derivation

   7. Applied rewrites 13.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]

   if -3.8999999999999999e223 < A < 5.40000000000000034e137

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in A around 0

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 56.1

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

   7. Applied rewrites 56.1%

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

   if 5.40000000000000034e137 < A

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

   8. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 23.3

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

   10. Applied rewrites 23.3%

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

Alternative 12: 52.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -2.4 \cdot 10^{+115}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{elif}\;A \leq 5.8 \cdot 10^{+51}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

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 -2.4e+115)
    (* 180.0 (/ (atan 0.0) PI))
    (if (<= A 5.8e+51)
      (* 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 <= -2.4e+115) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else if (A <= 5.8e+51) {
		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 <= -2.4e+115) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else if (A <= 5.8e+51) {
		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 <= -2.4e+115:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	elif A <= 5.8e+51:
		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 <= -2.4e+115)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	elseif (A <= 5.8e+51)
		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 <= -2.4e+115)
		tmp = 180.0 * (atan(0.0) / pi);
	elseif (A <= 5.8e+51)
		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, -2.4e+115], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5.8e+51], 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 < -2.4e115

   1. Initial program 54.0%

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

   2. Taylor expanded in C around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-rgt1-in N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 13.5

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

   4. Applied rewrites 13.5%

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

   5. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]
   6. Step-by-step derivation

   7. Applied rewrites 13.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]

   if -2.4e115 < A < 5.7999999999999997e51

   1. Initial program 54.0%

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

   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 39.9%

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

   if 5.7999999999999997e51 < A

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

   8. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 23.3

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

   10. Applied rewrites 23.3%

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

Alternative 13: 51.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq -3.6 \cdot 10^{-57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B\_m}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.3 \cdot 10^{+161}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \end{array} \end{array} \]

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 -3.6e-57)
    (* 180.0 (/ (atan (/ C B_m)) PI))
    (if (<= C 1.3e+161)
      (* 180.0 (/ (atan -1.0) PI))
      (* 180.0 (/ (atan 0.0) 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 <= -3.6e-57) {
		tmp = 180.0 * (atan((C / B_m)) / ((double) M_PI));
	} else if (C <= 1.3e+161) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(0.0) / ((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 <= -3.6e-57) {
		tmp = 180.0 * (Math.atan((C / B_m)) / Math.PI);
	} else if (C <= 1.3e+161) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(0.0) / 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 <= -3.6e-57:
		tmp = 180.0 * (math.atan((C / B_m)) / math.pi)
	elif C <= 1.3e+161:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(0.0) / 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 <= -3.6e-57)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B_m)) / pi));
	elseif (C <= 1.3e+161)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(0.0) / 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 <= -3.6e-57)
		tmp = 180.0 * (atan((C / B_m)) / pi);
	elseif (C <= 1.3e+161)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan(0.0) / 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, -3.6e-57], N[(180.0 * N[(N[ArcTan[N[(C / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.3e+161], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if C < -3.6000000000000002e-57

   1. Initial program 54.0%

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

   2. Taylor expanded in B around inf

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.7

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

   4. Applied rewrites 65.7%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 66.7

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

   7. Applied rewrites 66.7%

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

   8. Taylor expanded in C around inf

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

      1. lower-/.f64 23.7

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

   10. Applied rewrites 23.7%

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

   if -3.6000000000000002e-57 < C < 1.2999999999999999e161

   1. Initial program 54.0%

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

   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 39.9%

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

   if 1.2999999999999999e161 < C

   1. Initial program 54.0%

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

   2. Taylor expanded in C around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-rgt1-in N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 13.5

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

   4. Applied rewrites 13.5%

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

   5. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]
   6. Step-by-step derivation

   7. Applied rewrites 13.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 44.9% accurate, 3.3× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;B\_m \leq 9.5 \cdot 10^{-138}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

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 (<= B_m 9.5e-138)
    (* 180.0 (/ (atan 0.0) 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 (B_m <= 9.5e-138) {
		tmp = 180.0 * (atan(0.0) / ((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 (B_m <= 9.5e-138) {
		tmp = 180.0 * (Math.atan(0.0) / 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 B_m <= 9.5e-138:
		tmp = 180.0 * (math.atan(0.0) / 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 (B_m <= 9.5e-138)
		tmp = Float64(180.0 * Float64(atan(0.0) / 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 (B_m <= 9.5e-138)
		tmp = 180.0 * (atan(0.0) / 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[B$95$m, 9.5e-138], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if B < 9.49999999999999997e-138

   1. Initial program 54.0%

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

   2. Taylor expanded in C around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-rgt1-in N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 13.5

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

   4. Applied rewrites 13.5%

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

   5. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]
   6. Step-by-step derivation

   7. Applied rewrites 13.5%

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]

   if 9.49999999999999997e-138 < B

   1. Initial program 54.0%

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

   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 39.9%

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

Alternative 15: 39.9% 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 54.0%

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

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 39.9%

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

Reproduce

herbie shell --seed 2025140 
(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)))