ABCF->ab-angle angle

Percentage Accurate: 54.7% → 83.3%

Time: 4.8s

Alternatives: 11

Speedup: 2.5×

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: 54.7% 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: 83.3% accurate, 0.6× speedup

Math

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

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 (<=
       (*
        180.0
        (/
         (atan
          (*
           (/ 1.0 B_m)
           (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B_m 2.0))))))
         PI))
       -40.0)
    (* 180.0 (/ (atan (* (/ 1.0 B_m) (- (- C A) (hypot (- C A) B_m)))) PI))
    (*
     (* (atan (fma -1.0 (/ (+ A (* -1.0 A)) B_m) (* -0.5 (/ B_m C)))) 180.0)
     (/ 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 ((180.0 * (atan(((1.0 / B_m) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B_m, 2.0)))))) / ((double) M_PI))) <= -40.0) {
		tmp = 180.0 * (atan(((1.0 / B_m) * ((C - A) - hypot((C - A), B_m)))) / ((double) M_PI));
	} else {
		tmp = (atan(fma(-1.0, ((A + (-1.0 * A)) / B_m), (-0.5 * (B_m / C)))) * 180.0) * (1.0 / ((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)) <= -40.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B_m) * Float64(Float64(C - A) - hypot(Float64(C - A), B_m)))) / pi));
	else
		tmp = Float64(Float64(atan(fma(-1.0, Float64(Float64(A + Float64(-1.0 * A)) / B_m), Float64(-0.5 * Float64(B_m / C)))) * 180.0) * Float64(1.0 / 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], -40.0], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B$95$m), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(-1.0 * N[(N[(A + N[(-1.0 * A), $MachinePrecision]), $MachinePrecision] / B$95$m), $MachinePrecision] + N[(-0.5 * N[(B$95$m / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] * N[(1.0 / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -40

   1. Initial program 54.7%

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

      1. lift-sqrt.f64 N/A

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

      2. sqrt-fabs-rev N/A

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

      3. lift-sqrt.f64 N/A

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

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

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

      5. lift-sqrt.f64 N/A

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

      6. lift-sqrt.f64 N/A

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

      7. rem-square-sqrt N/A

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

      8. lift-+.f64 N/A

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

      9. lift-pow.f64 N/A

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

      10. unpow2 N/A

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

      11. lift-pow.f64 N/A

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

      12. unpow2 N/A

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

      13. sqr-neg-rev N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lift--.f64 N/A

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

      17. lift--.f64 N/A

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

      18. sub-negate-rev N/A

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

      19. lift--.f64 N/A

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

   3. Applied rewrites 79.0%

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

   if -40 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64)))

   1. Initial program 54.7%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.3

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

   4. Applied rewrites 66.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. mult-flip N/A

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

      5. lower-*.f64 N/A

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

   6. Applied rewrites 67.5%

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

   7. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 26.5

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

   9. Applied rewrites 26.5%

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

Alternative 2: 78.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -1.78 \cdot 10^{+108}:\\ \;\;\;\;\tan^{-1} \left(\frac{B\_m}{A} \cdot 0.5\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{-60}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B\_m} \cdot \left(C - \mathsf{hypot}\left(C, B\_m\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B\_m} - 1\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

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 -1.78e+108)
    (* (atan (* (/ B_m A) 0.5)) (/ 180.0 PI))
    (if (<= A 5e-60)
      (* 180.0 (/ (atan (* (/ 1.0 B_m) (- C (hypot C B_m)))) PI))
      (* (/ (atan (- (/ (- C A) B_m) 1.0)) PI) 180.0)))))

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 <= -1.78e+108) {
		tmp = atan(((B_m / A) * 0.5)) * (180.0 / ((double) M_PI));
	} else if (A <= 5e-60) {
		tmp = 180.0 * (atan(((1.0 / B_m) * (C - hypot(C, B_m)))) / ((double) M_PI));
	} else {
		tmp = (atan((((C - A) / B_m) - 1.0)) / ((double) M_PI)) * 180.0;
	}
	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 <= -1.78e+108) {
		tmp = Math.atan(((B_m / A) * 0.5)) * (180.0 / Math.PI);
	} else if (A <= 5e-60) {
		tmp = 180.0 * (Math.atan(((1.0 / B_m) * (C - Math.hypot(C, B_m)))) / Math.PI);
	} else {
		tmp = (Math.atan((((C - A) / B_m) - 1.0)) / Math.PI) * 180.0;
	}
	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 <= -1.78e+108:
		tmp = math.atan(((B_m / A) * 0.5)) * (180.0 / math.pi)
	elif A <= 5e-60:
		tmp = 180.0 * (math.atan(((1.0 / B_m) * (C - math.hypot(C, B_m)))) / math.pi)
	else:
		tmp = (math.atan((((C - A) / B_m) - 1.0)) / math.pi) * 180.0
	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 <= -1.78e+108)
		tmp = Float64(atan(Float64(Float64(B_m / A) * 0.5)) * Float64(180.0 / pi));
	elseif (A <= 5e-60)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B_m) * Float64(C - hypot(C, B_m)))) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) / B_m) - 1.0)) / pi) * 180.0);
	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 <= -1.78e+108)
		tmp = atan(((B_m / A) * 0.5)) * (180.0 / pi);
	elseif (A <= 5e-60)
		tmp = 180.0 * (atan(((1.0 / B_m) * (C - hypot(C, B_m)))) / pi);
	else
		tmp = (atan((((C - A) / B_m) - 1.0)) / pi) * 180.0;
	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, -1.78e+108], N[(N[ArcTan[N[(N[(B$95$m / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5e-60], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B$95$m), $MachinePrecision] * N[(C - N[Sqrt[C ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -1.78e108

   1. Initial program 54.7%

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

   2. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 24.7

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

   4. Applied rewrites 24.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

   6. Applied rewrites 24.8%

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

   if -1.78e108 < A < 5.0000000000000001e-60

   1. Initial program 54.7%

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

      1. lift-sqrt.f64 N/A

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

      2. sqrt-fabs-rev N/A

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

      3. lift-sqrt.f64 N/A

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

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

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

      5. lift-sqrt.f64 N/A

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

      6. lift-sqrt.f64 N/A

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

      7. rem-square-sqrt N/A

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

      8. lift-+.f64 N/A

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

      9. lift-pow.f64 N/A

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

      10. unpow2 N/A

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

      11. lift-pow.f64 N/A

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

      12. unpow2 N/A

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

      13. sqr-neg-rev N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lift--.f64 N/A

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

      17. lift--.f64 N/A

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

      18. sub-negate-rev N/A

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

      19. lift--.f64 N/A

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

   3. Applied rewrites 79.0%

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

   4. Taylor expanded in A around 0

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

   6. Applied rewrites 73.1%

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

   7. Taylor expanded in A around 0

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

   9. Applied rewrites 63.8%

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

   if 5.0000000000000001e-60 < A

   1. Initial program 54.7%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.3

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

   4. Applied rewrites 66.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 66.3

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

   6. Applied rewrites 67.5%

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

Alternative 3: 75.4% accurate, 0.6× speedup

Math

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

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))
       -40.0)
    (* (* (atan (- (/ (- C A) B_m) 1.0)) 180.0) (/ 1.0 PI))
    (*
     180.0
     (/ (atan (fma -1.0 (/ (+ A (* -1.0 A)) B_m) (* -0.5 (/ B_m C)))) 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))) <= -40.0) {
		tmp = (atan((((C - A) / B_m) - 1.0)) * 180.0) * (1.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(fma(-1.0, ((A + (-1.0 * A)) / B_m), (-0.5 * (B_m / C)))) / ((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)) <= -40.0)
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) / B_m) - 1.0)) * 180.0) * Float64(1.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(fma(-1.0, Float64(Float64(A + Float64(-1.0 * A)) / B_m), Float64(-0.5 * Float64(B_m / C)))) / 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], -40.0], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] * N[(1.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 * N[(N[(A + N[(-1.0 * A), $MachinePrecision]), $MachinePrecision] / B$95$m), $MachinePrecision] + N[(-0.5 * N[(B$95$m / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -40

   1. Initial program 54.7%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.3

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

   4. Applied rewrites 66.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. mult-flip N/A

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

      5. lower-*.f64 N/A

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

   6. Applied rewrites 67.5%

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

   if -40 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64)))

   1. Initial program 54.7%

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

   2. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 26.5

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

   4. Applied rewrites 26.5%

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

Alternative 4: 75.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -1.45 \cdot 10^{+108}:\\ \;\;\;\;\tan^{-1} \left(\frac{B\_m}{A} \cdot 0.5\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\left(\tan^{-1} \left(\frac{C - A}{B\_m} - 1\right) \cdot 180\right) \cdot \frac{1}{\pi}\\ \end{array} \end{array} \]

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 (<= A -1.45e+108)
    (* (atan (* (/ B_m A) 0.5)) (/ 180.0 PI))
    (* (* (atan (- (/ (- C A) B_m) 1.0)) 180.0) (/ 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 (A <= -1.45e+108) {
		tmp = atan(((B_m / A) * 0.5)) * (180.0 / ((double) M_PI));
	} else {
		tmp = (atan((((C - A) / B_m) - 1.0)) * 180.0) * (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 (A <= -1.45e+108) {
		tmp = Math.atan(((B_m / A) * 0.5)) * (180.0 / Math.PI);
	} else {
		tmp = (Math.atan((((C - A) / B_m) - 1.0)) * 180.0) * (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 A <= -1.45e+108:
		tmp = math.atan(((B_m / A) * 0.5)) * (180.0 / math.pi)
	else:
		tmp = (math.atan((((C - A) / B_m) - 1.0)) * 180.0) * (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 (A <= -1.45e+108)
		tmp = Float64(atan(Float64(Float64(B_m / A) * 0.5)) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) / B_m) - 1.0)) * 180.0) * Float64(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 (A <= -1.45e+108)
		tmp = atan(((B_m / A) * 0.5)) * (180.0 / pi);
	else
		tmp = (atan((((C - A) / B_m) - 1.0)) * 180.0) * (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[A, -1.45e+108], N[(N[ArcTan[N[(N[(B$95$m / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] * N[(1.0 / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < -1.45000000000000004e108

   1. Initial program 54.7%

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

   2. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 24.7

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

   4. Applied rewrites 24.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

   6. Applied rewrites 24.8%

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

   if -1.45000000000000004e108 < A

   1. Initial program 54.7%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.3

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

   4. Applied rewrites 66.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. mult-flip N/A

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

      5. lower-*.f64 N/A

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

   6. Applied rewrites 67.5%

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

Alternative 5: 74.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -1.45 \cdot 10^{+108}:\\ \;\;\;\;\tan^{-1} \left(\frac{B\_m}{A} \cdot 0.5\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B\_m} - 1\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

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 -1.45e+108)
    (* (atan (* (/ B_m A) 0.5)) (/ 180.0 PI))
    (* (/ (atan (- (/ (- C A) B_m) 1.0)) PI) 180.0))))

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 <= -1.45e+108) {
		tmp = atan(((B_m / A) * 0.5)) * (180.0 / ((double) M_PI));
	} else {
		tmp = (atan((((C - A) / B_m) - 1.0)) / ((double) M_PI)) * 180.0;
	}
	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 <= -1.45e+108) {
		tmp = Math.atan(((B_m / A) * 0.5)) * (180.0 / Math.PI);
	} else {
		tmp = (Math.atan((((C - A) / B_m) - 1.0)) / Math.PI) * 180.0;
	}
	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 <= -1.45e+108:
		tmp = math.atan(((B_m / A) * 0.5)) * (180.0 / math.pi)
	else:
		tmp = (math.atan((((C - A) / B_m) - 1.0)) / math.pi) * 180.0
	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 <= -1.45e+108)
		tmp = Float64(atan(Float64(Float64(B_m / A) * 0.5)) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) / B_m) - 1.0)) / pi) * 180.0);
	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 <= -1.45e+108)
		tmp = atan(((B_m / A) * 0.5)) * (180.0 / pi);
	else
		tmp = (atan((((C - A) / B_m) - 1.0)) / pi) * 180.0;
	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, -1.45e+108], N[(N[ArcTan[N[(N[(B$95$m / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < -1.45000000000000004e108

   1. Initial program 54.7%

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

   2. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 24.7

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

   4. Applied rewrites 24.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

   6. Applied rewrites 24.8%

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

   if -1.45000000000000004e108 < A

   1. Initial program 54.7%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.3

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

   4. Applied rewrites 66.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 66.3

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

   6. Applied rewrites 67.5%

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

Alternative 6: 69.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -1.45 \cdot 10^{+108}:\\ \;\;\;\;\tan^{-1} \left(\frac{B\_m}{A} \cdot 0.5\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 3.9 \cdot 10^{+120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B\_m}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A -1.45e+108)
    (* (atan (* (/ B_m A) 0.5)) (/ 180.0 PI))
    (if (<= A 3.9e+120)
      (* 180.0 (/ (atan (/ (- C B_m) B_m)) PI))
      (* 180.0 (/ (atan (/ (- C A) B_m)) PI))))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -1.45e+108) {
		tmp = atan(((B_m / A) * 0.5)) * (180.0 / ((double) M_PI));
	} else if (A <= 3.9e+120) {
		tmp = 180.0 * (atan(((C - B_m) / B_m)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - A) / B_m)) / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -1.45e+108) {
		tmp = Math.atan(((B_m / A) * 0.5)) * (180.0 / Math.PI);
	} else if (A <= 3.9e+120) {
		tmp = 180.0 * (Math.atan(((C - B_m) / B_m)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - A) / B_m)) / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if A <= -1.45e+108:
		tmp = math.atan(((B_m / A) * 0.5)) * (180.0 / math.pi)
	elif A <= 3.9e+120:
		tmp = 180.0 * (math.atan(((C - B_m) / B_m)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - A) / B_m)) / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= -1.45e+108)
		tmp = Float64(atan(Float64(Float64(B_m / A) * 0.5)) * Float64(180.0 / pi));
	elseif (A <= 3.9e+120)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B_m) / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / B_m)) / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (A <= -1.45e+108)
		tmp = atan(((B_m / A) * 0.5)) * (180.0 / pi);
	elseif (A <= 3.9e+120)
		tmp = 180.0 * (atan(((C - B_m) / B_m)) / pi);
	else
		tmp = 180.0 * (atan(((C - A) / B_m)) / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, -1.45e+108], N[(N[ArcTan[N[(N[(B$95$m / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 3.9e+120], N[(180.0 * N[(N[ArcTan[N[(N[(C - B$95$m), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -1.45000000000000004e108

   1. Initial program 54.7%

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

   2. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 24.7

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

   4. Applied rewrites 24.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

   6. Applied rewrites 24.8%

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

   if -1.45000000000000004e108 < A < 3.8999999999999998e120

   1. Initial program 54.7%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.3

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

   4. Applied rewrites 66.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. add-to-fraction N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-lft-identity N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 67.5

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

   6. Applied rewrites 67.5%

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

   7. Taylor expanded in A around 0

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

   9. Applied rewrites 56.3%

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

   if 3.8999999999999998e120 < A

   1. Initial program 54.7%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.3

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

   4. Applied rewrites 66.3%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 36.0

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

   7. Applied rewrites 36.0%

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

Alternative 7: 62.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq 3.9 \cdot 10^{+120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B\_m}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A 3.9e+120)
    (* 180.0 (/ (atan (/ (- C B_m) B_m)) PI))
    (* 180.0 (/ (atan (/ (- C A) B_m)) PI)))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= 3.9e+120) {
		tmp = 180.0 * (atan(((C - B_m) / B_m)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - A) / B_m)) / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= 3.9e+120) {
		tmp = 180.0 * (Math.atan(((C - B_m) / B_m)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - A) / B_m)) / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if A <= 3.9e+120:
		tmp = 180.0 * (math.atan(((C - B_m) / B_m)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - A) / B_m)) / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= 3.9e+120)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B_m) / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / B_m)) / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (A <= 3.9e+120)
		tmp = 180.0 * (atan(((C - B_m) / B_m)) / pi);
	else
		tmp = 180.0 * (atan(((C - A) / B_m)) / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, 3.9e+120], N[(180.0 * N[(N[ArcTan[N[(N[(C - B$95$m), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < 3.8999999999999998e120

   1. Initial program 54.7%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.3

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

   4. Applied rewrites 66.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. add-to-fraction N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-lft-identity N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 67.5

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

   6. Applied rewrites 67.5%

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

   7. Taylor expanded in A around 0

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

   9. Applied rewrites 56.3%

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

   if 3.8999999999999998e120 < A

   1. Initial program 54.7%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.3

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

   4. Applied rewrites 66.3%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 36.0

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

   7. Applied rewrites 36.0%

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

Alternative 8: 62.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq 3.9 \cdot 10^{+120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B\_m} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A 3.9e+120)
    (* 180.0 (/ (atan (- (/ C B_m) 1.0)) PI))
    (* 180.0 (/ (atan (/ (- C A) B_m)) PI)))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= 3.9e+120) {
		tmp = 180.0 * (atan(((C / B_m) - 1.0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - A) / B_m)) / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= 3.9e+120) {
		tmp = 180.0 * (Math.atan(((C / B_m) - 1.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - A) / B_m)) / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if A <= 3.9e+120:
		tmp = 180.0 * (math.atan(((C / B_m) - 1.0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - A) / B_m)) / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= 3.9e+120)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B_m) - 1.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / B_m)) / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (A <= 3.9e+120)
		tmp = 180.0 * (atan(((C / B_m) - 1.0)) / pi);
	else
		tmp = 180.0 * (atan(((C - A) / B_m)) / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, 3.9e+120], 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[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < 3.8999999999999998e120

   1. Initial program 54.7%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.3

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

   4. Applied rewrites 66.3%

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

   5. Taylor expanded in A around 0

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

   7. Applied rewrites 56.3%

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

   if 3.8999999999999998e120 < A

   1. Initial program 54.7%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.3

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

   4. Applied rewrites 66.3%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 36.0

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

   7. Applied rewrites 36.0%

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

Alternative 9: 55.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;B\_m \leq 3.3 \cdot 10^{+49}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= B_m 3.3e+49)
    (* 180.0 (/ (atan (/ (- C A) B_m)) PI))
    (* 180.0 (/ (atan -1.0) PI)))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (B_m <= 3.3e+49) {
		tmp = 180.0 * (atan(((C - A) / B_m)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (B_m <= 3.3e+49) {
		tmp = 180.0 * (Math.atan(((C - A) / B_m)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if B_m <= 3.3e+49:
		tmp = 180.0 * (math.atan(((C - A) / B_m)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (B_m <= 3.3e+49)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (B_m <= 3.3e+49)
		tmp = 180.0 * (atan(((C - A) / B_m)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[B$95$m, 3.3e+49], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if B < 3.2999999999999998e49

   1. Initial program 54.7%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.3

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

   4. Applied rewrites 66.3%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 36.0

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

   7. Applied rewrites 36.0%

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

   if 3.2999999999999998e49 < B

   1. Initial program 54.7%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 40.3%

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

Alternative 10: 46.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;B\_m \leq 1.65 \cdot 10^{+49}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= B_m 1.65e+49)
    (* 180.0 (/ (atan (/ C B_m)) PI))
    (* 180.0 (/ (atan -1.0) PI)))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (B_m <= 1.65e+49) {
		tmp = 180.0 * (atan((C / B_m)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (B_m <= 1.65e+49) {
		tmp = 180.0 * (Math.atan((C / B_m)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if B_m <= 1.65e+49:
		tmp = 180.0 * (math.atan((C / B_m)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (B_m <= 1.65e+49)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (B_m <= 1.65e+49)
		tmp = 180.0 * (atan((C / B_m)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[B$95$m, 1.65e+49], N[(180.0 * N[(N[ArcTan[N[(C / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if B < 1.6499999999999999e49

   1. Initial program 54.7%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.3

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

   4. Applied rewrites 66.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. add-to-fraction N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. *-lft-identity N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 67.5

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

   6. Applied rewrites 67.5%

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

   7. Taylor expanded in C around inf

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

      1. lower-/.f64 23.5

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

   9. Applied rewrites 23.5%

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

   if 1.6499999999999999e49 < B

   1. Initial program 54.7%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 40.3%

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

Alternative 11: 40.3% 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 54.7%

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

2. Taylor expanded in B around inf

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

4. Applied rewrites 40.3%

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

Reproduce

herbie shell --seed 2025155 
(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)))