ABCF->ab-angle angle

Percentage Accurate: 53.2% → 82.1%

Time: 5.0s

Alternatives: 8

Speedup: 2.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \frac{1}{\left|B\right|}\\ \mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;180 \cdot \frac{\tan^{-1} \left(t\_0 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {\left(\left|B\right|\right)}^{2}}\right)\right)}{\pi} \leq -40:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_0 \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(C - A, \left|B\right|\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\mathsf{fma}\left(\frac{\left|B\right|}{C}, -0.5, \frac{0}{\left|B\right|}\right)\right) \cdot \left(\frac{1}{\pi} \cdot 180\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
  :precision binary64
  (let* ((t_0 (/ 1.0 (fabs B))))
  (*
   (copysign 1.0 B)
   (if (<=
        (*
         180.0
         (/
          (atan
           (*
            t_0
            (-
             (- C A)
             (sqrt (+ (pow (- A C) 2.0) (pow (fabs B) 2.0))))))
          PI))
        -40.0)
     (*
      180.0
      (/ (atan (* t_0 (- (- C A) (hypot (- C A) (fabs B))))) PI))
     (*
      (atan (fma (/ (fabs B) C) -0.5 (/ 0.0 (fabs B))))
      (* (/ 1.0 PI) 180.0))))))

C

double code(double A, double B, double C) {
	double t_0 = 1.0 / fabs(B);
	double tmp;
	if ((180.0 * (atan((t_0 * ((C - A) - sqrt((pow((A - C), 2.0) + pow(fabs(B), 2.0)))))) / ((double) M_PI))) <= -40.0) {
		tmp = 180.0 * (atan((t_0 * ((C - A) - hypot((C - A), fabs(B))))) / ((double) M_PI));
	} else {
		tmp = atan(fma((fabs(B) / C), -0.5, (0.0 / fabs(B)))) * ((1.0 / ((double) M_PI)) * 180.0);
	}
	return copysign(1.0, B) * tmp;
}

Julia

function code(A, B, C)
	t_0 = Float64(1.0 / abs(B))
	tmp = 0.0
	if (Float64(180.0 * Float64(atan(Float64(t_0 * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (abs(B) ^ 2.0)))))) / pi)) <= -40.0)
		tmp = Float64(180.0 * Float64(atan(Float64(t_0 * Float64(Float64(C - A) - hypot(Float64(C - A), abs(B))))) / pi));
	else
		tmp = Float64(atan(fma(Float64(abs(B) / C), -0.5, Float64(0.0 / abs(B)))) * Float64(Float64(1.0 / pi) * 180.0));
	end
	return Float64(copysign(1.0, B) * tmp)
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(1.0 / N[Abs[B], $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(180.0 * N[(N[ArcTan[N[(t$95$0 * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[Abs[B], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], -40.0], N[(180.0 * N[(N[ArcTan[N[(t$95$0 * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + N[Abs[B], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(N[Abs[B], $MachinePrecision] / C), $MachinePrecision] * -0.5 + N[(0.0 / N[Abs[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[(1.0 / Pi), $MachinePrecision] * 180.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 53.2%

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

      1. lift-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 78.2%

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

   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 53.2%

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

   2. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 25.6%

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

   4. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 25.6%

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

Alternative 2: 75.4% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 2.5e+64)
		tmp = (atan((((((C - A) / abs(B)) - 1.0) * abs(B)) / abs(B))) * 180.0) / pi;
	else
		tmp = atan(((-0.5 * abs(B)) / C)) * ((1.0 / pi) * 180.0);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[C, 2.5e+64], N[(N[(N[ArcTan[N[(N[(N[(N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision] * N[Abs[B], $MachinePrecision]), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[ArcTan[N[(N[(-0.5 * N[Abs[B], $MachinePrecision]), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] * N[(N[(1.0 / Pi), $MachinePrecision] * 180.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < 2.5e64

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 48.9%

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

   4. Applied rewrites 48.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 50.2%

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

   if 2.5e64 < C

   1. Initial program 53.2%

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

   2. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 25.6%

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

   4. Applied rewrites 25.6%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. mult-flip N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lift-/.f64 N/A

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

      12. distribute-neg-frac N/A

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

      13. lower-/.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. distribute-rgt1-in N/A

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

      17. metadata-eval N/A

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

      18. mul0-lft N/A

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

      19. metadata-eval 25.6%

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

   6. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   8. Applied rewrites 25.6%

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

Alternative 3: 75.4% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 2.5e+64)
		tmp = (atan((((C - A) / abs(B)) - 1.0)) * 180.0) / pi;
	else
		tmp = atan(((-0.5 * abs(B)) / C)) * ((1.0 / pi) * 180.0);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[C, 2.5e+64], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[ArcTan[N[(N[(-0.5 * N[Abs[B], $MachinePrecision]), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] * N[(N[(1.0 / Pi), $MachinePrecision] * 180.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < 2.5e64

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 48.9%

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

   4. Applied rewrites 48.9%

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

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

   6. Applied rewrites 50.2%

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

   if 2.5e64 < C

   1. Initial program 53.2%

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

   2. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 25.6%

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

   4. Applied rewrites 25.6%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. mult-flip N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lift-/.f64 N/A

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

      12. distribute-neg-frac N/A

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

      13. lower-/.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. distribute-rgt1-in N/A

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

      17. metadata-eval N/A

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

      18. mul0-lft N/A

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

      19. metadata-eval 25.6%

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

   6. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   8. Applied rewrites 25.6%

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

Alternative 4: 75.4% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 2.5e+64)
		tmp = (atan((((C - A) / abs(B)) - 1.0)) * 180.0) / pi;
	else
		tmp = (atan(((-0.5 * abs(B)) / C)) * 180.0) / pi;
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[C, 2.5e+64], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(-0.5 * N[Abs[B], $MachinePrecision]), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < 2.5e64

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 48.9%

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

   4. Applied rewrites 48.9%

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

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

   6. Applied rewrites 50.2%

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

   if 2.5e64 < C

   1. Initial program 53.2%

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

   2. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 25.6%

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

   4. Applied rewrites 25.6%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. mult-flip N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lift-/.f64 N/A

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

      12. distribute-neg-frac N/A

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

      13. lower-/.f64 N/A

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

      14. lift-+.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. distribute-rgt1-in N/A

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

      17. metadata-eval N/A

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

      18. mul0-lft N/A

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

      19. metadata-eval 25.6%

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

   6. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   8. Applied rewrites 25.6%

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

Alternative 5: 58.0% accurate, 1.9× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq -6.2 \cdot 10^{+148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{\left|B\right|}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2 \cdot 10^{-105}:\\ \;\;\;\;-45\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{\left|B\right|}\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
  :precision binary64
  (*
 (copysign 1.0 B)
 (if (<= A -6.2e+148)
   (* 180.0 (/ (atan (* 0.5 (/ (fabs B) A))) PI))
   (if (<= A 2e-105)
     -45.0
     (* 180.0 (/ (atan (/ (- C A) (fabs B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.2e+148) {
		tmp = 180.0 * (atan((0.5 * (fabs(B) / A))) / ((double) M_PI));
	} else if (A <= 2e-105) {
		tmp = -45.0;
	} else {
		tmp = 180.0 * (atan(((C - A) / fabs(B))) / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.2e+148) {
		tmp = 180.0 * (Math.atan((0.5 * (Math.abs(B) / A))) / Math.PI);
	} else if (A <= 2e-105) {
		tmp = -45.0;
	} else {
		tmp = 180.0 * (Math.atan(((C - A) / Math.abs(B))) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.2e+148:
		tmp = 180.0 * (math.atan((0.5 * (math.fabs(B) / A))) / math.pi)
	elif A <= 2e-105:
		tmp = -45.0
	else:
		tmp = 180.0 * (math.atan(((C - A) / math.fabs(B))) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.2e+148)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(abs(B) / A))) / pi));
	elseif (A <= 2e-105)
		tmp = -45.0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / abs(B))) / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.2e+148)
		tmp = 180.0 * (atan((0.5 * (abs(B) / A))) / pi);
	elseif (A <= 2e-105)
		tmp = -45.0;
	else
		tmp = 180.0 * (atan(((C - A) / abs(B))) / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[A, -6.2e+148], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(N[Abs[B], $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2e-105], -45.0, N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -6.1999999999999995e148

   1. Initial program 53.2%

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

   2. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 26.1%

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

   4. Applied rewrites 26.1%

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

   if -6.1999999999999995e148 < A < 1.9999999999999999e-105

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.4%

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

   5. Evaluated real constant 21.4%

      \[\leadsto \color{blue}{-45} \]

   if 1.9999999999999999e-105 < A

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 48.9%

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

   4. Applied rewrites 48.9%

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

   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 34.3%

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

   7. Applied rewrites 34.3%

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

Alternative 6: 56.1% accurate, 1.9× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;C \leq -1.6 \cdot 10^{+194}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C + C}{\left|B\right|}\right) \cdot 180}{\pi}\\ \mathbf{elif}\;C \leq 6 \cdot 10^{+64}:\\ \;\;\;\;-45\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{\left|B\right|}{C}\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
  :precision binary64
  (*
 (copysign 1.0 B)
 (if (<= C -1.6e+194)
   (/ (* (atan (/ (+ C C) (fabs B))) 180.0) PI)
   (if (<= C 6e+64)
     -45.0
     (* 180.0 (/ (atan (* -0.5 (/ (fabs B) C))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.6e+194) {
		tmp = (atan(((C + C) / fabs(B))) * 180.0) / ((double) M_PI);
	} else if (C <= 6e+64) {
		tmp = -45.0;
	} else {
		tmp = 180.0 * (atan((-0.5 * (fabs(B) / C))) / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.6e+194) {
		tmp = (Math.atan(((C + C) / Math.abs(B))) * 180.0) / Math.PI;
	} else if (C <= 6e+64) {
		tmp = -45.0;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (Math.abs(B) / C))) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.6e+194:
		tmp = (math.atan(((C + C) / math.fabs(B))) * 180.0) / math.pi
	elif C <= 6e+64:
		tmp = -45.0
	else:
		tmp = 180.0 * (math.atan((-0.5 * (math.fabs(B) / C))) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.6e+194)
		tmp = Float64(Float64(atan(Float64(Float64(C + C) / abs(B))) * 180.0) / pi);
	elseif (C <= 6e+64)
		tmp = -45.0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(abs(B) / C))) / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.6e+194)
		tmp = (atan(((C + C) / abs(B))) * 180.0) / pi;
	elseif (C <= 6e+64)
		tmp = -45.0;
	else
		tmp = 180.0 * (atan((-0.5 * (abs(B) / C))) / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[C, -1.6e+194], N[(N[(N[ArcTan[N[(N[(C + C), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 6e+64], -45.0, N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(N[Abs[B], $MachinePrecision] / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if C < -1.6000000000000001e194

   1. Initial program 53.2%

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

   2. Taylor expanded in C around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 22.6%

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

   4. Applied rewrites 22.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 22.6%

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

   if -1.6000000000000001e194 < C < 6.0000000000000004e64

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.4%

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

   5. Evaluated real constant 21.4%

      \[\leadsto \color{blue}{-45} \]

   if 6.0000000000000004e64 < C

   1. Initial program 53.2%

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

   2. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 25.6%

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

   4. Applied rewrites 25.6%

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

   5. Taylor expanded in A around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 25.6%

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

   7. Applied rewrites 25.6%

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

Alternative 7: 54.7% accurate, 2.0× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;\left|B\right| \leq 6 \cdot 10^{+76}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{\left|B\right|}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;-45\\ \end{array} \]

FPCore

(FPCore (A B C)
  :precision binary64
  (*
 (copysign 1.0 B)
 (if (<= (fabs B) 6e+76)
   (* 180.0 (/ (atan (/ (- C A) (fabs B))) PI))
   -45.0)))

C

double code(double A, double B, double C) {
	double tmp;
	if (fabs(B) <= 6e+76) {
		tmp = 180.0 * (atan(((C - A) / fabs(B))) / ((double) M_PI));
	} else {
		tmp = -45.0;
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (Math.abs(B) <= 6e+76) {
		tmp = 180.0 * (Math.atan(((C - A) / Math.abs(B))) / Math.PI);
	} else {
		tmp = -45.0;
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if math.fabs(B) <= 6e+76:
		tmp = 180.0 * (math.atan(((C - A) / math.fabs(B))) / math.pi)
	else:
		tmp = -45.0
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (abs(B) <= 6e+76)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / abs(B))) / pi));
	else
		tmp = -45.0;
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (abs(B) <= 6e+76)
		tmp = 180.0 * (atan(((C - A) / abs(B))) / pi);
	else
		tmp = -45.0;
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[B], $MachinePrecision], 6e+76], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], -45.0]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if B < 5.9999999999999996e76

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 48.9%

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

   4. Applied rewrites 48.9%

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

   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 34.3%

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

   7. Applied rewrites 34.3%

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

   if 5.9999999999999996e76 < B

   1. Initial program 53.2%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.4%

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

   5. Evaluated real constant 21.4%

      \[\leadsto \color{blue}{-45} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 41.0% accurate, 10.6× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot -45 \]

FPCore

(FPCore (A B C)
  :precision binary64
  (* (copysign 1.0 B) -45.0))

C

double code(double A, double B, double C) {
	return copysign(1.0, B) * -45.0;
}

Java

public static double code(double A, double B, double C) {
	return Math.copySign(1.0, B) * -45.0;
}

Python

def code(A, B, C):
	return math.copysign(1.0, B) * -45.0

Julia

function code(A, B, C)
	return Float64(copysign(1.0, B) * -45.0)
end

MATLAB

function tmp = code(A, B, C)
	tmp = (sign(B) * abs(1.0)) * -45.0;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * -45.0), $MachinePrecision]

Derivation

1. Initial program 53.2%

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

2. Taylor expanded in B around inf

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

4. Applied rewrites 21.4%

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

5. Evaluated real constant 21.4%

   \[\leadsto \color{blue}{-45} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025212 
(FPCore (A B C)
  :name "ABCF->ab-angle angle"
  :precision binary64
  (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))) PI)))