ABCF->ab-angle angle

Percentage Accurate: 53.2% → 80.9%

Time: 4.9s

Alternatives: 12

Speedup: 2.3×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.2% 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: 80.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.2 \cdot 10^{+72}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(\frac{C}{A}, B, B\right)}{A} \cdot 0.5\right) \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.2e+72)
   (/ (* (atan (* (/ (fma (/ C A) B B) A) 0.5)) 180.0) PI)
   (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (hypot (- C A) B)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.2e+72) {
		tmp = (atan(((fma((C / A), B, B) / A) * 0.5)) * 180.0) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((C - A), B)))) / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.2e+72)
		tmp = Float64(Float64(atan(Float64(Float64(fma(Float64(C / A), B, B) / A) * 0.5)) * 180.0) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - hypot(Float64(C - A), B)))) / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.2e+72], N[(N[(N[ArcTan[N[(N[(N[(N[(C / A), $MachinePrecision] * B + B), $MachinePrecision] / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -4.2000000000000003e72

   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 48.7

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

   4. Applied rewrites 48.7%

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

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 49.6%

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

   7. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 33.2

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

   9. Applied rewrites 33.2%

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

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift-/.f64 N/A

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

       4. associate-*l/ N/A

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

       5. metadata-eval N/A

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

       6. associate-*r/ N/A

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

       7. lower-/.f64 N/A

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

   11. Applied rewrites 33.6%

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

   if -4.2000000000000003e72 < A

   1. Initial program 53.2%

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

      1. lift-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 77.6%

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

Alternative 2: 61.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.35 \cdot 10^{-82}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\mathsf{fma}\left(\frac{C}{A}, B, B\right)}{A} \cdot 0.5\right) \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} - 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.35e-82)
   (/ (* (atan (* (/ (fma (/ C A) B B) A) 0.5)) 180.0) PI)
   (* (/ 180.0 PI) (atan (- (/ (- C A) B) 1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.35e-82) {
		tmp = (atan(((fma((C / A), B, B) / A) * 0.5)) * 180.0) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((((C - A) / B) - 1.0));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.35e-82)
		tmp = Float64(Float64(atan(Float64(Float64(fma(Float64(C / A), B, B) / A) * 0.5)) * 180.0) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(C - A) / B) - 1.0)));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.35e-82], N[(N[(N[ArcTan[N[(N[(N[(N[(C / A), $MachinePrecision] * B + B), $MachinePrecision] / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.3500000000000001e-82

   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 48.7

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

   4. Applied rewrites 48.7%

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

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 49.6%

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

   7. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 33.2

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

   9. Applied rewrites 33.2%

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

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift-/.f64 N/A

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

       4. associate-*l/ N/A

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

       5. metadata-eval N/A

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

       6. associate-*r/ N/A

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

       7. lower-/.f64 N/A

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

   11. Applied rewrites 33.6%

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

   if -1.3500000000000001e-82 < 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 48.7

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

   4. Applied rewrites 48.7%

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

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 49.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 49.6

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 49.6

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

   8. Applied rewrites 49.6%

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

Alternative 3: 60.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1020000000:\\ \;\;\;\;\tan^{-1} \left(-1 \cdot \frac{-0.5 \cdot B}{A}\right) \cdot \left(\frac{1}{\pi} \cdot 180\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} - 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1020000000.0)
   (* (atan (* -1.0 (/ (* -0.5 B) A))) (* (/ 1.0 PI) 180.0))
   (* (/ 180.0 PI) (atan (- (/ (- C A) B) 1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1020000000.0) {
		tmp = atan((-1.0 * ((-0.5 * B) / A))) * ((1.0 / ((double) M_PI)) * 180.0);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((((C - A) / B) - 1.0));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1020000000.0) {
		tmp = Math.atan((-1.0 * ((-0.5 * B) / A))) * ((1.0 / Math.PI) * 180.0);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((((C - A) / B) - 1.0));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1020000000.0:
		tmp = math.atan((-1.0 * ((-0.5 * B) / A))) * ((1.0 / math.pi) * 180.0)
	else:
		tmp = (180.0 / math.pi) * math.atan((((C - A) / B) - 1.0))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1020000000.0)
		tmp = Float64(atan(Float64(-1.0 * Float64(Float64(-0.5 * B) / A))) * Float64(Float64(1.0 / pi) * 180.0));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(C - A) / B) - 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1020000000.0)
		tmp = atan((-1.0 * ((-0.5 * B) / A))) * ((1.0 / pi) * 180.0);
	else
		tmp = (180.0 / pi) * atan((((C - A) / B) - 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1020000000.0], N[(N[ArcTan[N[(-1.0 * N[(N[(-0.5 * B), $MachinePrecision] / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[(1.0 / Pi), $MachinePrecision] * 180.0), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.02e9

   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 48.7

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

   4. Applied rewrites 48.7%

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

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 49.6%

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

   7. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 33.2

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

   9. Applied rewrites 33.2%

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

   10. Taylor expanded in A around inf

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

       1. lower-*.f64 26.2

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

   12. Applied rewrites 26.2%

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

   if -1.02e9 < 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 48.7

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

   4. Applied rewrites 48.7%

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

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 49.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 49.6

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 49.6

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

   8. Applied rewrites 49.6%

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

Alternative 4: 60.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1020000000:\\ \;\;\;\;\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot \left(\frac{1}{\pi} \cdot 180\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} - 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1020000000.0)
   (* (atan (* 0.5 (/ B A))) (* (/ 1.0 PI) 180.0))
   (* (/ 180.0 PI) (atan (- (/ (- C A) B) 1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1020000000.0) {
		tmp = atan((0.5 * (B / A))) * ((1.0 / ((double) M_PI)) * 180.0);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((((C - A) / B) - 1.0));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1020000000.0) {
		tmp = Math.atan((0.5 * (B / A))) * ((1.0 / Math.PI) * 180.0);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((((C - A) / B) - 1.0));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1020000000.0:
		tmp = math.atan((0.5 * (B / A))) * ((1.0 / math.pi) * 180.0)
	else:
		tmp = (180.0 / math.pi) * math.atan((((C - A) / B) - 1.0))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1020000000.0)
		tmp = Float64(atan(Float64(0.5 * Float64(B / A))) * Float64(Float64(1.0 / pi) * 180.0));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(C - A) / B) - 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1020000000.0)
		tmp = atan((0.5 * (B / A))) * ((1.0 / pi) * 180.0);
	else
		tmp = (180.0 / pi) * atan((((C - A) / B) - 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1020000000.0], N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[(1.0 / Pi), $MachinePrecision] * 180.0), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.02e9

   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 48.7

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

   4. Applied rewrites 48.7%

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

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 49.6%

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

   7. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 26.2

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

   9. Applied rewrites 26.2%

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

   if -1.02e9 < 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 48.7

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

   4. Applied rewrites 48.7%

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

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 49.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 49.6

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 49.6

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

   8. Applied rewrites 49.6%

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

Alternative 5: 60.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1020000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - A}{B} - 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1020000000.0)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (* (/ 180.0 PI) (atan (- (/ (- C A) B) 1.0)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1020000000.0) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan((((C - A) / B) - 1.0));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1020000000.0) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan((((C - A) / B) - 1.0));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1020000000.0:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan((((C - A) / B) - 1.0))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1020000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(Float64(C - A) / B) - 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1020000000.0)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	else
		tmp = (180.0 / pi) * atan((((C - A) / B) - 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1020000000.0], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.02e9

   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 26.2

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

   4. Applied rewrites 26.2%

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

   if -1.02e9 < 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 48.7

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

   4. Applied rewrites 48.7%

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

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 49.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 49.6

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 49.6

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

   8. Applied rewrites 49.6%

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

Alternative 6: 56.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1020000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B} - 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1020000000.0)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 5e+100)
     (* (/ 180.0 PI) (atan (- (/ C B) 1.0)))
     (* (/ (atan (* (/ A B) -2.0)) PI) 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1020000000.0) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 5e+100) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C / B) - 1.0));
	} else {
		tmp = (atan(((A / B) * -2.0)) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1020000000.0) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 5e+100) {
		tmp = (180.0 / Math.PI) * Math.atan(((C / B) - 1.0));
	} else {
		tmp = (Math.atan(((A / B) * -2.0)) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1020000000.0:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 5e+100:
		tmp = (180.0 / math.pi) * math.atan(((C / B) - 1.0))
	else:
		tmp = (math.atan(((A / B) * -2.0)) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1020000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 5e+100)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C / B) - 1.0)));
	else
		tmp = Float64(Float64(atan(Float64(Float64(A / B) * -2.0)) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1020000000.0)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 5e+100)
		tmp = (180.0 / pi) * atan(((C / B) - 1.0));
	else
		tmp = (atan(((A / B) * -2.0)) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1020000000.0], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 5e+100], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.02e9

   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 26.2

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

   4. Applied rewrites 26.2%

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

   if -1.02e9 < A < 4.9999999999999999e100

   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 48.7

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

   4. Applied rewrites 48.7%

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

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 49.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 49.6

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 49.6

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

   8. Applied rewrites 49.6%

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

   9. Taylor expanded in A around 0

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

   11. Applied rewrites 38.4%

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

   if 4.9999999999999999e100 < 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 A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 23.1

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

   4. Applied rewrites 23.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 23.1

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 23.1

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

   6. Applied rewrites 23.1%

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

Alternative 7: 45.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B} - 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A}{B} \cdot -2\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A 5e+100)
   (* (/ 180.0 PI) (atan (- (/ C B) 1.0)))
   (* (/ (atan (* (/ A B) -2.0)) PI) 180.0)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= 5e+100) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C / B) - 1.0));
	} else {
		tmp = (atan(((A / B) * -2.0)) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= 5e+100) {
		tmp = (180.0 / Math.PI) * Math.atan(((C / B) - 1.0));
	} else {
		tmp = (Math.atan(((A / B) * -2.0)) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= 5e+100:
		tmp = (180.0 / math.pi) * math.atan(((C / B) - 1.0))
	else:
		tmp = (math.atan(((A / B) * -2.0)) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= 5e+100)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C / B) - 1.0)));
	else
		tmp = Float64(Float64(atan(Float64(Float64(A / B) * -2.0)) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= 5e+100)
		tmp = (180.0 / pi) * atan(((C / B) - 1.0));
	else
		tmp = (atan(((A / B) * -2.0)) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, 5e+100], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(A / B), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < 4.9999999999999999e100

   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 48.7

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

   4. Applied rewrites 48.7%

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

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 49.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 49.6

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 49.6

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

   8. Applied rewrites 49.6%

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

   9. Taylor expanded in A around 0

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

   11. Applied rewrites 38.4%

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

   if 4.9999999999999999e100 < 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 A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 23.1

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

   4. Applied rewrites 23.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 23.1

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 23.1

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

   6. Applied rewrites 23.1%

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

Alternative 8: 45.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C}{B} - 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A 5e+100)
   (* (/ 180.0 PI) (atan (- (/ C B) 1.0)))
   (* (/ (atan (/ (- A) B)) PI) 180.0)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= 5e+100) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C / B) - 1.0));
	} else {
		tmp = (atan((-A / B)) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= 5e+100) {
		tmp = (180.0 / Math.PI) * Math.atan(((C / B) - 1.0));
	} else {
		tmp = (Math.atan((-A / B)) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= 5e+100:
		tmp = (180.0 / math.pi) * math.atan(((C / B) - 1.0))
	else:
		tmp = (math.atan((-A / B)) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= 5e+100)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C / B) - 1.0)));
	else
		tmp = Float64(Float64(atan(Float64(Float64(-A) / B)) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= 5e+100)
		tmp = (180.0 / pi) * atan(((C / B) - 1.0));
	else
		tmp = (atan((-A / B)) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, 5e+100], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < 4.9999999999999999e100

   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 48.7

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

   4. Applied rewrites 48.7%

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

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 49.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 49.6

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 49.6

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

   8. Applied rewrites 49.6%

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

   9. Taylor expanded in A around 0

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

   11. Applied rewrites 38.4%

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

   if 4.9999999999999999e100 < 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 48.7

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

   4. Applied rewrites 48.7%

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

   5. Taylor expanded in A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 22.9

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

   7. Applied rewrites 22.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 22.9

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

   9. Applied rewrites 22.9%

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

Alternative 9: 45.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq 5 \cdot 10^{+100}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A 5e+100)
   (* 180.0 (/ (atan (- (/ C B) 1.0)) PI))
   (* (/ (atan (/ (- A) B)) PI) 180.0)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= 5e+100) {
		tmp = 180.0 * (atan(((C / B) - 1.0)) / ((double) M_PI));
	} else {
		tmp = (atan((-A / B)) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= 5e+100) {
		tmp = 180.0 * (Math.atan(((C / B) - 1.0)) / Math.PI);
	} else {
		tmp = (Math.atan((-A / B)) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= 5e+100:
		tmp = 180.0 * (math.atan(((C / B) - 1.0)) / math.pi)
	else:
		tmp = (math.atan((-A / B)) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= 5e+100)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) - 1.0)) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(-A) / B)) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= 5e+100)
		tmp = 180.0 * (atan(((C / B) - 1.0)) / pi);
	else
		tmp = (atan((-A / B)) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, 5e+100], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < 4.9999999999999999e100

   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 48.7

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

   4. Applied rewrites 48.7%

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

   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 38.4%

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

   if 4.9999999999999999e100 < 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 48.7

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

   4. Applied rewrites 48.7%

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

   5. Taylor expanded in A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 22.9

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

   7. Applied rewrites 22.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 22.9

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

   9. Applied rewrites 22.9%

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

Alternative 10: 44.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 320000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 320000.0)
   (* 180.0 (/ (atan (/ (- C A) B)) PI))
   (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 320000.0) {
		tmp = 180.0 * (atan(((C - A) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 320000.0) {
		tmp = 180.0 * (Math.atan(((C - A) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 320000.0:
		tmp = 180.0 * (math.atan(((C - A) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 320000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 320000.0)
		tmp = 180.0 * (atan(((C - A) / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 320000.0], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 3.2e5

   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 48.7

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

   4. Applied rewrites 48.7%

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

   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 34.6

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

   7. Applied rewrites 34.6%

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

   if 3.2e5 < 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 20.6%

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

Alternative 11: 34.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 6.6 \cdot 10^{-78}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 6.6e-78)
   (* 180.0 (/ (atan (/ C B)) PI))
   (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 6.6e-78) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 6.6e-78) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 6.6e-78:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 6.6e-78)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 6.6e-78)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 6.6e-78], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 6.59999999999999963e-78

   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 48.7

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

   4. Applied rewrites 48.7%

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

   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 34.6

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

   7. Applied rewrites 34.6%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 23.0%

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

   if 6.59999999999999963e-78 < 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 20.6%

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

Alternative 12: 20.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ 180 \cdot \frac{\tan^{-1} -1}{\pi} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 53.2%

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

2. Taylor expanded in B around inf

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

4. Applied rewrites 20.6%

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

Reproduce

herbie shell --seed 2025159 
(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)))