ABCF->ab-angle angle

Percentage Accurate: 53.3% → 81.7%

Time: 7.4s

Alternatives: 9

Speedup: 2.1×

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: 53.3% 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: 81.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -5.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -5.2e+109)
   (* (/ (atan (* 0.5 (/ B A))) PI) 180.0)
   (* 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 <= -5.2e+109) {
		tmp = (atan((0.5 * (B / A))) / ((double) M_PI)) * 180.0;
	} else {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((C - A), B)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.2e+109) {
		tmp = (Math.atan((0.5 * (B / A))) / Math.PI) * 180.0;
	} else {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.hypot((C - A), B)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.2e+109:
		tmp = (math.atan((0.5 * (B / A))) / math.pi) * 180.0
	else:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.hypot((C - A), B)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.2e+109)
		tmp = Float64(Float64(atan(Float64(0.5 * Float64(B / A))) / pi) * 180.0);
	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

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.2e+109)
		tmp = (atan((0.5 * (B / A))) / pi) * 180.0;
	else
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((C - A), B)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -5.2e+109], N[(N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $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 < -5.1999999999999997e109

   1. Initial program 53.3%

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

   2. Taylor expanded in C around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 22.9

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

   4. Applied rewrites 22.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 22.9

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. count-2-rev N/A

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

      9. lower-+.f64 22.9

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

   6. Applied rewrites 22.9%

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

   7. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 25.6

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

   9. Applied rewrites 25.6%

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

   if -5.1999999999999997e109 < A

   1. Initial program 53.3%

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

      1. lift-sqrt.f64 N/A

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

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

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

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

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

      13. lift-pow.f64 N/A

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

      14. unpow2 N/A

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

      15. sqr-neg-rev N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lift--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lift--.f64 N/A

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

      22. remove-double-neg N/A

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

   3. Applied rewrites 78.5%

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

Alternative 2: 73.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9.2 \cdot 10^{+108}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi} \cdot 180\\ \mathbf{elif}\;A \leq 1.35 \cdot 10^{-157}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \mathsf{hypot}\left(C, B\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9.2e+108)
   (* (/ (atan (* 0.5 (/ B A))) PI) 180.0)
   (if (<= A 1.35e-157)
     (* 180.0 (/ (atan (* (/ 1.0 B) (- C (hypot C B)))) PI))
     (* (/ (atan (- (/ C B) (+ 1.0 (/ A B)))) PI) 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.2e+108) {
		tmp = (atan((0.5 * (B / A))) / ((double) M_PI)) * 180.0;
	} else if (A <= 1.35e-157) {
		tmp = 180.0 * (atan(((1.0 / B) * (C - hypot(C, B)))) / ((double) M_PI));
	} else {
		tmp = (atan(((C / B) - (1.0 + (A / B)))) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.2e+108) {
		tmp = (Math.atan((0.5 * (B / A))) / Math.PI) * 180.0;
	} else if (A <= 1.35e-157) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * (C - Math.hypot(C, B)))) / Math.PI);
	} else {
		tmp = (Math.atan(((C / B) - (1.0 + (A / B)))) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -9.2e+108:
		tmp = (math.atan((0.5 * (B / A))) / math.pi) * 180.0
	elif A <= 1.35e-157:
		tmp = 180.0 * (math.atan(((1.0 / B) * (C - math.hypot(C, B)))) / math.pi)
	else:
		tmp = (math.atan(((C / B) - (1.0 + (A / B)))) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -9.2e+108)
		tmp = Float64(Float64(atan(Float64(0.5 * Float64(B / A))) / pi) * 180.0);
	elseif (A <= 1.35e-157)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(C - hypot(C, B)))) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(C / B) - Float64(1.0 + Float64(A / B)))) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -9.2e+108)
		tmp = (atan((0.5 * (B / A))) / pi) * 180.0;
	elseif (A <= 1.35e-157)
		tmp = 180.0 * (atan(((1.0 / B) * (C - hypot(C, B)))) / pi);
	else
		tmp = (atan(((C / B) - (1.0 + (A / B)))) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -9.2e+108], N[(N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[A, 1.35e-157], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(C - N[Sqrt[C ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - N[(1.0 + N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -9.1999999999999996e108

   1. Initial program 53.3%

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

   2. Taylor expanded in C around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 22.9

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

   4. Applied rewrites 22.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 22.9

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. count-2-rev N/A

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

      9. lower-+.f64 22.9

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

   6. Applied rewrites 22.9%

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

   7. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 25.6

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

   9. Applied rewrites 25.6%

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

   if -9.1999999999999996e108 < A < 1.35e-157

   1. Initial program 53.3%

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

      1. lift-sqrt.f64 N/A

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

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

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

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

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

      13. lift-pow.f64 N/A

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

      14. unpow2 N/A

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

      15. sqr-neg-rev N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lift--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lift--.f64 N/A

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

      22. remove-double-neg N/A

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

   3. Applied rewrites 78.5%

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

   4. Taylor expanded in A around 0

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

   6. Applied rewrites 72.5%

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

   7. Taylor expanded in A around 0

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

   9. Applied rewrites 64.1%

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

   if 1.35e-157 < A

   1. Initial program 53.3%

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

   2. Taylor expanded in C around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 22.9

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

   4. Applied rewrites 22.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 22.9

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. count-2-rev N/A

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

      9. lower-+.f64 22.9

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

   6. Applied rewrites 22.9%

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

   7. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 49.3

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

   9. Applied rewrites 49.3%

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

Alternative 3: 60.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 2.05 \cdot 10^{+61}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{-0.5}{C}, B, 0\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 2.05e+61)
   (* (/ (atan (- (/ C B) (+ 1.0 (/ A B)))) PI) 180.0)
   (* 180.0 (/ (atan (fma (/ -0.5 C) B 0.0)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.05e+61) {
		tmp = (atan(((C / B) - (1.0 + (A / B)))) / ((double) M_PI)) * 180.0;
	} else {
		tmp = 180.0 * (atan(fma((-0.5 / C), B, 0.0)) / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 2.05e+61)
		tmp = Float64(Float64(atan(Float64(Float64(C / B) - Float64(1.0 + Float64(A / B)))) / pi) * 180.0);
	else
		tmp = Float64(180.0 * Float64(atan(fma(Float64(-0.5 / C), B, 0.0)) / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 2.05e+61], N[(N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - N[(1.0 + N[(A / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 / C), $MachinePrecision] * B + 0.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 2.04999999999999986e61

   1. Initial program 53.3%

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

   2. Taylor expanded in C around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 22.9

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

   4. Applied rewrites 22.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 22.9

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*r/ N/A

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

      7. lower-/.f64 N/A

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

      8. count-2-rev N/A

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

      9. lower-+.f64 22.9

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

   6. Applied rewrites 22.9%

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

   7. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 49.3

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

   9. Applied rewrites 49.3%

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

   if 2.04999999999999986e61 < C

   1. Initial program 53.3%

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

   2. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 26.8

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

   4. Applied rewrites 26.8%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. add-flip N/A

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

      4. mul-1-neg N/A

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

      5. lift-/.f64 N/A

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

      6. distribute-neg-frac2 N/A

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

      7. distribute-frac-neg N/A

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

      8. frac-2neg N/A

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

      9. mult-flip N/A

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

      10. lift-/.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. mul-1-neg N/A

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

      14. sub-flip-reverse N/A

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

      15. sub-negate-rev N/A

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

      16. sub-flip-reverse N/A

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

      17. mul-1-neg N/A

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

      18. lift-*.f64 N/A

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

      19. lift-+.f64 N/A

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

      20. *-commutative N/A

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

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

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

   6. Applied rewrites 26.8%

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

Alternative 4: 47.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.12 \cdot 10^{-130}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.05 \cdot 10^{+61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{-0.5}{C}, B, 0\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.12e-130)
   (* 180.0 (/ (atan (/ (- C A) B)) PI))
   (if (<= C 2.05e+61)
     (* 180.0 (/ (atan -1.0) PI))
     (* 180.0 (/ (atan (fma (/ -0.5 C) B 0.0)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.12e-130) {
		tmp = 180.0 * (atan(((C - A) / B)) / ((double) M_PI));
	} else if (C <= 2.05e+61) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(fma((-0.5 / C), B, 0.0)) / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.12e-130)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / B)) / pi));
	elseif (C <= 2.05e+61)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(fma(Float64(-0.5 / C), B, 0.0)) / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.12e-130], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.05e+61], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(-0.5 / C), $MachinePrecision] * B + 0.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.12e-130

   1. Initial program 53.3%

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

   2. Taylor expanded in B around -inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 49.5

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

   4. Applied rewrites 49.5%

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

   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 -1.12e-130 < C < 2.04999999999999986e61

   1. Initial program 53.3%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.2%

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

   if 2.04999999999999986e61 < C

   1. Initial program 53.3%

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

   2. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 26.8

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

   4. Applied rewrites 26.8%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. add-flip N/A

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

      4. mul-1-neg N/A

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

      5. lift-/.f64 N/A

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

      6. distribute-neg-frac2 N/A

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

      7. distribute-frac-neg N/A

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

      8. frac-2neg N/A

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

      9. mult-flip N/A

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

      10. lift-/.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. mul-1-neg N/A

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

      14. sub-flip-reverse N/A

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

      15. sub-negate-rev N/A

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

      16. sub-flip-reverse N/A

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

      17. mul-1-neg N/A

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

      18. lift-*.f64 N/A

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

      19. lift-+.f64 N/A

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

      20. *-commutative N/A

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

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

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

   6. Applied rewrites 26.8%

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

Alternative 5: 47.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.12 \cdot 10^{-130}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.05 \cdot 10^{+61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.12e-130)
   (* 180.0 (/ (atan (/ (- C A) B)) PI))
   (if (<= C 2.05e+61)
     (* 180.0 (/ (atan -1.0) PI))
     (* (/ (atan (* -0.5 (/ B C))) PI) 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.12e-130) {
		tmp = 180.0 * (atan(((C - A) / B)) / ((double) M_PI));
	} else if (C <= 2.05e+61) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = (atan((-0.5 * (B / C))) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.12e-130) {
		tmp = 180.0 * (Math.atan(((C - A) / B)) / Math.PI);
	} else if (C <= 2.05e+61) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = (Math.atan((-0.5 * (B / C))) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.12e-130:
		tmp = 180.0 * (math.atan(((C - A) / B)) / math.pi)
	elif C <= 2.05e+61:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = (math.atan((-0.5 * (B / C))) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.12e-130)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / B)) / pi));
	elseif (C <= 2.05e+61)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(Float64(atan(Float64(-0.5 * Float64(B / C))) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.12e-130)
		tmp = 180.0 * (atan(((C - A) / B)) / pi);
	elseif (C <= 2.05e+61)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = (atan((-0.5 * (B / C))) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.12e-130], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.05e+61], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.12e-130

   1. Initial program 53.3%

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

   2. Taylor expanded in B around -inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 49.5

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

   4. Applied rewrites 49.5%

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

   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 -1.12e-130 < C < 2.04999999999999986e61

   1. Initial program 53.3%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.2%

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

   if 2.04999999999999986e61 < C

   1. Initial program 53.3%

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

   2. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 26.8

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

   4. Applied rewrites 26.8%

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

   6. Applied rewrites 26.7%

      \[\leadsto 180 \cdot \color{blue}{\left(\frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, 0\right)\right)}{\sqrt[3]{\pi}} \cdot \frac{1}{{\pi}^{0.6666666666666666}}\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{180 \cdot \left(\frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, 0\right)\right)}{\sqrt[3]{\pi}} \cdot \frac{1}{{\pi}^{\frac{2}{3}}}\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, \frac{-1}{2}, 0\right)\right)}{\sqrt[3]{\pi}} \cdot \frac{1}{{\pi}^{\frac{2}{3}}}\right) \cdot 180} \]

      3. lower-*.f64 26.7

         \[\leadsto \color{blue}{\left(\frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, 0\right)\right)}{\sqrt[3]{\pi}} \cdot \frac{1}{{\pi}^{0.6666666666666666}}\right) \cdot 180} \]

   8. Applied rewrites 26.8%

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

Alternative 6: 47.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -1.12 \cdot 10^{-130}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 2.05 \cdot 10^{+61}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -1.12e-130)
   (* 180.0 (/ (atan (/ (- C A) B)) PI))
   (if (<= C 2.05e+61)
     (* 180.0 (/ (atan -1.0) PI))
     (* (atan (* -0.5 (/ B C))) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.12e-130) {
		tmp = 180.0 * (atan(((C - A) / B)) / ((double) M_PI));
	} else if (C <= 2.05e+61) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = atan((-0.5 * (B / C))) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -1.12e-130) {
		tmp = 180.0 * (Math.atan(((C - A) / B)) / Math.PI);
	} else if (C <= 2.05e+61) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = Math.atan((-0.5 * (B / C))) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -1.12e-130:
		tmp = 180.0 * (math.atan(((C - A) / B)) / math.pi)
	elif C <= 2.05e+61:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = math.atan((-0.5 * (B / C))) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -1.12e-130)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / B)) / pi));
	elseif (C <= 2.05e+61)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(atan(Float64(-0.5 * Float64(B / C))) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -1.12e-130)
		tmp = 180.0 * (atan(((C - A) / B)) / pi);
	elseif (C <= 2.05e+61)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = atan((-0.5 * (B / C))) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -1.12e-130], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 2.05e+61], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -1.12e-130

   1. Initial program 53.3%

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

   2. Taylor expanded in B around -inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 49.5

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

   4. Applied rewrites 49.5%

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

   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 -1.12e-130 < C < 2.04999999999999986e61

   1. Initial program 53.3%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.2%

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

   if 2.04999999999999986e61 < C

   1. Initial program 53.3%

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

   2. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 26.8

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

   4. Applied rewrites 26.8%

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

   6. Applied rewrites 26.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. +-rgt-identity N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

   8. Applied rewrites 26.9%

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

Alternative 7: 44.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 2.2 \cdot 10^{+24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 2.2e+24)
   (* 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 <= 2.2e+24) {
		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 <= 2.2e+24) {
		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 <= 2.2e+24:
		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 <= 2.2e+24)
		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 <= 2.2e+24)
		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, 2.2e+24], 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 < 2.20000000000000002e24

   1. Initial program 53.3%

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

   2. Taylor expanded in B around -inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 49.5

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

   4. Applied rewrites 49.5%

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

   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 2.20000000000000002e24 < B

   1. Initial program 53.3%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.2%

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

Alternative 8: 34.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq 8.2 \cdot 10^{+57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A 8.2e+57)
   (* 180.0 (/ (atan -1.0) PI))
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= 8.2e+57) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= 8.2e+57) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= 8.2e+57:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= 8.2e+57)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= 8.2e+57)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, 8.2e+57], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < 8.2e57

   1. Initial program 53.3%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 21.2%

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

   if 8.2e57 < A

   1. Initial program 53.3%

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

   2. Taylor expanded in B around -inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 49.5

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

   4. Applied rewrites 49.5%

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

   5. Taylor expanded in C around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 39.1

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

   7. Applied rewrites 39.1%

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

Alternative 9: 21.2% 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 53.3%

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

2. Taylor expanded in B around inf

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

4. Applied rewrites 21.2%

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

Reproduce

herbie shell --seed 2025151 
(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)))