ABCF->ab-angle angle

Percentage Accurate: 53.4% → 81.6%

Time: 4.6s

Alternatives: 9

Speedup: 2.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;C \leq 6.2 \cdot 10^{+163}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{B}{C} \cdot -0.5\right) \cdot \frac{180}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 6.2e+163)
   (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (hypot (- C A) B)))) PI))
   (* (atan (* (/ B C) -0.5)) (/ 180.0 PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 6.2e+163) {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((C - A), B)))) / ((double) M_PI));
	} else {
		tmp = atan(((B / C) * -0.5)) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 6.2e+163) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.hypot((C - A), B)))) / Math.PI);
	} else {
		tmp = Math.atan(((B / C) * -0.5)) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 6.2e+163:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.hypot((C - A), B)))) / math.pi)
	else:
		tmp = math.atan(((B / C) * -0.5)) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 6.2e+163)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - hypot(Float64(C - A), B)))) / pi));
	else
		tmp = Float64(atan(Float64(Float64(B / C) * -0.5)) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 6.2e+163)
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((C - A), B)))) / pi);
	else
		tmp = atan(((B / C) * -0.5)) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 6.2e+163], 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], N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 6.20000000000000057e163

   1. Initial program 53.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 77.9%

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

   if 6.20000000000000057e163 < C

   1. Initial program 53.4%

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

   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 26.2%

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

   4. Applied rewrites 26.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 26.3%

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

      1. lift-fma.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div0 N/A

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

      4. +-rgt-identity N/A

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

      5. lower-*.f64 26.3%

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

   8. Applied rewrites 26.3%

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

Alternative 2: 75.6% accurate, 1.8× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;C \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \left(A + \left|B\right|\right)}{\left|B\right|}\right) \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left|B\right|}{C} \cdot -0.5\right) \cdot \frac{180}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= C 2.6e+118)
    (/ (* (atan (/ (- C (+ A (fabs B))) (fabs B))) 180.0) PI)
    (* (atan (* (/ (fabs B) C) -0.5)) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.6e+118) {
		tmp = (atan(((C - (A + fabs(B))) / fabs(B))) * 180.0) / ((double) M_PI);
	} else {
		tmp = atan(((fabs(B) / C) * -0.5)) * (180.0 / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.6e+118) {
		tmp = (Math.atan(((C - (A + Math.abs(B))) / Math.abs(B))) * 180.0) / Math.PI;
	} else {
		tmp = Math.atan(((Math.abs(B) / C) * -0.5)) * (180.0 / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 2.6e+118:
		tmp = (math.atan(((C - (A + math.fabs(B))) / math.fabs(B))) * 180.0) / math.pi
	else:
		tmp = math.atan(((math.fabs(B) / C) * -0.5)) * (180.0 / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 2.6e+118)
		tmp = Float64(Float64(atan(Float64(Float64(C - Float64(A + abs(B))) / abs(B))) * 180.0) / pi);
	else
		tmp = Float64(atan(Float64(Float64(abs(B) / C) * -0.5)) * Float64(180.0 / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 2.6e+118)
		tmp = (atan(((C - (A + abs(B))) / abs(B))) * 180.0) / pi;
	else
		tmp = atan(((abs(B) / C) * -0.5)) * (180.0 / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[C, 2.6e+118], N[(N[(N[ArcTan[N[(N[(C - N[(A + N[Abs[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[ArcTan[N[(N[(N[Abs[B], $MachinePrecision] / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < 2.60000000000000016e118

   1. Initial program 53.4%

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

   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 50.2%

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

   4. Applied rewrites 50.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 51.1%

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

   if 2.60000000000000016e118 < C

   1. Initial program 53.4%

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

   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 26.2%

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

   4. Applied rewrites 26.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 26.3%

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

      1. lift-fma.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div0 N/A

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

      4. +-rgt-identity N/A

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

      5. lower-*.f64 26.3%

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

   8. Applied rewrites 26.3%

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

Alternative 3: 75.6% accurate, 1.8× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;C \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;\left(\tan^{-1} \left(\frac{C - \left(A + \left|B\right|\right)}{\left|B\right|}\right) \cdot 180\right) \cdot 0.3183098861837907\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left|B\right|}{C} \cdot -0.5\right) \cdot \frac{180}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= C 2.6e+118)
    (* (* (atan (/ (- C (+ A (fabs B))) (fabs B))) 180.0) 0.3183098861837907)
    (* (atan (* (/ (fabs B) C) -0.5)) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.6e+118) {
		tmp = (atan(((C - (A + fabs(B))) / fabs(B))) * 180.0) * 0.3183098861837907;
	} else {
		tmp = atan(((fabs(B) / C) * -0.5)) * (180.0 / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.6e+118) {
		tmp = (Math.atan(((C - (A + Math.abs(B))) / Math.abs(B))) * 180.0) * 0.3183098861837907;
	} else {
		tmp = Math.atan(((Math.abs(B) / C) * -0.5)) * (180.0 / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 2.6e+118:
		tmp = (math.atan(((C - (A + math.fabs(B))) / math.fabs(B))) * 180.0) * 0.3183098861837907
	else:
		tmp = math.atan(((math.fabs(B) / C) * -0.5)) * (180.0 / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 2.6e+118)
		tmp = Float64(Float64(atan(Float64(Float64(C - Float64(A + abs(B))) / abs(B))) * 180.0) * 0.3183098861837907);
	else
		tmp = Float64(atan(Float64(Float64(abs(B) / C) * -0.5)) * Float64(180.0 / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 2.6e+118)
		tmp = (atan(((C - (A + abs(B))) / abs(B))) * 180.0) * 0.3183098861837907;
	else
		tmp = atan(((abs(B) / C) * -0.5)) * (180.0 / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[C, 2.6e+118], N[(N[(N[ArcTan[N[(N[(C - N[(A + N[Abs[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] * 0.3183098861837907), $MachinePrecision], N[(N[ArcTan[N[(N[(N[Abs[B], $MachinePrecision] / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < 2.60000000000000016e118

   1. Initial program 53.4%

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

   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 50.2%

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

   4. Applied rewrites 50.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. mult-flip N/A

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

      5. lift-/.f64 N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 51.1%

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

   7. Evaluated real constant 51.1%

      \[\leadsto \left(\tan^{-1} \left(\frac{C - \left(A + B\right)}{B}\right) \cdot 180\right) \cdot \color{blue}{0.3183098861837907} \]

   if 2.60000000000000016e118 < C

   1. Initial program 53.4%

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

   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 26.2%

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

   4. Applied rewrites 26.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 26.3%

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

      1. lift-fma.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div0 N/A

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

      4. +-rgt-identity N/A

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

      5. lower-*.f64 26.3%

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

   8. Applied rewrites 26.3%

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

Alternative 4: 68.9% accurate, 2.0× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;C \leq 820000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{\left|B\right|} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left|B\right|}{C} \cdot -0.5\right) \cdot \frac{180}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= C 820000.0)
    (* 180.0 (/ (atan (- (/ C (fabs B)) 1.0)) PI))
    (* (atan (* (/ (fabs B) C) -0.5)) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 820000.0) {
		tmp = 180.0 * (atan(((C / fabs(B)) - 1.0)) / ((double) M_PI));
	} else {
		tmp = atan(((fabs(B) / C) * -0.5)) * (180.0 / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 820000.0) {
		tmp = 180.0 * (Math.atan(((C / Math.abs(B)) - 1.0)) / Math.PI);
	} else {
		tmp = Math.atan(((Math.abs(B) / C) * -0.5)) * (180.0 / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 820000.0:
		tmp = 180.0 * (math.atan(((C / math.fabs(B)) - 1.0)) / math.pi)
	else:
		tmp = math.atan(((math.fabs(B) / C) * -0.5)) * (180.0 / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 820000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / abs(B)) - 1.0)) / pi));
	else
		tmp = Float64(atan(Float64(Float64(abs(B) / C) * -0.5)) * Float64(180.0 / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 820000.0)
		tmp = 180.0 * (atan(((C / abs(B)) - 1.0)) / pi);
	else
		tmp = atan(((abs(B) / C) * -0.5)) * (180.0 / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[C, 820000.0], N[(180.0 * N[(N[ArcTan[N[(N[(C / N[Abs[B], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(N[Abs[B], $MachinePrecision] / C), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < 8.2e5

   1. Initial program 53.4%

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

   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 50.2%

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

   4. Applied rewrites 50.2%

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

   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 39.4%

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

   if 8.2e5 < C

   1. Initial program 53.4%

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

   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 26.2%

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

   4. Applied rewrites 26.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 26.3%

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

      1. lift-fma.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div0 N/A

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

      4. +-rgt-identity N/A

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

      5. lower-*.f64 26.3%

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

   8. Applied rewrites 26.3%

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

Alternative 5: 66.6% accurate, 1.8× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq -4.2 \cdot 10^{+161}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left|B\right|}{A} \cdot 0.5\right) \cdot 57.29577951308232\\ \mathbf{elif}\;A \leq 3 \cdot 10^{+91}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{\left|B\right|} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{\left|B\right|}\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= A -4.2e+161)
    (* (atan (* (/ (fabs B) A) 0.5)) 57.29577951308232)
    (if (<= A 3e+91)
      (* 180.0 (/ (atan (- (/ C (fabs B)) 1.0)) PI))
      (* 180.0 (/ (atan (/ (- C A) (fabs B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.2e+161) {
		tmp = atan(((fabs(B) / A) * 0.5)) * 57.29577951308232;
	} else if (A <= 3e+91) {
		tmp = 180.0 * (atan(((C / fabs(B)) - 1.0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - A) / fabs(B))) / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.2e+161) {
		tmp = Math.atan(((Math.abs(B) / A) * 0.5)) * 57.29577951308232;
	} else if (A <= 3e+91) {
		tmp = 180.0 * (Math.atan(((C / Math.abs(B)) - 1.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - A) / Math.abs(B))) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.2e+161:
		tmp = math.atan(((math.fabs(B) / A) * 0.5)) * 57.29577951308232
	elif A <= 3e+91:
		tmp = 180.0 * (math.atan(((C / math.fabs(B)) - 1.0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - A) / math.fabs(B))) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.2e+161)
		tmp = Float64(atan(Float64(Float64(abs(B) / A) * 0.5)) * 57.29577951308232);
	elseif (A <= 3e+91)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / abs(B)) - 1.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / abs(B))) / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.2e+161)
		tmp = atan(((abs(B) / A) * 0.5)) * 57.29577951308232;
	elseif (A <= 3e+91)
		tmp = 180.0 * (atan(((C / abs(B)) - 1.0)) / pi);
	else
		tmp = 180.0 * (atan(((C - A) / abs(B))) / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[A, -4.2e+161], N[(N[ArcTan[N[(N[(N[Abs[B], $MachinePrecision] / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] * 57.29577951308232), $MachinePrecision], If[LessEqual[A, 3e+91], N[(180.0 * N[(N[ArcTan[N[(N[(C / N[Abs[B], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -4.2e161

   1. Initial program 53.4%

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

   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 25.6%

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

   4. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 25.7%

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

   7. Evaluated real constant 25.7%

      \[\leadsto \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right) \cdot \color{blue}{57.29577951308232} \]

   if -4.2e161 < A < 3.00000000000000006e91

   1. Initial program 53.4%

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

   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 50.2%

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

   4. Applied rewrites 50.2%

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

   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 39.4%

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

   if 3.00000000000000006e91 < A

   1. Initial program 53.4%

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

   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 50.2%

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

   4. Applied rewrites 50.2%

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

   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 35.2%

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

   7. Applied rewrites 35.2%

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

Alternative 6: 58.2% accurate, 1.8× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq -5.8 \cdot 10^{+81}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left|B\right|}{A} \cdot 0.5\right) \cdot 57.29577951308232\\ \mathbf{elif}\;A \leq 4.5 \cdot 10^{-81}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{\left|B\right|}\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= A -5.8e+81)
    (* (atan (* (/ (fabs B) A) 0.5)) 57.29577951308232)
    (if (<= A 4.5e-81)
      (* 180.0 (/ (atan -1.0) PI))
      (* 180.0 (/ (atan (/ (- C A) (fabs B))) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.8e+81) {
		tmp = atan(((fabs(B) / A) * 0.5)) * 57.29577951308232;
	} else if (A <= 4.5e-81) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - A) / fabs(B))) / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.8e+81) {
		tmp = Math.atan(((Math.abs(B) / A) * 0.5)) * 57.29577951308232;
	} else if (A <= 4.5e-81) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - A) / Math.abs(B))) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.8e+81:
		tmp = math.atan(((math.fabs(B) / A) * 0.5)) * 57.29577951308232
	elif A <= 4.5e-81:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - A) / math.fabs(B))) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.8e+81)
		tmp = Float64(atan(Float64(Float64(abs(B) / A) * 0.5)) * 57.29577951308232);
	elseif (A <= 4.5e-81)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / abs(B))) / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.8e+81)
		tmp = atan(((abs(B) / A) * 0.5)) * 57.29577951308232;
	elseif (A <= 4.5e-81)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan(((C - A) / abs(B))) / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[A, -5.8e+81], N[(N[ArcTan[N[(N[(N[Abs[B], $MachinePrecision] / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] * 57.29577951308232), $MachinePrecision], If[LessEqual[A, 4.5e-81], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / N[Abs[B], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -5.7999999999999999e81

   1. Initial program 53.4%

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

   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 25.6%

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

   4. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 25.7%

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

   7. Evaluated real constant 25.7%

      \[\leadsto \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right) \cdot \color{blue}{57.29577951308232} \]

   if -5.7999999999999999e81 < A < 4.5e-81

   1. Initial program 53.4%

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

   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 21.6%

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

   if 4.5e-81 < A

   1. Initial program 53.4%

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

   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 50.2%

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

   4. Applied rewrites 50.2%

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

   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 35.2%

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

   7. Applied rewrites 35.2%

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

Alternative 7: 49.8% accurate, 2.2× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;A \leq -5.8 \cdot 10^{+81}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left|B\right|}{A} \cdot 0.5\right) \cdot 57.29577951308232\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= A -5.8e+81)
    (* (atan (* (/ (fabs B) A) 0.5)) 57.29577951308232)
    (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.8e+81) {
		tmp = atan(((fabs(B) / A) * 0.5)) * 57.29577951308232;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -5.8e+81) {
		tmp = Math.atan(((Math.abs(B) / A) * 0.5)) * 57.29577951308232;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -5.8e+81:
		tmp = math.atan(((math.fabs(B) / A) * 0.5)) * 57.29577951308232
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -5.8e+81)
		tmp = Float64(atan(Float64(Float64(abs(B) / A) * 0.5)) * 57.29577951308232);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -5.8e+81)
		tmp = atan(((abs(B) / A) * 0.5)) * 57.29577951308232;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[A, -5.8e+81], N[(N[ArcTan[N[(N[(N[Abs[B], $MachinePrecision] / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] * 57.29577951308232), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < -5.7999999999999999e81

   1. Initial program 53.4%

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

   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 25.6%

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

   4. Applied rewrites 25.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 25.7%

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

   7. Evaluated real constant 25.7%

      \[\leadsto \tan^{-1} \left(\frac{B}{A} \cdot 0.5\right) \cdot \color{blue}{57.29577951308232} \]

   if -5.7999999999999999e81 < A

   1. Initial program 53.4%

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

   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 21.6%

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

Alternative 8: 44.9% accurate, 2.4× speedup

Math

\[\mathsf{copysign}\left(1, B\right) \cdot \begin{array}{l} \mathbf{if}\;\left|B\right| \leq 1.15 \cdot 10^{-138}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  (copysign 1.0 B)
  (if (<= (fabs B) 1.15e-138)
    (* 180.0 (/ (atan 0.0) PI))
    (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (fabs(B) <= 1.15e-138) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return copysign(1.0, B) * tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (Math.abs(B) <= 1.15e-138) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return Math.copySign(1.0, B) * tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if math.fabs(B) <= 1.15e-138:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return math.copysign(1.0, B) * tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (abs(B) <= 1.15e-138)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return Float64(copysign(1.0, B) * tmp)
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (abs(B) <= 1.15e-138)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = (sign(B) * abs(1.0)) * tmp;
end

Wolfram

code[A_, B_, C_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[B], $MachinePrecision], 1.15e-138], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if B < 1.14999999999999995e-138

   1. Initial program 53.4%

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

   2. Taylor expanded in C around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 13.0%

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

   4. Applied rewrites 13.0%

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

   5. Taylor expanded in A around 0

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

   7. Applied rewrites 13.0%

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

   if 1.14999999999999995e-138 < B

   1. Initial program 53.4%

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

   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 21.6%

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

Alternative 9: 40.0% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 53.4%

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

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 21.6%

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

Reproduce

herbie shell --seed 2025188 
(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)))