ABCF->ab-angle angle

Percentage Accurate: 53.5% → 80.7%

Time: 19.2s

Alternatives: 13

Speedup: 2.4×

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: 53.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.95 \cdot 10^{+57}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.95e+57)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (* 180.0 (/ (atan (/ (- C (+ A (hypot B (- A C)))) B)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.95e+57) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.95e+57) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan(((C - (A + Math.hypot(B, (A - C)))) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.95e+57:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	else:
		tmp = 180.0 * (math.atan(((C - (A + math.hypot(B, (A - C)))) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.95e+57)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - Float64(A + hypot(B, Float64(A - C)))) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.95e+57)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	else
		tmp = 180.0 * (atan(((C - (A + hypot(B, (A - C)))) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.95e+57], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[(A + N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.94999999999999984e57

   1. Initial program 18.7%

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

   3. Applied egg-rr 42.5%

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

   4. Taylor expanded in A around -inf 66.7%

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

   if -1.94999999999999984e57 < A

   1. Initial program 67.1%

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

   3. Simplified 86.7%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.95 \cdot 10^{+57}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Alternative 2: 80.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 1.95 \cdot 10^{+92}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 1.95e+92)
   (* 180.0 (/ (atan (/ (- (- A) (hypot (- A C) B)) B)) PI))
   (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.95e+92) {
		tmp = 180.0 * (atan(((-A - hypot((A - C), B)) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.95e+92) {
		tmp = 180.0 * (Math.atan(((-A - Math.hypot((A - C), B)) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 1.95e+92:
		tmp = 180.0 * (math.atan(((-A - math.hypot((A - C), B)) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 1.95e+92)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - hypot(Float64(A - C), B)) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 1.95e+92)
		tmp = 180.0 * (atan(((-A - hypot((A - C), B)) / B)) / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 1.95e+92], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 1.95000000000000006e92

   1. Initial program 65.5%

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

      1. associate-*l/ 65.5%

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

      2. *-un-lft-identity 65.5%

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

      3. +-commutative 65.5%

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

      4. unpow2 65.5%

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

      5. unpow2 65.5%

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

      6. hypot-udef 83.3%

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

      7. div-sub 80.5%

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

      8. hypot-udef 64.6%

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

      9. unpow2 64.6%

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

      10. unpow2 64.6%

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

      11. +-commutative 64.6%

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

      12. unpow2 64.6%

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

      13. unpow2 64.6%

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

      14. hypot-def 80.5%

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

   3. Applied egg-rr 80.5%

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

   4. Taylor expanded in C around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. distribute-neg-frac 78.5%

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

   6. Simplified 78.5%

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

      1. sub-neg 78.5%

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

      2. distribute-frac-neg 78.5%

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

      3. distribute-neg-out 78.5%

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

      4. add-sqr-sqrt 50.4%

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

      5. sqrt-unprod 75.9%

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

      6. sqr-neg 75.9%

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

      7. sqrt-unprod 28.9%

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

      8. add-sqr-sqrt 60.4%

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

      9. div-inv 62.6%

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

      10. div-inv 60.4%

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

      11. distribute-rgt-out 61.5%

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

      12. add-sqr-sqrt 28.9%

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

      13. sqrt-unprod 75.9%

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

      14. sqr-neg 75.9%

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

      15. sqrt-unprod 50.4%

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

      16. add-sqr-sqrt 82.6%

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

   8. Applied egg-rr 82.6%

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

      1. associate-*l/ 82.6%

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

      2. *-lft-identity 82.6%

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

      3. distribute-neg-frac 82.6%

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

   10. Simplified 82.6%

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

   if 1.95000000000000006e92 < C

   1. Initial program 15.6%

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

   2. Taylor expanded in C around inf 29.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B} + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{B \cdot C}\right)}}{\pi} \]
   3. Step-by-step derivation

      1. associate-*r/ 29.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\color{blue}{\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}} + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{B \cdot C}\right)}{\pi} \]

      2. distribute-rgt1-in 29.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B} + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{B \cdot C}\right)}{\pi} \]

      3. associate-*r* 29.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(-1 \cdot \left(-1 + 1\right)\right) \cdot A}}{B} + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{B \cdot C}\right)}{\pi} \]

      4. metadata-eval 29.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(-1 \cdot \color{blue}{0}\right) \cdot A}{B} + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{B \cdot C}\right)}{\pi} \]

      5. metadata-eval 29.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0} \cdot A}{B} + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{B \cdot C}\right)}{\pi} \]

      6. metadata-eval 29.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(-1 + 1\right)} \cdot A}{B} + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{B \cdot C}\right)}{\pi} \]

      7. *-commutative 29.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{A \cdot \left(-1 + 1\right)}}{B} + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{B \cdot C}\right)}{\pi} \]

      8. metadata-eval 29.3%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot \color{blue}{0}}{B} + -0.5 \cdot \frac{\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{B \cdot C}\right)}{\pi} \]

      9. associate-*r/ 29.2%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \color{blue}{\frac{-0.5 \cdot \left(\left({A}^{2} + {B}^{2}\right) - {\left(-1 \cdot A\right)}^{2}\right)}{B \cdot C}}\right)}{\pi} \]

      10. +-commutative 29.2%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \left(\color{blue}{\left({B}^{2} + {A}^{2}\right)} - {\left(-1 \cdot A\right)}^{2}\right)}{B \cdot C}\right)}{\pi} \]

      11. associate--l+ 37.9%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \color{blue}{\left({B}^{2} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)\right)}}{B \cdot C}\right)}{\pi} \]

      12. mul-1-neg 37.9%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \left({B}^{2} + \left({A}^{2} - {\color{blue}{\left(-A\right)}}^{2}\right)\right)}{B \cdot C}\right)}{\pi} \]

   4. Simplified 37.9%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \left({B}^{2} + \left({A}^{2} - {\left(-A\right)}^{2}\right)\right)}{B \cdot C}\right)}}{\pi} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 37.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \left({B}^{2} + \left({A}^{2} - \color{blue}{\sqrt{{\left(-A\right)}^{2}} \cdot \sqrt{{\left(-A\right)}^{2}}}\right)\right)}{B \cdot C}\right)}{\pi} \]

      2. unpow2 37.9%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \left({B}^{2} + \left(\color{blue}{A \cdot A} - \sqrt{{\left(-A\right)}^{2}} \cdot \sqrt{{\left(-A\right)}^{2}}\right)\right)}{B \cdot C}\right)}{\pi} \]

      3. difference-of-squares 38.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \left({B}^{2} + \color{blue}{\left(A + \sqrt{{\left(-A\right)}^{2}}\right) \cdot \left(A - \sqrt{{\left(-A\right)}^{2}}\right)}\right)}{B \cdot C}\right)}{\pi} \]

      4. unpow2 38.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \left({B}^{2} + \left(A + \sqrt{\color{blue}{\left(-A\right) \cdot \left(-A\right)}}\right) \cdot \left(A - \sqrt{{\left(-A\right)}^{2}}\right)\right)}{B \cdot C}\right)}{\pi} \]

      5. sqr-neg 38.4%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \left({B}^{2} + \left(A + \sqrt{\color{blue}{A \cdot A}}\right) \cdot \left(A - \sqrt{{\left(-A\right)}^{2}}\right)\right)}{B \cdot C}\right)}{\pi} \]

      6. sqrt-prod 14.0%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \left({B}^{2} + \left(A + \color{blue}{\sqrt{A} \cdot \sqrt{A}}\right) \cdot \left(A - \sqrt{{\left(-A\right)}^{2}}\right)\right)}{B \cdot C}\right)}{\pi} \]

      7. add-sqr-sqrt 27.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \left({B}^{2} + \left(A + \color{blue}{A}\right) \cdot \left(A - \sqrt{{\left(-A\right)}^{2}}\right)\right)}{B \cdot C}\right)}{\pi} \]

      8. unpow2 27.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \left({B}^{2} + \left(A + A\right) \cdot \left(A - \sqrt{\color{blue}{\left(-A\right) \cdot \left(-A\right)}}\right)\right)}{B \cdot C}\right)}{\pi} \]

      9. sqr-neg 27.1%

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \left({B}^{2} + \left(A + A\right) \cdot \left(A - \sqrt{\color{blue}{A \cdot A}}\right)\right)}{B \cdot C}\right)}{\pi} \]

      10. sqrt-prod 9.6%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \left({B}^{2} + \left(A + A\right) \cdot \left(A - \color{blue}{\sqrt{A} \cdot \sqrt{A}}\right)\right)}{B \cdot C}\right)}{\pi} \]

      11. add-sqr-sqrt 51.0%

          \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \left({B}^{2} + \left(A + A\right) \cdot \left(A - \color{blue}{A}\right)\right)}{B \cdot C}\right)}{\pi} \]

   6. Applied egg-rr 51.0%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot 0}{B} + \frac{-0.5 \cdot \left({B}^{2} + \color{blue}{\left(A + A\right) \cdot \left(A - A\right)}\right)}{B \cdot C}\right)}{\pi} \]

   7. Taylor expanded in A around 0 78.5%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 1.95 \cdot 10^{+92}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \end{array} \]

Alternative 3: 47.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ t_2 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{if}\;A \leq -1.55 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -1.2 \cdot 10^{-195}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.7 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;A \leq 6.4 \cdot 10^{-93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 2.35 \cdot 10^{-91}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan -1.0) PI)))
        (t_1 (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI)))
        (t_2 (* 180.0 (/ (atan 1.0) PI))))
   (if (<= A -1.55e-97)
     t_1
     (if (<= A -1.2e-195)
       t_0
       (if (<= A -1.7e-261)
         t_1
         (if (<= A 1.5e-137)
           t_2
           (if (<= A 6.4e-93)
             t_0
             (if (<= A 2.35e-91)
               t_2
               (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(-1.0) / ((double) M_PI));
	double t_1 = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	double t_2 = 180.0 * (atan(1.0) / ((double) M_PI));
	double tmp;
	if (A <= -1.55e-97) {
		tmp = t_1;
	} else if (A <= -1.2e-195) {
		tmp = t_0;
	} else if (A <= -1.7e-261) {
		tmp = t_1;
	} else if (A <= 1.5e-137) {
		tmp = t_2;
	} else if (A <= 6.4e-93) {
		tmp = t_0;
	} else if (A <= 2.35e-91) {
		tmp = t_2;
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(-1.0) / Math.PI);
	double t_1 = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	double t_2 = 180.0 * (Math.atan(1.0) / Math.PI);
	double tmp;
	if (A <= -1.55e-97) {
		tmp = t_1;
	} else if (A <= -1.2e-195) {
		tmp = t_0;
	} else if (A <= -1.7e-261) {
		tmp = t_1;
	} else if (A <= 1.5e-137) {
		tmp = t_2;
	} else if (A <= 6.4e-93) {
		tmp = t_0;
	} else if (A <= 2.35e-91) {
		tmp = t_2;
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(-1.0) / math.pi)
	t_1 = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	t_2 = 180.0 * (math.atan(1.0) / math.pi)
	tmp = 0
	if A <= -1.55e-97:
		tmp = t_1
	elif A <= -1.2e-195:
		tmp = t_0
	elif A <= -1.7e-261:
		tmp = t_1
	elif A <= 1.5e-137:
		tmp = t_2
	elif A <= 6.4e-93:
		tmp = t_0
	elif A <= 2.35e-91:
		tmp = t_2
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(-1.0) / pi))
	t_1 = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi))
	t_2 = Float64(180.0 * Float64(atan(1.0) / pi))
	tmp = 0.0
	if (A <= -1.55e-97)
		tmp = t_1;
	elseif (A <= -1.2e-195)
		tmp = t_0;
	elseif (A <= -1.7e-261)
		tmp = t_1;
	elseif (A <= 1.5e-137)
		tmp = t_2;
	elseif (A <= 6.4e-93)
		tmp = t_0;
	elseif (A <= 2.35e-91)
		tmp = t_2;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(-1.0) / pi);
	t_1 = 180.0 * (atan(((0.5 * B) / A)) / pi);
	t_2 = 180.0 * (atan(1.0) / pi);
	tmp = 0.0;
	if (A <= -1.55e-97)
		tmp = t_1;
	elseif (A <= -1.2e-195)
		tmp = t_0;
	elseif (A <= -1.7e-261)
		tmp = t_1;
	elseif (A <= 1.5e-137)
		tmp = t_2;
	elseif (A <= 6.4e-93)
		tmp = t_0;
	elseif (A <= 2.35e-91)
		tmp = t_2;
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -1.55e-97], t$95$1, If[LessEqual[A, -1.2e-195], t$95$0, If[LessEqual[A, -1.7e-261], t$95$1, If[LessEqual[A, 1.5e-137], t$95$2, If[LessEqual[A, 6.4e-93], t$95$0, If[LessEqual[A, 2.35e-91], t$95$2, N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if A < -1.55000000000000001e-97 or -1.2e-195 < A < -1.7e-261

   1. Initial program 30.1%

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

   2. Taylor expanded in A around -inf 57.3%

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

      1. associate-*r/ 57.3%

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

      2. *-commutative 57.3%

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

   4. Simplified 57.3%

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

   if -1.55000000000000001e-97 < A < -1.2e-195 or 1.4999999999999999e-137 < A < 6.3999999999999997e-93

   1. Initial program 65.0%

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

   2. Taylor expanded in B around inf 57.7%

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

   if -1.7e-261 < A < 1.4999999999999999e-137 or 6.3999999999999997e-93 < A < 2.35000000000000003e-91

   1. Initial program 68.9%

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

   2. Taylor expanded in B around -inf 44.4%

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

   if 2.35000000000000003e-91 < A

   1. Initial program 78.8%

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

   2. Taylor expanded in A around inf 70.3%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.55 \cdot 10^{-97}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.2 \cdot 10^{-195}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq -1.7 \cdot 10^{-261}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.5 \cdot 10^{-137}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 6.4 \cdot 10^{-93}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 2.35 \cdot 10^{-91}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 4: 47.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} 1}{\pi}\\ t_1 := 180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{if}\;A \leq -3.7 \cdot 10^{-96}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.05 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq -6.8 \cdot 10^{-261}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-137}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;A \leq 1.15 \cdot 10^{-91}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan 1.0) PI))) (t_1 (* 180.0 (/ (atan -1.0) PI))))
   (if (<= A -3.7e-96)
     (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
     (if (<= A -1.05e-197)
       t_1
       (if (<= A -6.8e-261)
         (* 180.0 (/ (atan (/ (* 0.5 B) A)) PI))
         (if (<= A 2.6e-137)
           t_0
           (if (<= A 3.8e-93)
             t_1
             (if (<= A 1.15e-91)
               t_0
               (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))))))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(1.0) / ((double) M_PI));
	double t_1 = 180.0 * (atan(-1.0) / ((double) M_PI));
	double tmp;
	if (A <= -3.7e-96) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= -1.05e-197) {
		tmp = t_1;
	} else if (A <= -6.8e-261) {
		tmp = 180.0 * (atan(((0.5 * B) / A)) / ((double) M_PI));
	} else if (A <= 2.6e-137) {
		tmp = t_0;
	} else if (A <= 3.8e-93) {
		tmp = t_1;
	} else if (A <= 1.15e-91) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(1.0) / Math.PI);
	double t_1 = 180.0 * (Math.atan(-1.0) / Math.PI);
	double tmp;
	if (A <= -3.7e-96) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= -1.05e-197) {
		tmp = t_1;
	} else if (A <= -6.8e-261) {
		tmp = 180.0 * (Math.atan(((0.5 * B) / A)) / Math.PI);
	} else if (A <= 2.6e-137) {
		tmp = t_0;
	} else if (A <= 3.8e-93) {
		tmp = t_1;
	} else if (A <= 1.15e-91) {
		tmp = t_0;
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(1.0) / math.pi)
	t_1 = 180.0 * (math.atan(-1.0) / math.pi)
	tmp = 0
	if A <= -3.7e-96:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= -1.05e-197:
		tmp = t_1
	elif A <= -6.8e-261:
		tmp = 180.0 * (math.atan(((0.5 * B) / A)) / math.pi)
	elif A <= 2.6e-137:
		tmp = t_0
	elif A <= 3.8e-93:
		tmp = t_1
	elif A <= 1.15e-91:
		tmp = t_0
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(1.0) / pi))
	t_1 = Float64(180.0 * Float64(atan(-1.0) / pi))
	tmp = 0.0
	if (A <= -3.7e-96)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= -1.05e-197)
		tmp = t_1;
	elseif (A <= -6.8e-261)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(0.5 * B) / A)) / pi));
	elseif (A <= 2.6e-137)
		tmp = t_0;
	elseif (A <= 3.8e-93)
		tmp = t_1;
	elseif (A <= 1.15e-91)
		tmp = t_0;
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(1.0) / pi);
	t_1 = 180.0 * (atan(-1.0) / pi);
	tmp = 0.0;
	if (A <= -3.7e-96)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= -1.05e-197)
		tmp = t_1;
	elseif (A <= -6.8e-261)
		tmp = 180.0 * (atan(((0.5 * B) / A)) / pi);
	elseif (A <= 2.6e-137)
		tmp = t_0;
	elseif (A <= 3.8e-93)
		tmp = t_1;
	elseif (A <= 1.15e-91)
		tmp = t_0;
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[A, -3.7e-96], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, -1.05e-197], t$95$1, If[LessEqual[A, -6.8e-261], N[(180.0 * N[(N[ArcTan[N[(N[(0.5 * B), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.6e-137], t$95$0, If[LessEqual[A, 3.8e-93], t$95$1, If[LessEqual[A, 1.15e-91], t$95$0, N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if A < -3.69999999999999986e-96

   1. Initial program 26.8%

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

   3. Applied egg-rr 49.1%

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

   4. Taylor expanded in A around -inf 57.3%

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

   if -3.69999999999999986e-96 < A < -1.05e-197 or 2.6e-137 < A < 3.7999999999999999e-93

   1. Initial program 65.0%

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

   2. Taylor expanded in B around inf 57.7%

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

   if -1.05e-197 < A < -6.8e-261

   1. Initial program 62.0%

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

   2. Taylor expanded in A around -inf 58.2%

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

      1. associate-*r/ 58.2%

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

      2. *-commutative 58.2%

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

   4. Simplified 58.2%

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

   if -6.8e-261 < A < 2.6e-137 or 3.7999999999999999e-93 < A < 1.14999999999999998e-91

   1. Initial program 68.9%

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

   2. Taylor expanded in B around -inf 44.4%

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

   if 1.14999999999999998e-91 < A

   1. Initial program 78.8%

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

   2. Taylor expanded in A around inf 70.3%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-2 \cdot \frac{A}{B}\right)}}{\pi} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.7 \cdot 10^{-96}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -1.05 \cdot 10^{-197}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq -6.8 \cdot 10^{-261}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-137}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 3.8 \cdot 10^{-93}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{elif}\;A \leq 1.15 \cdot 10^{-91}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 5: 47.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.3 \cdot 10^{-76}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 90000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.3e-76)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 90000.0)
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.3e-76) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 90000.0) {
		tmp = 180.0 * (atan((-2.0 * (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 <= -5.3e-76) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 90000.0) {
		tmp = 180.0 * (Math.atan((-2.0 * (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 <= -5.3e-76:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 90000.0:
		tmp = 180.0 * (math.atan((-2.0 * (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 <= -5.3e-76)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 90000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(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 <= -5.3e-76)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 90000.0)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5.3e-76], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 90000.0], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -5.3e-76

   1. Initial program 55.0%

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

   2. Taylor expanded in B around -inf 58.2%

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

   if -5.3e-76 < B < 9e4

   1. Initial program 64.6%

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

   2. Taylor expanded in A around inf 43.9%

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

   if 9e4 < B

   1. Initial program 47.5%

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

   2. Taylor expanded in B around inf 62.3%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5.3 \cdot 10^{-76}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 90000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 6: 56.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 0.033:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.6e+17)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (if (<= A 0.033)
     (/ (* 180.0 (atan (+ 1.0 (/ C B)))) PI)
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.6e+17) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= 0.033) {
		tmp = (180.0 * atan((1.0 + (C / B)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.6e+17) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= 0.033) {
		tmp = (180.0 * Math.atan((1.0 + (C / B)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.6e+17:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= 0.033:
		tmp = (180.0 * math.atan((1.0 + (C / B)))) / math.pi
	else:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.6e+17)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= 0.033)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(C / B)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.6e+17)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= 0.033)
		tmp = (180.0 * atan((1.0 + (C / B)))) / pi;
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.6e+17], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 0.033], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.6e17

   1. Initial program 22.2%

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

   3. Applied egg-rr 45.2%

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

   4. Taylor expanded in A around -inf 63.6%

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

   if -8.6e17 < A < 0.033000000000000002

   1. Initial program 62.7%

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

   3. Applied egg-rr 83.6%

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

   4. Taylor expanded in B around -inf 54.5%

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

   5. Taylor expanded in B around 0 54.6%

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

      1. associate--l+ 54.6%

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

      2. div-sub 54.6%

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

   7. Simplified 54.6%

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

   8. Taylor expanded in A around 0 53.5%

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

   if 0.033000000000000002 < A

   1. Initial program 80.2%

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

   2. Taylor expanded in A around inf 73.5%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 0.033:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 7: 59.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -6.8 \cdot 10^{+20}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.9 \cdot 10^{-93}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -6.8e+20)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (if (<= A 2.9e-93)
     (/ (* 180.0 (atan (+ 1.0 (/ C B)))) PI)
     (/ (* 180.0 (atan (/ (- B A) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.8e+20) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else if (A <= 2.9e-93) {
		tmp = (180.0 * atan((1.0 + (C / B)))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(((B - A) / B))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -6.8e+20) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else if (A <= 2.9e-93) {
		tmp = (180.0 * Math.atan((1.0 + (C / B)))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan(((B - A) / B))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -6.8e+20:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	elif A <= 2.9e-93:
		tmp = (180.0 * math.atan((1.0 + (C / B)))) / math.pi
	else:
		tmp = (180.0 * math.atan(((B - A) / B))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -6.8e+20)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	elseif (A <= 2.9e-93)
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(C / B)))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B - A) / B))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -6.8e+20)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	elseif (A <= 2.9e-93)
		tmp = (180.0 * atan((1.0 + (C / B)))) / pi;
	else
		tmp = (180.0 * atan(((B - A) / B))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -6.8e+20], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 2.9e-93], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(B - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -6.8e20

   1. Initial program 22.2%

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

   3. Applied egg-rr 45.2%

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

   4. Taylor expanded in A around -inf 63.6%

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

   if -6.8e20 < A < 2.8999999999999998e-93

   1. Initial program 60.9%

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

   3. Applied egg-rr 82.0%

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

   4. Taylor expanded in B around -inf 51.3%

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

   5. Taylor expanded in B around 0 51.3%

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

      1. associate--l+ 51.3%

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

      2. div-sub 51.3%

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

   7. Simplified 51.3%

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

   8. Taylor expanded in A around 0 51.4%

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

   if 2.8999999999999998e-93 < A

   1. Initial program 79.1%

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

   3. Applied egg-rr 96.7%

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

   4. Taylor expanded in B around -inf 81.5%

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

   5. Taylor expanded in C around 0 81.4%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -6.8 \cdot 10^{+20}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.9 \cdot 10^{-93}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 8: 60.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.4 \cdot 10^{+17}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.4e+17)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.4e+17) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.4e+17) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.4e+17:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.4e+17)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.4e+17)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.4e+17], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -4.4e17

   1. Initial program 22.2%

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

   3. Applied egg-rr 45.2%

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

   4. Taylor expanded in A around -inf 63.6%

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

   if -4.4e17 < A

   1. Initial program 69.2%

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

   2. Taylor expanded in B around -inf 65.1%

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

      1. associate--l+ 65.1%

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

      2. div-sub 65.1%

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

   4. Simplified 65.1%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -4.4 \cdot 10^{+17}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 9: 60.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.75 \cdot 10^{+19}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.75e+19)
   (/ (* 180.0 (atan (* 0.5 (/ B A)))) PI)
   (/ (* 180.0 (atan (+ 1.0 (/ (- C A) B)))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.75e+19) {
		tmp = (180.0 * atan((0.5 * (B / A)))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((1.0 + ((C - A) / B)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.75e+19) {
		tmp = (180.0 * Math.atan((0.5 * (B / A)))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan((1.0 + ((C - A) / B)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -1.75e+19:
		tmp = (180.0 * math.atan((0.5 * (B / A)))) / math.pi
	else:
		tmp = (180.0 * math.atan((1.0 + ((C - A) / B)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.75e+19)
		tmp = Float64(Float64(180.0 * atan(Float64(0.5 * Float64(B / A)))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(1.0 + Float64(Float64(C - A) / B)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -1.75e+19)
		tmp = (180.0 * atan((0.5 * (B / A)))) / pi;
	else
		tmp = (180.0 * atan((1.0 + ((C - A) / B)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.75e+19], N[(N[(180.0 * N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -1.75e19

   1. Initial program 22.2%

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

   3. Applied egg-rr 45.2%

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

   4. Taylor expanded in A around -inf 63.6%

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

   if -1.75e19 < A

   1. Initial program 69.2%

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

   3. Applied egg-rr 88.7%

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

   4. Taylor expanded in B around -inf 65.1%

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

   5. Taylor expanded in B around 0 65.1%

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

      1. associate--l+ 65.1%

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

      2. div-sub 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.75 \cdot 10^{+19}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \]

Alternative 10: 47.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.25 \cdot 10^{-77}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1200000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.25e-77)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1200000.0)
     (* 180.0 (/ (atan (/ (- A) B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.25e-77) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1200000.0) {
		tmp = 180.0 * (atan((-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 <= -1.25e-77) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1200000.0) {
		tmp = 180.0 * (Math.atan((-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 <= -1.25e-77:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1200000.0:
		tmp = 180.0 * (math.atan((-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 <= -1.25e-77)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1200000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-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 <= -1.25e-77)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1200000.0)
		tmp = 180.0 * (atan((-A / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.25e-77], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1200000.0], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.24999999999999991e-77

   1. Initial program 55.0%

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

   2. Taylor expanded in B around -inf 58.2%

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

   if -1.24999999999999991e-77 < B < 1.2e6

   1. Initial program 64.6%

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

   3. Simplified 70.8%

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

      1. +-commutative 70.8%

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

      2. add-sqr-sqrt 68.0%

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

      3. fma-def 67.9%

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

   5. Applied egg-rr 67.9%

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

   6. Taylor expanded in A around inf 43.3%

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

      1. mul-1-neg 43.3%

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

   8. Simplified 43.3%

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

   if 1.2e6 < B

   1. Initial program 47.5%

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

   2. Taylor expanded in B around inf 62.3%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.25 \cdot 10^{-77}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1200000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 11: 47.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.15 \cdot 10^{-97}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 640000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.15e-97)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 640000.0)
     (* 180.0 (/ (atan (/ C B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.15e-97) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 640000.0) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.15e-97) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 640000.0) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.15e-97:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 640000.0:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.15e-97)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 640000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.15e-97)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 640000.0)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.15e-97], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 640000.0], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.14999999999999997e-97

   1. Initial program 58.1%

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

   2. Taylor expanded in B around -inf 57.3%

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

   if -1.14999999999999997e-97 < B < 6.4e5

   1. Initial program 62.5%

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

   3. Simplified 69.1%

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

      1. +-commutative 69.1%

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

      2. add-sqr-sqrt 66.1%

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

      3. fma-def 66.0%

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

   5. Applied egg-rr 66.0%

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

   6. Taylor expanded in C around inf 40.0%

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

   if 6.4e5 < B

   1. Initial program 47.5%

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

   2. Taylor expanded in B around inf 62.3%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -1.15 \cdot 10^{-97}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 640000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 12: 40.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = 180.0 * (atan(1.0) / ((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 <= -5e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5e-310:
		tmp = 180.0 * (math.atan(1.0) / 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 <= -5e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / 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 <= -5e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5e-310], N[(180.0 * N[(N[ArcTan[1.0], $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 < -4.999999999999985e-310

   1. Initial program 58.9%

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

   2. Taylor expanded in B around -inf 47.0%

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

   if -4.999999999999985e-310 < B

   1. Initial program 55.6%

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

   2. Taylor expanded in B around inf 37.9%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 13: 21.3% accurate, 2.5× 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 57.1%

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

2. Taylor expanded in B around inf 21.9%

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

3. Final simplification 21.9%

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

Reproduce

herbie shell --seed 2023301 
(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)))