ABCF->ab-angle angle

Percentage Accurate: 53.3% → 81.8%

Time: 7.0s

Alternatives: 13

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ t_1 := \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right) \cdot 180}{\pi}\\ \mathbf{if}\;t\_0 \leq -10:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (*
          180.0
          (/
           (atan
            (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
           PI)))
        (t_1 (/ (* (atan (/ (- (- C A) (hypot (- A C) B)) B)) 180.0) PI)))
   (if (<= t_0 -10.0)
     t_1
     (if (<= t_0 0.0) (* 180.0 (/ (atan (* 0.5 (/ B A))) PI)) t_1))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
	double t_1 = (atan((((C - A) - hypot((A - C), B)) / B)) * 180.0) / ((double) M_PI);
	double tmp;
	if (t_0 <= -10.0) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
	double t_1 = (Math.atan((((C - A) - Math.hypot((A - C), B)) / B)) * 180.0) / Math.PI;
	double tmp;
	if (t_0 <= -10.0) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)
	t_1 = (math.atan((((C - A) - math.hypot((A - C), B)) / B)) * 180.0) / math.pi
	tmp = 0
	if t_0 <= -10.0:
		tmp = t_1
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	else:
		tmp = t_1
	return tmp

Julia

function code(A, B, C)
	t_0 = 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))
	t_1 = Float64(Float64(atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B)) * 180.0) / pi)
	tmp = 0.0
	if (t_0 <= -10.0)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
	t_1 = (atan((((C - A) - hypot((A - C), B)) / B)) * 180.0) / pi;
	tmp = 0.0;
	if (t_0 <= -10.0)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, Block[{t$95$1 = N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]}, If[LessEqual[t$95$0, -10.0], t$95$1, If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -10 or -0.0 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64)))

   1. Initial program 58.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 86.7%

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

   if -10 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -0.0

   1. Initial program 18.2%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-fma.f64 18.2

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

      5. lift-pow.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 18.2

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

   3. Applied rewrites 18.2%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. +-commutative N/A

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

      4. lift-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. difference-of-squares N/A

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

      7. +-commutative N/A

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

      8. lift-+.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-*.f64 16.8

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

   5. Applied rewrites 16.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. flip-+ N/A

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

      6. lift--.f64 N/A

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

      7. frac-times N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. difference-of-squares N/A

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 8.6

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

   7. Applied rewrites 8.6%

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

   8. Taylor expanded in A around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}}{\pi} \]
   9. 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 49.8

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

   10. Applied rewrites 49.8%

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

Alternative 2: 72.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
	double tmp;
	if (t_0 <= -40.0) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (B + A)) / B));
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - ((-1.0 * B) + A)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)
	tmp = 0
	if t_0 <= -40.0:
		tmp = (180.0 / math.pi) * math.atan(((C - (B + A)) / B))
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - ((-1.0 * B) + A)) / B))
	return tmp

Julia

function code(A, B, C)
	t_0 = 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))
	tmp = 0.0
	if (t_0 <= -40.0)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(B + A)) / B)));
	elseif (t_0 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(Float64(-1.0 * B) + A)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
	tmp = 0.0;
	if (t_0 <= -40.0)
		tmp = (180.0 / pi) * atan(((C - (B + A)) / B));
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	else
		tmp = (180.0 / pi) * atan(((C - ((-1.0 * B) + A)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, If[LessEqual[t$95$0, -40.0], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(N[(-1.0 * B), $MachinePrecision] + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 60.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 87.4%

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

   5. Applied rewrites 82.8%

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

   7. Applied rewrites 82.8%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 76.8%

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

   if -40 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -0.0

   1. Initial program 18.2%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-fma.f64 18.2

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

      5. lift-pow.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 18.2

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

   3. Applied rewrites 18.2%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. +-commutative N/A

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

      4. lift-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. difference-of-squares N/A

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

      7. +-commutative N/A

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

      8. lift-+.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-*.f64 16.8

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

   5. Applied rewrites 16.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. flip-+ N/A

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

      6. lift--.f64 N/A

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

      7. frac-times N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. difference-of-squares N/A

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 8.6

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

   7. Applied rewrites 8.6%

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

   8. Taylor expanded in A around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}}{\pi} \]
   9. 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 49.8

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

   10. Applied rewrites 49.8%

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

   if -0.0 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64)))

   1. Initial program 57.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 86.1%

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

   5. Applied rewrites 81.1%

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

   7. Applied rewrites 81.1%

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

   8. Taylor expanded in B around -inf

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

      1. lower-*.f64 74.9

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

   10. Applied rewrites 74.9%

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

Alternative 3: 67.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (B + A)) / B));
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else {
		tmp = (Math.atan(((C - (-1.0 * B)) / B)) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_0 <= -0.5:
		tmp = (180.0 / math.pi) * math.atan(((C - (B + A)) / B))
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	else:
		tmp = (math.atan(((C - (-1.0 * B)) / B)) * 180.0) / math.pi
	return tmp

Julia

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

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = (180.0 / pi) * atan(((C - (B + A)) / B));
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	else
		tmp = (atan(((C - (-1.0 * B)) / B)) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = 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]}, If[LessEqual[t$95$0, -0.5], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(C - N[(-1.0 * B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -0.5

   1. Initial program 60.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 87.4%

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

   5. Applied rewrites 82.8%

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

   7. Applied rewrites 82.8%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 76.8%

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

   if -0.5 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -0.0

   1. Initial program 18.2%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-fma.f64 18.2

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

      5. lift-pow.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 18.2

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

   3. Applied rewrites 18.2%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. +-commutative N/A

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

      4. lift-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. difference-of-squares N/A

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

      7. +-commutative N/A

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

      8. lift-+.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-*.f64 16.8

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

   5. Applied rewrites 16.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. flip-+ N/A

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

      6. lift--.f64 N/A

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

      7. frac-times N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. difference-of-squares N/A

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 8.6

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

   7. Applied rewrites 8.6%

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

   8. Taylor expanded in A around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}}{\pi} \]
   9. 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 49.8

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

   10. Applied rewrites 49.8%

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

   if -0.0 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 57.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 86.1%

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

   5. Applied rewrites 81.1%

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

      1. lift-+.f64 N/A

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

   7. Applied rewrites 0.2%

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

   8. Taylor expanded in B around -inf

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

      1. lower-*.f64 63.1

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

   10. Applied rewrites 63.1%

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

Alternative 4: 79.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.6 \cdot 10^{+195}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \left(\mathsf{hypot}\left(B, A - C\right) + A\right)}{B}\right) \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.6e+195)
   (/ (* (atan (* 0.5 (/ B A))) 180.0) PI)
   (/ (* (atan (/ (- C (+ (hypot B (- A C)) A)) B)) 180.0) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.6e+195) {
		tmp = (atan((0.5 * (B / A))) * 180.0) / ((double) M_PI);
	} else {
		tmp = (atan(((C - (hypot(B, (A - C)) + A)) / B)) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.6e+195) {
		tmp = (Math.atan((0.5 * (B / A))) * 180.0) / Math.PI;
	} else {
		tmp = (Math.atan(((C - (Math.hypot(B, (A - C)) + A)) / B)) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.6e+195:
		tmp = (math.atan((0.5 * (B / A))) * 180.0) / math.pi
	else:
		tmp = (math.atan(((C - (math.hypot(B, (A - C)) + A)) / B)) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.6e+195)
		tmp = Float64(Float64(atan(Float64(0.5 * Float64(B / A))) * 180.0) / pi);
	else
		tmp = Float64(Float64(atan(Float64(Float64(C - Float64(hypot(B, Float64(A - C)) + A)) / B)) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.6e+195)
		tmp = (atan((0.5 * (B / A))) * 180.0) / pi;
	else
		tmp = (atan(((C - (hypot(B, (A - C)) + A)) / B)) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.6e+195], N[(N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(C - N[(N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision] + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -4.6000000000000002e195

   1. Initial program 9.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 54.8%

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

   5. Applied rewrites 18.5%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. associate--r+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-div N/A

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

      8. frac-sub N/A

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

      9. lift-*.f64 N/A

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

      10. div-sub N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 N/A

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

   7. Applied rewrites 4.6%

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

   8. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 85.6

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

   10. Applied rewrites 85.6%

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

   if -4.6000000000000002e195 < A

   1. Initial program 57.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 80.2%

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

   5. Applied rewrites 78.3%

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

Alternative 5: 79.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.6 \cdot 10^{+195}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(\mathsf{hypot}\left(A - C, B\right) + A\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.6e+195)
   (/ (* (atan (* 0.5 (/ B A))) 180.0) PI)
   (* (/ 180.0 PI) (atan (/ (- C (+ (hypot (- A C) B) A)) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.6e+195) {
		tmp = (atan((0.5 * (B / A))) * 180.0) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (hypot((A - C), B) + A)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.6e+195) {
		tmp = (Math.atan((0.5 * (B / A))) * 180.0) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (Math.hypot((A - C), B) + A)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.6e+195:
		tmp = (math.atan((0.5 * (B / A))) * 180.0) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (math.hypot((A - C), B) + A)) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.6e+195)
		tmp = Float64(Float64(atan(Float64(0.5 * Float64(B / A))) * 180.0) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(hypot(Float64(A - C), B) + A)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.6e+195)
		tmp = (atan((0.5 * (B / A))) * 180.0) / pi;
	else
		tmp = (180.0 / pi) * atan(((C - (hypot((A - C), B) + A)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.6e+195], N[(N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision] + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -4.6000000000000002e195

   1. Initial program 9.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 54.8%

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

   5. Applied rewrites 18.5%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. associate--r+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-div N/A

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

      8. frac-sub N/A

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

      9. lift-*.f64 N/A

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

      10. div-sub N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 N/A

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

   7. Applied rewrites 4.6%

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

   8. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 85.6

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

   10. Applied rewrites 85.6%

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

   if -4.6000000000000002e195 < A

   1. Initial program 57.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 80.2%

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

   5. Applied rewrites 78.3%

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

   7. Applied rewrites 78.4%

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

Alternative 6: 76.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 7 \cdot 10^{+91}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(\mathsf{hypot}\left(A, B\right) + A\right)}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\mathsf{fma}\left(-1, \frac{A + -1 \cdot A}{B}, -0.5 \cdot \frac{B}{C}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 7e+91)
   (* (/ 180.0 PI) (atan (/ (- C (+ (hypot A B) A)) B)))
   (* (/ 180.0 PI) (atan (fma -1.0 (/ (+ A (* -1.0 A)) B) (* -0.5 (/ B C)))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 7e+91) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (hypot(A, B) + A)) / B));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(fma(-1.0, ((A + (-1.0 * A)) / B), (-0.5 * (B / C))));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 7e+91)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(hypot(A, B) + A)) / B)));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(fma(-1.0, Float64(Float64(A + Float64(-1.0 * A)) / B), Float64(-0.5 * Float64(B / C)))));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 7e+91], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision] + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(-1.0 * N[(N[(A + N[(-1.0 * A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision] + N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 7.00000000000000001e91

   1. Initial program 60.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 83.0%

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

   5. Applied rewrites 77.5%

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

   7. Applied rewrites 77.5%

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

   8. Taylor expanded in A around inf

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

   10. Applied rewrites 76.4%

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

   if 7.00000000000000001e91 < C

   1. Initial program 18.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 53.5%

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

   5. Applied rewrites 50.4%

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

   7. Applied rewrites 50.5%

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

   8. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 76.0

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

   10. Applied rewrites 76.0%

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

Alternative 7: 56.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{-77}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right) \cdot 180}{\pi}\\ \mathbf{elif}\;A \leq 1.02 \cdot 10^{+43}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9.5e-77)
   (/ (* (atan (* 0.5 (/ B A))) 180.0) PI)
   (if (<= A 1.02e+43)
     (* (/ 180.0 PI) (atan (/ (- C B) B)))
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.5e-77) {
		tmp = (atan((0.5 * (B / A))) * 180.0) / ((double) M_PI);
	} else if (A <= 1.02e+43) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	} 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 <= -9.5e-77) {
		tmp = (Math.atan((0.5 * (B / A))) * 180.0) / Math.PI;
	} else if (A <= 1.02e+43) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -9.5e-77:
		tmp = (math.atan((0.5 * (B / A))) * 180.0) / math.pi
	elif A <= 1.02e+43:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	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 <= -9.5e-77)
		tmp = Float64(Float64(atan(Float64(0.5 * Float64(B / A))) * 180.0) / pi);
	elseif (A <= 1.02e+43)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	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 <= -9.5e-77)
		tmp = (atan((0.5 * (B / A))) * 180.0) / pi;
	elseif (A <= 1.02e+43)
		tmp = (180.0 / pi) * atan(((C - B) / B));
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -9.5e-77], N[(N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.02e+43], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $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 < -9.5000000000000005e-77

   1. Initial program 29.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 60.7%

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

   5. Applied rewrites 45.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. associate--r+ N/A

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

      6. lift--.f64 N/A

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

      7. sub-div N/A

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

      8. frac-sub N/A

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

      9. lift-*.f64 N/A

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

      10. div-sub N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 N/A

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

   7. Applied rewrites 19.9%

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

   8. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 58.1

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

   10. Applied rewrites 58.1%

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

   if -9.5000000000000005e-77 < A < 1.02e43

   1. Initial program 59.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 82.1%

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

   5. Applied rewrites 82.1%

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

   7. Applied rewrites 82.1%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 49.0%

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

   if 1.02e43 < A

   1. Initial program 77.3%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-fma.f64 77.3

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

      5. lift-pow.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 77.3

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

   3. Applied rewrites 77.3%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. +-commutative N/A

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

      4. lift-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. difference-of-squares N/A

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

      7. +-commutative N/A

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

      8. lift-+.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-*.f64 76.7

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

   5. Applied rewrites 76.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. flip-+ N/A

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

      6. lift--.f64 N/A

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

      7. frac-times N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. difference-of-squares N/A

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 21.8

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

   7. Applied rewrites 21.8%

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

   8. Taylor expanded in A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 71.3

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

   10. Applied rewrites 71.3%

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

Alternative 8: 56.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -9.5 \cdot 10^{-77}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.02 \cdot 10^{+43}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -9.5e-77)
   (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
   (if (<= A 1.02e+43)
     (* (/ 180.0 PI) (atan (/ (- C B) B)))
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -9.5e-77) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else if (A <= 1.02e+43) {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	} 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 <= -9.5e-77) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else if (A <= 1.02e+43) {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	} else {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -9.5e-77:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	elif A <= 1.02e+43:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	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 <= -9.5e-77)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	elseif (A <= 1.02e+43)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	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 <= -9.5e-77)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	elseif (A <= 1.02e+43)
		tmp = (180.0 / pi) * atan(((C - B) / B));
	else
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -9.5e-77], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.02e+43], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $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 < -9.5000000000000005e-77

   1. Initial program 29.6%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-fma.f64 29.6

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

      5. lift-pow.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 29.6

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

   3. Applied rewrites 29.6%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. +-commutative N/A

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

      4. lift-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. difference-of-squares N/A

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

      7. +-commutative N/A

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

      8. lift-+.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-*.f64 26.6

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

   5. Applied rewrites 26.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. flip-+ N/A

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

      6. lift--.f64 N/A

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

      7. frac-times N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. difference-of-squares N/A

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 13.6

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

   7. Applied rewrites 13.6%

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

   8. Taylor expanded in A around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}}{\pi} \]
   9. 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 58.1

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

   10. Applied rewrites 58.1%

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

   if -9.5000000000000005e-77 < A < 1.02e43

   1. Initial program 59.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 82.1%

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

   5. Applied rewrites 82.1%

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

   7. Applied rewrites 82.1%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 49.0%

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

   if 1.02e43 < A

   1. Initial program 77.3%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-fma.f64 77.3

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

      5. lift-pow.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 77.3

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

   3. Applied rewrites 77.3%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. +-commutative N/A

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

      4. lift-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. difference-of-squares N/A

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

      7. +-commutative N/A

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

      8. lift-+.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-*.f64 76.7

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

   5. Applied rewrites 76.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. flip-+ N/A

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

      6. lift--.f64 N/A

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

      7. frac-times N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. difference-of-squares N/A

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 21.8

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

   7. Applied rewrites 21.8%

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

   8. Taylor expanded in A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 71.3

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

   10. Applied rewrites 71.3%

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

Alternative 9: 50.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.3 \cdot 10^{-11}:\\ \;\;\;\;\frac{\tan^{-1} 1 \cdot 180}{\pi}\\ \mathbf{elif}\;B \leq 5 \cdot 10^{-257}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.3e-11)
   (/ (* (atan 1.0) 180.0) PI)
   (if (<= B 5e-257)
     (* 180.0 (/ (atan (* -2.0 (/ A B))) PI))
     (* (/ 180.0 PI) (atan (/ (- C B) B))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.3e-11) {
		tmp = (atan(1.0) * 180.0) / ((double) M_PI);
	} else if (B <= 5e-257) {
		tmp = 180.0 * (atan((-2.0 * (A / B))) / ((double) M_PI));
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.3e-11) {
		tmp = (Math.atan(1.0) * 180.0) / Math.PI;
	} else if (B <= 5e-257) {
		tmp = 180.0 * (Math.atan((-2.0 * (A / B))) / Math.PI);
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.3e-11:
		tmp = (math.atan(1.0) * 180.0) / math.pi
	elif B <= 5e-257:
		tmp = 180.0 * (math.atan((-2.0 * (A / B))) / math.pi)
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.3e-11)
		tmp = Float64(Float64(atan(1.0) * 180.0) / pi);
	elseif (B <= 5e-257)
		tmp = Float64(180.0 * Float64(atan(Float64(-2.0 * Float64(A / B))) / pi));
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.3e-11)
		tmp = (atan(1.0) * 180.0) / pi;
	elseif (B <= 5e-257)
		tmp = 180.0 * (atan((-2.0 * (A / B))) / pi);
	else
		tmp = (180.0 / pi) * atan(((C - B) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.3e-11], N[(N[(N[ArcTan[1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 5e-257], N[(180.0 * N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.30000000000000014e-11

   1. Initial program 46.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 77.9%

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

   5. Applied rewrites 77.9%

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

      1. lift-+.f64 N/A

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

   7. Applied rewrites 0.0%

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

   8. Taylor expanded in B around -inf

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

   10. Applied rewrites 59.6%

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

   if -2.30000000000000014e-11 < B < 4.99999999999999989e-257

   1. Initial program 59.4%

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

      1. lift-+.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-fma.f64 59.4

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

      5. lift-pow.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 59.4

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

   3. Applied rewrites 59.4%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. +-commutative N/A

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

      4. lift-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. difference-of-squares N/A

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

      7. +-commutative N/A

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

      8. lift-+.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-*.f64 57.2

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

   5. Applied rewrites 57.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-+.f64 N/A

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

      5. flip-+ N/A

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

      6. lift--.f64 N/A

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

      7. frac-times N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. difference-of-squares N/A

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

      11. lift-+.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 29.7

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

   7. Applied rewrites 29.7%

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

   8. Taylor expanded in A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 31.7

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

   10. Applied rewrites 31.7%

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

   if 4.99999999999999989e-257 < 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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 77.8%

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

   5. Applied rewrites 74.1%

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

   7. Applied rewrites 74.1%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 57.7%

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

Alternative 10: 60.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-11}:\\ \;\;\;\;\frac{\tan^{-1} 1 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-11)
   (/ (* (atan 1.0) 180.0) PI)
   (* (/ 180.0 PI) (atan (/ (- C (+ B A)) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-11) {
		tmp = (atan(1.0) * 180.0) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - (B + A)) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-11) {
		tmp = (Math.atan(1.0) * 180.0) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - (B + A)) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5e-11:
		tmp = (math.atan(1.0) * 180.0) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - (B + A)) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5e-11)
		tmp = Float64(Float64(atan(1.0) * 180.0) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - Float64(B + A)) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5e-11)
		tmp = (atan(1.0) * 180.0) / pi;
	else
		tmp = (180.0 / pi) * atan(((C - (B + A)) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5e-11], N[(N[(N[ArcTan[1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -5.00000000000000018e-11

   1. Initial program 46.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 77.9%

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

   5. Applied rewrites 77.9%

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

      1. lift-+.f64 N/A

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

   7. Applied rewrites 0.0%

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

   8. Taylor expanded in B around -inf

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

   10. Applied rewrites 59.6%

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

   if -5.00000000000000018e-11 < B

   1. Initial program 55.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 77.7%

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

   5. Applied rewrites 70.9%

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

   7. Applied rewrites 70.9%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 60.5%

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

Alternative 11: 51.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.4 \cdot 10^{-127}:\\ \;\;\;\;\frac{\tan^{-1} 1 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.4e-127)
   (/ (* (atan 1.0) 180.0) PI)
   (* (/ 180.0 PI) (atan (/ (- C B) B)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.4e-127) {
		tmp = (atan(1.0) * 180.0) / ((double) M_PI);
	} else {
		tmp = (180.0 / ((double) M_PI)) * atan(((C - B) / B));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.4e-127) {
		tmp = (Math.atan(1.0) * 180.0) / Math.PI;
	} else {
		tmp = (180.0 / Math.PI) * Math.atan(((C - B) / B));
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.4e-127:
		tmp = (math.atan(1.0) * 180.0) / math.pi
	else:
		tmp = (180.0 / math.pi) * math.atan(((C - B) / B))
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3.4e-127)
		tmp = Float64(Float64(atan(1.0) * 180.0) / pi);
	else
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(Float64(C - B) / B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3.4e-127)
		tmp = (atan(1.0) * 180.0) / pi;
	else
		tmp = (180.0 / pi) * atan(((C - B) / B));
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.4e-127], N[(N[(N[ArcTan[1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -3.3999999999999999e-127

   1. Initial program 49.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 75.4%

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

   5. Applied rewrites 73.9%

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

      1. lift-+.f64 N/A

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

   7. Applied rewrites 0.0%

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

   8. Taylor expanded in B around -inf

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

   10. Applied rewrites 50.5%

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

   if -3.3999999999999999e-127 < B

   1. Initial program 55.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 79.1%

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

   5. Applied rewrites 72.1%

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

   7. Applied rewrites 72.1%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 51.8%

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

Alternative 12: 39.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.9 \cdot 10^{-305}:\\ \;\;\;\;\frac{\tan^{-1} 1 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} -1 \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.9e-305)
   (/ (* (atan 1.0) 180.0) PI)
   (/ (* (atan -1.0) 180.0) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.9e-305) {
		tmp = (atan(1.0) * 180.0) / ((double) M_PI);
	} else {
		tmp = (atan(-1.0) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.9e-305) {
		tmp = (Math.atan(1.0) * 180.0) / Math.PI;
	} else {
		tmp = (Math.atan(-1.0) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.9e-305:
		tmp = (math.atan(1.0) * 180.0) / math.pi
	else:
		tmp = (math.atan(-1.0) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.9e-305)
		tmp = Float64(Float64(atan(1.0) * 180.0) / pi);
	else
		tmp = Float64(Float64(atan(-1.0) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.9e-305)
		tmp = (atan(1.0) * 180.0) / pi;
	else
		tmp = (atan(-1.0) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.9e-305], N[(N[(N[ArcTan[1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(N[ArcTan[-1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -2.89999999999999988e-305

   1. Initial program 52.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 77.0%

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

   5. Applied rewrites 71.8%

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

      1. lift-+.f64 N/A

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

   7. Applied rewrites 0.0%

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

   8. Taylor expanded in B around -inf

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

   10. Applied rewrites 39.9%

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

   if -2.89999999999999988e-305 < B

   1. Initial program 54.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   3. Applied rewrites 78.6%

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

   5. Applied rewrites 73.6%

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

      1. lift-+.f64 N/A

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

   7. Applied rewrites 32.5%

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

   8. Taylor expanded in B around inf

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

   10. Applied rewrites 39.9%

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

Alternative 13: 21.0% accurate, 3.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 53.3%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. associate-*r/ N/A

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

   4. lower-/.f64 N/A

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

3. Applied rewrites 77.8%

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

5. Applied rewrites 72.7%

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

   1. lift-+.f64 N/A

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

7. Applied rewrites 16.3%

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

8. Taylor expanded in B around inf

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

10. Applied rewrites 21.0%

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

Reproduce

herbie shell --seed 2025106 
(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)))