ABCF->ab-angle angle

Percentage Accurate: 54.0% → 88.1%

Time: 5.5s

Alternatives: 14

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: 54.0% 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: 88.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ t_1 := \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)\\ \mathbf{if}\;t\_0 \leq -0.2:\\ \;\;\;\;\frac{t\_1 \cdot 180}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{\pi} \cdot 180\\ \end{array} \end{array} \]

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))))
   (if (<= t_0 -0.2)
     (/ (* t_1 180.0) PI)
     (if (<= t_0 0.0)
       (* 180.0 (/ (atan (* -0.5 (/ B (- C A)))) PI))
       (* (/ t_1 PI) 180.0)))))

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));
	double tmp;
	if (t_0 <= -0.2) {
		tmp = (t_1 * 180.0) / ((double) M_PI);
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / ((double) M_PI));
	} else {
		tmp = (t_1 / ((double) M_PI)) * 180.0;
	}
	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));
	double tmp;
	if (t_0 <= -0.2) {
		tmp = (t_1 * 180.0) / Math.PI;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / (C - A)))) / Math.PI);
	} else {
		tmp = (t_1 / Math.PI) * 180.0;
	}
	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))
	tmp = 0
	if t_0 <= -0.2:
		tmp = (t_1 * 180.0) / math.pi
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan((-0.5 * (B / (C - A)))) / math.pi)
	else:
		tmp = (t_1 / math.pi) * 180.0
	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 = atan(Float64(Float64(Float64(C - A) - hypot(Float64(A - C), B)) / B))
	tmp = 0.0
	if (t_0 <= -0.2)
		tmp = Float64(Float64(t_1 * 180.0) / pi);
	elseif (t_0 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / pi));
	else
		tmp = Float64(Float64(t_1 / pi) * 180.0);
	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));
	tmp = 0.0;
	if (t_0 <= -0.2)
		tmp = (t_1 * 180.0) / pi;
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / pi);
	else
		tmp = (t_1 / pi) * 180.0;
	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[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(A - C), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$0, -0.2], N[(N[(t$95$1 * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 / Pi), $MachinePrecision] * 180.0), $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))) < -0.20000000000000001

   1. Initial program 60.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 87.1%

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

   if -0.20000000000000001 < (*.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 17.8%

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

      1. lift-+.f64 N/A

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

      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. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 17.8

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 17.8

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

   3. Applied rewrites 17.8%

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

      1. lift--.f64 N/A

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

      2. flip3-- N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-out N/A

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

      9. lift-+.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 8.2

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

   5. Applied rewrites 8.2%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. lift-pow.f64 N/A

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

      4. difference-cubes N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-*.f64 9.2

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

      12. lift-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 9.2

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

   7. Applied rewrites 9.2%

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

   8. Taylor expanded in B around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 97.4

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

   10. Applied rewrites 97.4%

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

   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 59.0%

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

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

      3. lower-*.f64 59.0

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

   3. Applied rewrites 86.3%

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

Alternative 2: 88.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ t_1 := \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right)}{\pi} \cdot 180\\ \mathbf{if}\;t\_0 \leq -0.2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)) PI) 180.0)))
   (if (<= t_0 -0.2)
     t_1
     (if (<= t_0 0.0) (* 180.0 (/ (atan (* -0.5 (/ B (- C 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)) / ((double) M_PI)) * 180.0;
	double tmp;
	if (t_0 <= -0.2) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan((-0.5 * (B / (C - 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)) / Math.PI) * 180.0;
	double tmp;
	if (t_0 <= -0.2) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / (C - 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)) / math.pi) * 180.0
	tmp = 0
	if t_0 <= -0.2:
		tmp = t_1
	elif t_0 <= 0.0:
		tmp = 180.0 * (math.atan((-0.5 * (B / (C - 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)) / pi) * 180.0)
	tmp = 0.0
	if (t_0 <= -0.2)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / Float64(C - 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)) / pi) * 180.0;
	tmp = 0.0;
	if (t_0 <= -0.2)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = 180.0 * (atan((-0.5 * (B / (C - 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] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]}, If[LessEqual[t$95$0, -0.2], t$95$1, If[LessEqual[t$95$0, 0.0], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $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))) < -0.20000000000000001 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 59.8%

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

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

      3. lower-*.f64 59.8

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

   3. Applied rewrites 86.7%

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

   if -0.20000000000000001 < (*.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 17.8%

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

      1. lift-+.f64 N/A

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

      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. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 17.8

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 17.8

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

   3. Applied rewrites 17.8%

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

      1. lift--.f64 N/A

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

      2. flip3-- N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-out N/A

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

      9. lift-+.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 8.2

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

   5. Applied rewrites 8.2%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. lift-pow.f64 N/A

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

      4. difference-cubes N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-*.f64 9.2

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

      12. lift-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 9.2

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

   7. Applied rewrites 9.2%

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

   8. Taylor expanded in B around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 97.4

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

   10. Applied rewrites 97.4%

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

Alternative 3: 79.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ \mathbf{if}\;t\_0 \leq -40:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right) \cdot 180}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0.05:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \left(-1 \cdot B + A\right)}{B}\right) \cdot 180}{\pi}\\ \end{array} \end{array} \]

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)
     (/ (* (atan (/ (- C (+ B A)) B)) 180.0) PI)
     (if (<= t_0 0.05)
       (* 180.0 (/ (atan (* -0.5 (/ B (- C A)))) PI))
       (/ (* (atan (/ (- C (+ (* -1.0 B) A)) B)) 180.0) PI)))))

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 = (atan(((C - (B + A)) / B)) * 180.0) / ((double) M_PI);
	} else if (t_0 <= 0.05) {
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / ((double) M_PI));
	} else {
		tmp = (atan(((C - ((-1.0 * B) + A)) / B)) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((1.0 / 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 = (Math.atan(((C - (B + A)) / B)) * 180.0) / Math.PI;
	} else if (t_0 <= 0.05) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / (C - A)))) / Math.PI);
	} else {
		tmp = (Math.atan(((C - ((-1.0 * B) + A)) / B)) * 180.0) / Math.PI;
	}
	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 = (math.atan(((C - (B + A)) / B)) * 180.0) / math.pi
	elif t_0 <= 0.05:
		tmp = 180.0 * (math.atan((-0.5 * (B / (C - A)))) / math.pi)
	else:
		tmp = (math.atan(((C - ((-1.0 * B) + A)) / B)) * 180.0) / math.pi
	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(atan(Float64(Float64(C - Float64(B + A)) / B)) * 180.0) / pi);
	elseif (t_0 <= 0.05)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(C - Float64(Float64(-1.0 * B) + A)) / B)) * 180.0) / pi);
	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 = (atan(((C - (B + A)) / B)) * 180.0) / pi;
	elseif (t_0 <= 0.05)
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / pi);
	else
		tmp = (atan(((C - ((-1.0 * B) + A)) / B)) * 180.0) / pi;
	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[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[t$95$0, 0.05], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(C - N[(N[(-1.0 * B), $MachinePrecision] + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $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 60.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 87.0%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 82.5%

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

   6. Taylor expanded in B around inf

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

   8. Applied rewrites 77.1%

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

   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))) < 0.050000000000000003

   1. Initial program 18.0%

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

      1. lift-+.f64 N/A

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

      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. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 18.0

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 18.0

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

   3. Applied rewrites 18.0%

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

      1. lift--.f64 N/A

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

      2. flip3-- N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-out N/A

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

      9. lift-+.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 8.4

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

   5. Applied rewrites 8.4%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. lift-pow.f64 N/A

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

      4. difference-cubes N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-*.f64 9.3

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

      12. lift-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 9.3

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

   7. Applied rewrites 9.3%

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

   8. Taylor expanded in B around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 95.5

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

   10. Applied rewrites 95.5%

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

   if 0.050000000000000003 < (*.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 59.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 86.2%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 81.9%

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

   6. Taylor expanded in B around -inf

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

      1. lower-*.f64 76.0

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

   8. Applied rewrites 76.0%

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

Alternative 4: 81.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 6.5:\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - \mathsf{hypot}\left(B, A - C\right)\right) - A}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 6.5)
   (* (atan (/ (- (- C (hypot B (- A C))) A) B)) (/ 180.0 PI))
   (* 180.0 (/ (atan (* -0.5 (/ B (- C A)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 6.5) {
		tmp = atan((((C - hypot(B, (A - C))) - A) / B)) * (180.0 / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 6.5) {
		tmp = Math.atan((((C - Math.hypot(B, (A - C))) - A) / B)) * (180.0 / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / (C - A)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 6.5:
		tmp = math.atan((((C - math.hypot(B, (A - C))) - A) / B)) * (180.0 / math.pi)
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / (C - A)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 6.5)
		tmp = Float64(atan(Float64(Float64(Float64(C - hypot(B, Float64(A - C))) - A) / B)) * Float64(180.0 / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 6.5)
		tmp = atan((((C - hypot(B, (A - C))) - A) / B)) * (180.0 / pi);
	else
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 6.5], N[(N[ArcTan[N[(N[(N[(C - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] - A), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 6.5

   1. Initial program 63.4%

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

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

      3. lower-*.f64 63.4

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

   3. Applied rewrites 84.5%

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

   5. Applied rewrites 84.6%

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

   if 6.5 < C

   1. Initial program 25.9%

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

      1. lift-+.f64 N/A

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

      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. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 25.9

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 25.9

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

   3. Applied rewrites 25.9%

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

      1. lift--.f64 N/A

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

      2. flip3-- N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-out N/A

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

      9. lift-+.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 8.7

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

   5. Applied rewrites 8.7%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. lift-pow.f64 N/A

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

      4. difference-cubes N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-*.f64 9.3

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

      12. lift-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 9.3

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

   7. Applied rewrites 9.3%

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

   8. Taylor expanded in B around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 71.2

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

   10. Applied rewrites 71.2%

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

Alternative 5: 76.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 6.5:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \left(\mathsf{hypot}\left(B, A\right) + A\right)}{B}\right) \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 6.5)
   (/ (* (atan (/ (- C (+ (hypot B A) A)) B)) 180.0) PI)
   (* 180.0 (/ (atan (* -0.5 (/ B (- C A)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 6.5) {
		tmp = (atan(((C - (hypot(B, A) + A)) / B)) * 180.0) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 6.5) {
		tmp = (Math.atan(((C - (Math.hypot(B, A) + A)) / B)) * 180.0) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / (C - A)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 6.5:
		tmp = (math.atan(((C - (math.hypot(B, A) + A)) / B)) * 180.0) / math.pi
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / (C - A)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 6.5)
		tmp = Float64(Float64(atan(Float64(Float64(C - Float64(hypot(B, A) + A)) / B)) * 180.0) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 6.5)
		tmp = (atan(((C - (hypot(B, A) + A)) / B)) * 180.0) / pi;
	else
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 6.5], N[(N[(N[ArcTan[N[(N[(C - N[(N[Sqrt[B ^ 2 + A ^ 2], $MachinePrecision] + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 6.5

   1. Initial program 63.4%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 84.5%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 79.7%

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

   6. Taylor expanded in A around inf

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

   8. Applied rewrites 78.8%

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

   if 6.5 < C

   1. Initial program 25.9%

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

      1. lift-+.f64 N/A

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

      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. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 25.9

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 25.9

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

   3. Applied rewrites 25.9%

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

      1. lift--.f64 N/A

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

      2. flip3-- N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-out N/A

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

      9. lift-+.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 8.7

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

   5. Applied rewrites 8.7%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. lift-pow.f64 N/A

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

      4. difference-cubes N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-*.f64 9.3

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

      12. lift-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 9.3

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

   7. Applied rewrites 9.3%

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

   8. Taylor expanded in B around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 71.2

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

   10. Applied rewrites 71.2%

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

Alternative 6: 60.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.8 \cdot 10^{+101}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - -1 \cdot B}{B}\right) \cdot 180}{\pi}\\ \mathbf{elif}\;B \leq 7.5 \cdot 10^{-83}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right) \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.8e+101)
   (/ (* (atan (/ (- C (* -1.0 B)) B)) 180.0) PI)
   (if (<= B 7.5e-83)
     (* 180.0 (/ (atan (* -0.5 (/ B (- C A)))) PI))
     (/ (* (atan (/ (- C (+ B A)) B)) 180.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.8e+101) {
		tmp = (atan(((C - (-1.0 * B)) / B)) * 180.0) / ((double) M_PI);
	} else if (B <= 7.5e-83) {
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / ((double) M_PI));
	} else {
		tmp = (atan(((C - (B + A)) / B)) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.8e+101) {
		tmp = (Math.atan(((C - (-1.0 * B)) / B)) * 180.0) / Math.PI;
	} else if (B <= 7.5e-83) {
		tmp = 180.0 * (Math.atan((-0.5 * (B / (C - A)))) / Math.PI);
	} else {
		tmp = (Math.atan(((C - (B + A)) / B)) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.8e+101:
		tmp = (math.atan(((C - (-1.0 * B)) / B)) * 180.0) / math.pi
	elif B <= 7.5e-83:
		tmp = 180.0 * (math.atan((-0.5 * (B / (C - A)))) / math.pi)
	else:
		tmp = (math.atan(((C - (B + A)) / B)) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.8e+101)
		tmp = Float64(Float64(atan(Float64(Float64(C - Float64(-1.0 * B)) / B)) * 180.0) / pi);
	elseif (B <= 7.5e-83)
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.8e+101)
		tmp = (atan(((C - (-1.0 * B)) / B)) * 180.0) / pi;
	elseif (B <= 7.5e-83)
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / pi);
	else
		tmp = (atan(((C - (B + A)) / B)) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.8e+101], N[(N[(N[ArcTan[N[(N[(C - N[(-1.0 * B), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 7.5e-83], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.79999999999999981e101

   1. Initial program 38.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 84.7%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 84.7%

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

   6. Taylor expanded in B around -inf

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

      1. lower-*.f64 77.0

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

   8. Applied rewrites 77.0%

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

   if -2.79999999999999981e101 < B < 7.4999999999999997e-83

   1. Initial program 60.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 60.3

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 60.3

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

   3. Applied rewrites 60.3%

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

      1. lift--.f64 N/A

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

      2. flip3-- N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-out N/A

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

      9. lift-+.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 31.8

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

   5. Applied rewrites 31.8%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. lift-pow.f64 N/A

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

      4. difference-cubes N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-*.f64 32.2

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

      12. lift-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 32.2

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

   7. Applied rewrites 32.2%

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

   8. Taylor expanded in B around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 46.0

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

   10. Applied rewrites 46.0%

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

   if 7.4999999999999997e-83 < B

   1. Initial program 52.4%

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

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 77.0%

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

   6. Taylor expanded in B around inf

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

   8. Applied rewrites 74.2%

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

Alternative 7: 53.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 2.9 \cdot 10^{-299}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - B}{B}\right) \cdot 180}{\pi}\\ \mathbf{elif}\;C \leq 1.9 \cdot 10^{-183}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 2.9e-299)
   (/ (* (atan (/ (- C B) B)) 180.0) PI)
   (if (<= C 1.9e-183)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (* (/ (atan (* -0.5 (/ B C))) PI) 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.9e-299) {
		tmp = (atan(((C - B) / B)) * 180.0) / ((double) M_PI);
	} else if (C <= 1.9e-183) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else {
		tmp = (atan((-0.5 * (B / C))) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.9e-299) {
		tmp = (Math.atan(((C - B) / B)) * 180.0) / Math.PI;
	} else if (C <= 1.9e-183) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else {
		tmp = (Math.atan((-0.5 * (B / C))) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 2.9e-299:
		tmp = (math.atan(((C - B) / B)) * 180.0) / math.pi
	elif C <= 1.9e-183:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	else:
		tmp = (math.atan((-0.5 * (B / C))) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 2.9e-299)
		tmp = Float64(Float64(atan(Float64(Float64(C - B) / B)) * 180.0) / pi);
	elseif (C <= 1.9e-183)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	else
		tmp = Float64(Float64(atan(Float64(-0.5 * Float64(B / C))) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 2.9e-299)
		tmp = (atan(((C - B) / B)) * 180.0) / pi;
	elseif (C <= 1.9e-183)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	else
		tmp = (atan((-0.5 * (B / C))) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 2.9e-299], N[(N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[C, 1.9e-183], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < 2.90000000000000026e-299

   1. Initial program 68.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 88.8%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 84.3%

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

   6. Taylor expanded in B around inf

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

   8. Applied rewrites 58.4%

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

   if 2.90000000000000026e-299 < C < 1.8999999999999998e-183

   1. Initial program 57.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 57.1

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 57.1

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

   3. Applied rewrites 57.1%

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

      1. lift--.f64 N/A

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

      2. flip3-- N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-out N/A

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

      9. lift-+.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 31.1

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

   5. Applied rewrites 31.1%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. lift-pow.f64 N/A

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

      4. difference-cubes N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-*.f64 31.3

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

      12. lift-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 31.3

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

   7. Applied rewrites 31.3%

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

   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 30.3

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

   10. Applied rewrites 30.3%

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

   if 1.8999999999999998e-183 < C

   1. Initial program 34.9%

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

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

      3. lower-*.f64 34.9

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

   3. Applied rewrites 62.0%

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

   5. Applied rewrites 46.6%

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

   6. Taylor expanded in C around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 53.6

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

   8. Applied rewrites 53.6%

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

Alternative 8: 50.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{\tan^{-1} 1 \cdot 180}{\pi}\\ \mathbf{elif}\;B \leq 9 \cdot 10^{-179}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - B}{B}\right) \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7.5e+28)
   (/ (* (atan 1.0) 180.0) PI)
   (if (<= B 9e-179)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (/ (* (atan (/ (- C B) B)) 180.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.5e+28) {
		tmp = (atan(1.0) * 180.0) / ((double) M_PI);
	} else if (B <= 9e-179) {
		tmp = 180.0 * (atan((0.5 * (B / A))) / ((double) M_PI));
	} else {
		tmp = (atan(((C - B) / B)) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.5e+28) {
		tmp = (Math.atan(1.0) * 180.0) / Math.PI;
	} else if (B <= 9e-179) {
		tmp = 180.0 * (Math.atan((0.5 * (B / A))) / Math.PI);
	} else {
		tmp = (Math.atan(((C - B) / B)) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7.5e+28:
		tmp = (math.atan(1.0) * 180.0) / math.pi
	elif B <= 9e-179:
		tmp = 180.0 * (math.atan((0.5 * (B / A))) / math.pi)
	else:
		tmp = (math.atan(((C - B) / B)) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -7.5e+28)
		tmp = Float64(Float64(atan(1.0) * 180.0) / pi);
	elseif (B <= 9e-179)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B / A))) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(C - B) / B)) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -7.5e+28)
		tmp = (atan(1.0) * 180.0) / pi;
	elseif (B <= 9e-179)
		tmp = 180.0 * (atan((0.5 * (B / A))) / pi);
	else
		tmp = (atan(((C - B) / B)) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7.5e+28], N[(N[(N[ArcTan[1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 9e-179], 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 - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -7.4999999999999998e28

   1. Initial program 45.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 79.8%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 79.8%

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

   6. Taylor expanded in B around -inf

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

   8. Applied rewrites 63.0%

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

   if -7.4999999999999998e28 < B < 8.99999999999999984e-179

   1. Initial program 60.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 60.3

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 60.3

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

   3. Applied rewrites 60.3%

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

      1. lift--.f64 N/A

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

      2. flip3-- N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-out N/A

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

      9. lift-+.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 30.9

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

   5. Applied rewrites 30.9%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. lift-pow.f64 N/A

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

      4. difference-cubes N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-*.f64 31.4

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

      12. lift-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 31.4

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

   7. Applied rewrites 31.4%

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

   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 31.6

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

   10. Applied rewrites 31.6%

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

   if 8.99999999999999984e-179 < B

   1. Initial program 53.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 76.9%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 74.7%

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

   6. Taylor expanded in B around inf

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

   8. Applied rewrites 60.5%

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

Alternative 9: 49.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.9 \cdot 10^{-86}:\\ \;\;\;\;\frac{\tan^{-1} 1 \cdot 180}{\pi}\\ \mathbf{elif}\;B \leq 2.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - C}{B}\right) \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - B}{B}\right) \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.9e-86)
   (/ (* (atan 1.0) 180.0) PI)
   (if (<= B 2.5e-203)
     (/ (* (atan (/ (- C C) B)) 180.0) PI)
     (/ (* (atan (/ (- C B) B)) 180.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.9e-86) {
		tmp = (atan(1.0) * 180.0) / ((double) M_PI);
	} else if (B <= 2.5e-203) {
		tmp = (atan(((C - C) / B)) * 180.0) / ((double) M_PI);
	} else {
		tmp = (atan(((C - B) / B)) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.9e-86) {
		tmp = (Math.atan(1.0) * 180.0) / Math.PI;
	} else if (B <= 2.5e-203) {
		tmp = (Math.atan(((C - C) / B)) * 180.0) / Math.PI;
	} else {
		tmp = (Math.atan(((C - B) / B)) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.9e-86:
		tmp = (math.atan(1.0) * 180.0) / math.pi
	elif B <= 2.5e-203:
		tmp = (math.atan(((C - C) / B)) * 180.0) / math.pi
	else:
		tmp = (math.atan(((C - B) / B)) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.9e-86)
		tmp = Float64(Float64(atan(1.0) * 180.0) / pi);
	elseif (B <= 2.5e-203)
		tmp = Float64(Float64(atan(Float64(Float64(C - C) / B)) * 180.0) / pi);
	else
		tmp = Float64(Float64(atan(Float64(Float64(C - B) / B)) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.9e-86)
		tmp = (atan(1.0) * 180.0) / pi;
	elseif (B <= 2.5e-203)
		tmp = (atan(((C - C) / B)) * 180.0) / pi;
	else
		tmp = (atan(((C - B) / B)) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.9e-86], N[(N[(N[ArcTan[1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[B, 2.5e-203], N[(N[(N[ArcTan[N[(N[(C - C), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.8999999999999999e-86

   1. Initial program 51.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 76.3%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 75.9%

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

   6. Taylor expanded in B around -inf

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

   8. Applied rewrites 54.1%

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

   if -2.8999999999999999e-86 < B < 2.5000000000000001e-203

   1. Initial program 59.5%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 79.9%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 66.3%

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

   6. Taylor expanded in A around -inf

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

   8. Applied rewrites 29.5%

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

   if 2.5000000000000001e-203 < B

   1. Initial program 52.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 76.6%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 74.1%

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

   6. Taylor expanded in B around inf

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

   8. Applied rewrites 59.2%

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

Alternative 10: 62.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 3.1 \cdot 10^{-125}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right) \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 3.1e-125)
   (/ (* (atan (/ (- C (+ B A)) B)) 180.0) PI)
   (* 180.0 (/ (atan (* -0.5 (/ B (- C A)))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 3.1e-125) {
		tmp = (atan(((C - (B + A)) / B)) * 180.0) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 3.1e-125) {
		tmp = (Math.atan(((C - (B + A)) / B)) * 180.0) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((-0.5 * (B / (C - A)))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 3.1e-125:
		tmp = (math.atan(((C - (B + A)) / B)) * 180.0) / math.pi
	else:
		tmp = 180.0 * (math.atan((-0.5 * (B / (C - A)))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 3.1e-125)
		tmp = Float64(Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) * 180.0) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 3.1e-125)
		tmp = (atan(((C - (B + A)) / B)) * 180.0) / pi;
	else
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 3.1e-125], N[(N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 3.10000000000000013e-125

   1. Initial program 65.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 86.9%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 81.9%

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

   6. Taylor expanded in B around inf

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

   8. Applied rewrites 61.9%

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

   if 3.10000000000000013e-125 < C

   1. Initial program 32.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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. lift--.f64 N/A

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

      5. sub-negate2 N/A

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

      6. lift--.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate2 N/A

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

      9. lift--.f64 N/A

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

      10. sqr-neg-rev N/A

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

      11. lower-fma.f64 32.2

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

      12. lift-pow.f64 N/A

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

      13. unpow2 N/A

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

      14. lower-*.f64 32.2

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

   3. Applied rewrites 32.2%

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

      1. lift--.f64 N/A

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

      2. flip3-- N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-rgt-out N/A

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

      9. lift-+.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 16.6

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

   5. Applied rewrites 16.6%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. lift-pow.f64 N/A

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

      4. difference-cubes N/A

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

      5. lift-*.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-*.f64 17.0

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

      12. lift-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 17.0

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

   7. Applied rewrites 17.0%

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

   8. Taylor expanded in B around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 63.3

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

   10. Applied rewrites 63.3%

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

Alternative 11: 60.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 1.18 \cdot 10^{-26}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right) \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 1.18e-26)
   (/ (* (atan (/ (- C (+ B A)) B)) 180.0) PI)
   (* (/ (atan (* -0.5 (/ B C))) PI) 180.0)))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.18e-26) {
		tmp = (atan(((C - (B + A)) / B)) * 180.0) / ((double) M_PI);
	} else {
		tmp = (atan((-0.5 * (B / C))) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.18e-26) {
		tmp = (Math.atan(((C - (B + A)) / B)) * 180.0) / Math.PI;
	} else {
		tmp = (Math.atan((-0.5 * (B / C))) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 1.18e-26:
		tmp = (math.atan(((C - (B + A)) / B)) * 180.0) / math.pi
	else:
		tmp = (math.atan((-0.5 * (B / C))) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 1.18e-26)
		tmp = Float64(Float64(atan(Float64(Float64(C - Float64(B + A)) / B)) * 180.0) / pi);
	else
		tmp = Float64(Float64(atan(Float64(-0.5 * Float64(B / C))) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 1.18e-26)
		tmp = (atan(((C - (B + A)) / B)) * 180.0) / pi;
	else
		tmp = (atan((-0.5 * (B / C))) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 1.18e-26], N[(N[(N[ArcTan[N[(N[(C - N[(B + A), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 1.17999999999999996e-26

   1. Initial program 63.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 85.1%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 80.2%

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

   6. Taylor expanded in B around inf

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

   8. Applied rewrites 59.9%

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

   if 1.17999999999999996e-26 < C

   1. Initial program 27.4%

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

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

      3. lower-*.f64 27.4

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

   3. Applied rewrites 56.9%

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

   5. Applied rewrites 36.7%

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

   6. Taylor expanded in C around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 63.3

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

   8. Applied rewrites 63.3%

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

Alternative 12: 51.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{\tan^{-1} 1 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - B}{B}\right) \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.2e-19)
   (/ (* (atan 1.0) 180.0) PI)
   (/ (* (atan (/ (- C B) B)) 180.0) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.2e-19) {
		tmp = (atan(1.0) * 180.0) / ((double) M_PI);
	} else {
		tmp = (atan(((C - B) / B)) * 180.0) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.2e-19) {
		tmp = (Math.atan(1.0) * 180.0) / Math.PI;
	} else {
		tmp = (Math.atan(((C - B) / B)) * 180.0) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.2e-19:
		tmp = (math.atan(1.0) * 180.0) / math.pi
	else:
		tmp = (math.atan(((C - B) / B)) * 180.0) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.2e-19)
		tmp = Float64(Float64(atan(1.0) * 180.0) / pi);
	else
		tmp = Float64(Float64(atan(Float64(Float64(C - B) / B)) * 180.0) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.2e-19)
		tmp = (atan(1.0) * 180.0) / pi;
	else
		tmp = (atan(((C - B) / B)) * 180.0) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.2e-19], N[(N[(N[ArcTan[1.0], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(C - B), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -2.1999999999999998e-19

   1. Initial program 49.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 78.3%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 78.3%

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

   6. Taylor expanded in B around -inf

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

   8. Applied rewrites 59.2%

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

   if -2.1999999999999998e-19 < B

   1. Initial program 55.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 77.0%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 70.5%

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

   6. Taylor expanded in B around inf

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

   8. Applied rewrites 48.5%

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

Alternative 13: 40.1% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.4 \cdot 10^{-302}:\\ \;\;\;\;\frac{\tan^{-1} 1 \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} -1 \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.4e-302)
   (/ (* (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 <= -1.4e-302) {
		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 <= -1.4e-302) {
		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 <= -1.4e-302:
		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 <= -1.4e-302)
		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 <= -1.4e-302)
		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, -1.4e-302], 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 < -1.4e-302

   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 76.7%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate2 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate2 N/A

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

      16. lift--.f64 N/A

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

      17. sqr-neg-rev N/A

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

      18. +-commutative N/A

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

      19. lift-fma.f64 N/A

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

   5. Applied rewrites 72.5%

      \[\leadsto \frac{\tan^{-1} \left(\frac{\color{blue}{C - \left(\mathsf{hypot}\left(B, A - C\right) + A\right)}}{B}\right) \cdot 180}{\pi} \]

   6. Taylor expanded in B around -inf

      \[\leadsto \frac{\tan^{-1} \color{blue}{1} \cdot 180}{\pi} \]
   7. Step-by-step derivation

   8. Applied rewrites 40.8%

      \[\leadsto \frac{\tan^{-1} \color{blue}{1} \cdot 180}{\pi} \]

   if -1.4e-302 < 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 78.0%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right) \cdot 180}{\pi}} \]
   4. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}}{B}\right) \cdot 180}{\pi} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right)} - \mathsf{hypot}\left(A - C, B\right)}{B}\right) \cdot 180}{\pi} \]

      3. associate--l- N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{\color{blue}{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}}{B}\right) \cdot 180}{\pi} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{\color{blue}{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}}{B}\right) \cdot 180}{\pi} \]

      5. lift-hypot.f64 N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{\left(A - C\right) \cdot \left(A - C\right) + B \cdot B}}\right)}{B}\right) \cdot 180}{\pi} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}\right)}{B}\right) \cdot 180}{\pi} \]

      7. +-commutative N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \cdot 180}{\pi} \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + \left(A - C\right) \cdot \left(A - C\right)}\right)}{B}\right) \cdot 180}{\pi} \]

      9. lower-sqrt.f64 N/A

         \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \cdot 180}{\pi} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + \left(A - C\right) \cdot \left(A - C\right)}\right)}{B}\right) \cdot 180}{\pi} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right)} \cdot \left(A - C\right)}\right)}{B}\right) \cdot 180}{\pi} \]

      12. sub-negate2 N/A

          \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(\mathsf{neg}\left(\left(C - A\right)\right)\right)} \cdot \left(A - C\right)}\right)}{B}\right) \cdot 180}{\pi} \]

      13. lift--.f64 N/A

          \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \left(\mathsf{neg}\left(\color{blue}{\left(C - A\right)}\right)\right) \cdot \left(A - C\right)}\right)}{B}\right) \cdot 180}{\pi} \]

      14. lift--.f64 N/A

          \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \left(\mathsf{neg}\left(\left(C - A\right)\right)\right) \cdot \color{blue}{\left(A - C\right)}}\right)}{B}\right) \cdot 180}{\pi} \]

      15. sub-negate2 N/A

          \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \left(\mathsf{neg}\left(\left(C - A\right)\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(C - A\right)\right)\right)}}\right)}{B}\right) \cdot 180}{\pi} \]

      16. lift--.f64 N/A

          \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \left(\mathsf{neg}\left(\left(C - A\right)\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(C - A\right)}\right)\right)}\right)}{B}\right) \cdot 180}{\pi} \]

      17. sqr-neg-rev N/A

          \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(C - A\right) \cdot \left(C - A\right)}}\right)}{B}\right) \cdot 180}{\pi} \]

      18. +-commutative N/A

          \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{\left(C - A\right) \cdot \left(C - A\right) + B \cdot B}}\right)}{B}\right) \cdot 180}{\pi} \]

      19. lift-fma.f64 N/A

          \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}}\right)}{B}\right) \cdot 180}{\pi} \]

   5. Applied rewrites 72.9%

      \[\leadsto \frac{\tan^{-1} \left(\frac{\color{blue}{C - \left(\mathsf{hypot}\left(B, A - C\right) + A\right)}}{B}\right) \cdot 180}{\pi} \]

   6. Taylor expanded in B around inf

      \[\leadsto \frac{\tan^{-1} \color{blue}{-1} \cdot 180}{\pi} \]
   7. Step-by-step derivation

   8. Applied rewrites 39.4%

      \[\leadsto \frac{\tan^{-1} \color{blue}{-1} \cdot 180}{\pi} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 20.8% 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 54.0%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
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 77.4%

   \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}{B}\right) \cdot 180}{\pi}} \]
4. Step-by-step derivation

   1. lift--.f64 N/A

      \[\leadsto \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \mathsf{hypot}\left(A - C, B\right)}}{B}\right) \cdot 180}{\pi} \]

   2. lift--.f64 N/A

      \[\leadsto \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right)} - \mathsf{hypot}\left(A - C, B\right)}{B}\right) \cdot 180}{\pi} \]

   3. associate--l- N/A

      \[\leadsto \frac{\tan^{-1} \left(\frac{\color{blue}{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}}{B}\right) \cdot 180}{\pi} \]

   4. lower--.f64 N/A

      \[\leadsto \frac{\tan^{-1} \left(\frac{\color{blue}{C - \left(A + \mathsf{hypot}\left(A - C, B\right)\right)}}{B}\right) \cdot 180}{\pi} \]

   5. lift-hypot.f64 N/A

      \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{\left(A - C\right) \cdot \left(A - C\right) + B \cdot B}}\right)}{B}\right) \cdot 180}{\pi} \]

   6. lift-*.f64 N/A

      \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\left(A - C\right) \cdot \left(A - C\right) + \color{blue}{B \cdot B}}\right)}{B}\right) \cdot 180}{\pi} \]

   7. +-commutative N/A

      \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \cdot 180}{\pi} \]

   8. lift-*.f64 N/A

      \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + \left(A - C\right) \cdot \left(A - C\right)}\right)}{B}\right) \cdot 180}{\pi} \]

   9. lower-sqrt.f64 N/A

      \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \color{blue}{\sqrt{B \cdot B + \left(A - C\right) \cdot \left(A - C\right)}}\right)}{B}\right) \cdot 180}{\pi} \]

   10. lift-*.f64 N/A

       \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{B \cdot B} + \left(A - C\right) \cdot \left(A - C\right)}\right)}{B}\right) \cdot 180}{\pi} \]

   11. lift--.f64 N/A

       \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(A - C\right)} \cdot \left(A - C\right)}\right)}{B}\right) \cdot 180}{\pi} \]

   12. sub-negate2 N/A

       \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(\mathsf{neg}\left(\left(C - A\right)\right)\right)} \cdot \left(A - C\right)}\right)}{B}\right) \cdot 180}{\pi} \]

   13. lift--.f64 N/A

       \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \left(\mathsf{neg}\left(\color{blue}{\left(C - A\right)}\right)\right) \cdot \left(A - C\right)}\right)}{B}\right) \cdot 180}{\pi} \]

   14. lift--.f64 N/A

       \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \left(\mathsf{neg}\left(\left(C - A\right)\right)\right) \cdot \color{blue}{\left(A - C\right)}}\right)}{B}\right) \cdot 180}{\pi} \]

   15. sub-negate2 N/A

       \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \left(\mathsf{neg}\left(\left(C - A\right)\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(C - A\right)\right)\right)}}\right)}{B}\right) \cdot 180}{\pi} \]

   16. lift--.f64 N/A

       \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \left(\mathsf{neg}\left(\left(C - A\right)\right)\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(C - A\right)}\right)\right)}\right)}{B}\right) \cdot 180}{\pi} \]

   17. sqr-neg-rev N/A

       \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{B \cdot B + \color{blue}{\left(C - A\right) \cdot \left(C - A\right)}}\right)}{B}\right) \cdot 180}{\pi} \]

   18. +-commutative N/A

       \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{\left(C - A\right) \cdot \left(C - A\right) + B \cdot B}}\right)}{B}\right) \cdot 180}{\pi} \]

   19. lift-fma.f64 N/A

       \[\leadsto \frac{\tan^{-1} \left(\frac{C - \left(A + \sqrt{\color{blue}{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}}\right)}{B}\right) \cdot 180}{\pi} \]

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. Taylor expanded in B around inf

   \[\leadsto \frac{\tan^{-1} \color{blue}{-1} \cdot 180}{\pi} \]
7. Step-by-step derivation

8. Applied rewrites 20.8%

   \[\leadsto \frac{\tan^{-1} \color{blue}{-1} \cdot 180}{\pi} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2025111 
(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)))