ABCF->ab-angle angle

Percentage Accurate: 53.7% → 88.3%

Time: 12.1s

Alternatives: 15

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.7% 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: 88.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)}{B}\right)}{\pi}\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_1 \leq -0.001:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ (- (- C A) (hypot (- C A) B)) B))) PI))
        (t_1
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_1 -0.001)
     t_0
     (if (<= t_1 0.0) (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI)) t_0))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan((((C - A) - hypot((C - A), B)) / B))) / ((double) M_PI);
	double t_1 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_1 <= -0.001) {
		tmp = t_0;
	} else if (t_1 <= 0.0) {
		tmp = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan((((C - A) - Math.hypot((C - A), B)) / B))) / Math.PI;
	double t_1 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_1 <= -0.001) {
		tmp = t_0;
	} else if (t_1 <= 0.0) {
		tmp = 180.0 * (Math.atan((B * (0.5 / (A - C)))) / Math.PI);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan((((C - A) - math.hypot((C - A), B)) / B))) / math.pi
	t_1 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_1 <= -0.001:
		tmp = t_0
	elif t_1 <= 0.0:
		tmp = 180.0 * (math.atan((B * (0.5 / (A - C)))) / math.pi)
	else:
		tmp = t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(Float64(C - A), B)) / B))) / pi)
	t_1 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_1 <= -0.001)
		tmp = t_0;
	elseif (t_1 <= 0.0)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan((((C - A) - hypot((C - A), B)) / B))) / pi;
	t_1 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_1 <= -0.001)
		tmp = t_0;
	elseif (t_1 <= 0.0)
		tmp = 180.0 * (atan((B * (0.5 / (A - C)))) / pi);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -0.001], t$95$0, If[LessEqual[t$95$1, 0.0], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -1e-3 or -0.0 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 58.3%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 85.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 58.3%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-hypot.f64 85.6

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

   8. Applied rewrites 85.6%

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

   if -1e-3 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -0.0

   1. Initial program 19.8%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 19.8%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. remove-double-neg N/A

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

      16. sub-neg N/A

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

      17. lower-/.f64 N/A

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

      18. lower--.f64 98.5

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

   7. Applied rewrites 98.5%

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

Alternative 2: 69.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_2 := 180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{if}\;t\_1 \leq -0.001:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;t\_1 \leq 10^{+284}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (+ (/ (- C A) B) -1.0)) PI)))
        (t_1
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
        (t_2 (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI))))
   (if (<= t_1 -0.001)
     t_0
     (if (<= t_1 5e-50)
       t_2
       (if (<= t_1 2.0)
         (* 180.0 (/ (atan 1.0) PI))
         (if (<= t_1 1e+284) t_0 t_2))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((((C - A) / B) + -1.0)) / ((double) M_PI));
	double t_1 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double t_2 = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	double tmp;
	if (t_1 <= -0.001) {
		tmp = t_0;
	} else if (t_1 <= 5e-50) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (t_1 <= 1e+284) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan((((C - A) / B) + -1.0)) / Math.PI);
	double t_1 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double t_2 = 180.0 * (Math.atan((B * (0.5 / (A - C)))) / Math.PI);
	double tmp;
	if (t_1 <= -0.001) {
		tmp = t_0;
	} else if (t_1 <= 5e-50) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (t_1 <= 1e+284) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan((((C - A) / B) + -1.0)) / math.pi)
	t_1 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	t_2 = 180.0 * (math.atan((B * (0.5 / (A - C)))) / math.pi)
	tmp = 0
	if t_1 <= -0.001:
		tmp = t_0
	elif t_1 <= 5e-50:
		tmp = t_2
	elif t_1 <= 2.0:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif t_1 <= 1e+284:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + -1.0)) / pi))
	t_1 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	t_2 = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi))
	tmp = 0.0
	if (t_1 <= -0.001)
		tmp = t_0;
	elseif (t_1 <= 5e-50)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (t_1 <= 1e+284)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan((((C - A) / B) + -1.0)) / pi);
	t_1 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	t_2 = 180.0 * (atan((B * (0.5 / (A - C)))) / pi);
	tmp = 0.0;
	if (t_1 <= -0.001)
		tmp = t_0;
	elseif (t_1 <= 5e-50)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (t_1 <= 1e+284)
		tmp = t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = 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]}, Block[{t$95$2 = N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -0.001], t$95$0, If[LessEqual[t$95$1, 5e-50], t$95$2, If[LessEqual[t$95$1, 2.0], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+284], t$95$0, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -1e-3 or 2 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 1.00000000000000008e284

   1. Initial program 62.7%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 79.8

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

   5. Applied rewrites 79.8%

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

   if -1e-3 < (*.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)))))) < 4.99999999999999968e-50 or 1.00000000000000008e284 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 34.3%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. remove-double-neg N/A

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

      16. sub-neg N/A

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

      17. lower-/.f64 N/A

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

      18. lower--.f64 61.6

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

   7. Applied rewrites 61.6%

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

   if 4.99999999999999968e-50 < (*.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)))))) < 2

   1. Initial program 94.6%

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

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 100.0%

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

Alternative 3: 67.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_1 \leq -0.001:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B \cdot \left(\frac{C - A}{B} + -1\right)\right)\right)}{\pi}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-50}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 10^{+284}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\mathsf{fma}\left(B, B, C \cdot C\right)}}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI)))
        (t_1
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_1 -0.001)
     (* 180.0 (/ (atan (* (/ 1.0 B) (* B (+ (/ (- C A) B) -1.0)))) PI))
     (if (<= t_1 5e-50)
       t_0
       (if (<= t_1 1e+284)
         (/ (* 180.0 (atan (/ (- C (sqrt (fma B B (* C C)))) B))) PI)
         t_0)))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	double t_1 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_1 <= -0.001) {
		tmp = 180.0 * (atan(((1.0 / B) * (B * (((C - A) / B) + -1.0)))) / ((double) M_PI));
	} else if (t_1 <= 5e-50) {
		tmp = t_0;
	} else if (t_1 <= 1e+284) {
		tmp = (180.0 * atan(((C - sqrt(fma(B, B, (C * C)))) / B))) / ((double) M_PI);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi))
	t_1 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_1 <= -0.001)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(B * Float64(Float64(Float64(C - A) / B) + -1.0)))) / pi));
	elseif (t_1 <= 5e-50)
		tmp = t_0;
	elseif (t_1 <= 1e+284)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - sqrt(fma(B, B, Float64(C * C)))) / B))) / pi);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -0.001], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(B * N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-50], t$95$0, If[LessEqual[t$95$1, 1e+284], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[N[(B * B + N[(C * C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -1e-3

   1. Initial program 58.7%

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

   3. Taylor expanded in B around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate--r+ N/A

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

      4. div-sub N/A

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 78.1

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

   5. Applied rewrites 78.1%

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

   if -1e-3 < (*.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)))))) < 4.99999999999999968e-50 or 1.00000000000000008e284 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 34.3%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. remove-double-neg N/A

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

      16. sub-neg N/A

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

      17. lower-/.f64 N/A

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

      18. lower--.f64 61.6

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

   7. Applied rewrites 61.6%

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

   if 4.99999999999999968e-50 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 1.00000000000000008e284

   1. Initial program 96.9%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 99.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 96.9%

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

   7. Taylor expanded in A around 0

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

      1. lower--.f64 N/A

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

      2. lower-sqrt.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-fma.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 87.7

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

   9. Applied rewrites 87.7%

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

Alternative 4: 67.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{if}\;t\_0 \leq -0.001:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 10^{+284}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \sqrt{\mathsf{fma}\left(B, B, C \cdot C\right)}}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
        (t_1 (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI))))
   (if (<= t_0 -0.001)
     (* 180.0 (/ (atan (+ (/ (- C A) B) -1.0)) PI))
     (if (<= t_0 5e-50)
       t_1
       (if (<= t_0 1e+284)
         (/ (* 180.0 (atan (/ (- C (sqrt (fma B B (* C C)))) B))) PI)
         t_1)))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double t_1 = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	double tmp;
	if (t_0 <= -0.001) {
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / ((double) M_PI));
	} else if (t_0 <= 5e-50) {
		tmp = t_1;
	} else if (t_0 <= 1e+284) {
		tmp = (180.0 * atan(((C - sqrt(fma(B, B, (C * C)))) / B))) / ((double) M_PI);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	t_1 = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi))
	tmp = 0.0
	if (t_0 <= -0.001)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + -1.0)) / pi));
	elseif (t_0 <= 5e-50)
		tmp = t_1;
	elseif (t_0 <= 1e+284)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(C - sqrt(fma(B, B, Float64(C * C)))) / B))) / pi);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.001], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e-50], t$95$1, If[LessEqual[t$95$0, 1e+284], N[(N[(180.0 * N[ArcTan[N[(N[(C - N[Sqrt[N[(B * B + N[(C * C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -1e-3

   1. Initial program 58.7%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 78.1

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

   5. Applied rewrites 78.1%

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

   if -1e-3 < (*.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)))))) < 4.99999999999999968e-50 or 1.00000000000000008e284 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 34.3%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. remove-double-neg N/A

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

      16. sub-neg N/A

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

      17. lower-/.f64 N/A

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

      18. lower--.f64 61.6

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

   7. Applied rewrites 61.6%

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

   if 4.99999999999999968e-50 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 1.00000000000000008e284

   1. Initial program 96.9%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 99.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 96.9%

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

   7. Taylor expanded in A around 0

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

      1. lower--.f64 N/A

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

      2. lower-sqrt.f64 N/A

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

      3. unpow2 N/A

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

      4. lower-fma.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 87.7

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

   9. Applied rewrites 87.7%

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

Alternative 5: 67.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_1 := 180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{if}\;t\_0 \leq -0.001:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 10^{+284}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \sqrt{\mathsf{fma}\left(B, B, C \cdot C\right)}}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
        (t_1 (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI))))
   (if (<= t_0 -0.001)
     (* 180.0 (/ (atan (+ (/ (- C A) B) -1.0)) PI))
     (if (<= t_0 5e-50)
       t_1
       (if (<= t_0 1e+284)
         (* 180.0 (/ (atan (/ (- C (sqrt (fma B B (* C C)))) B)) PI))
         t_1)))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double t_1 = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	double tmp;
	if (t_0 <= -0.001) {
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / ((double) M_PI));
	} else if (t_0 <= 5e-50) {
		tmp = t_1;
	} else if (t_0 <= 1e+284) {
		tmp = 180.0 * (atan(((C - sqrt(fma(B, B, (C * C)))) / B)) / ((double) M_PI));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	t_1 = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi))
	tmp = 0.0
	if (t_0 <= -0.001)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + -1.0)) / pi));
	elseif (t_0 <= 5e-50)
		tmp = t_1;
	elseif (t_0 <= 1e+284)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - sqrt(fma(B, B, Float64(C * C)))) / B)) / pi));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.001], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e-50], t$95$1, If[LessEqual[t$95$0, 1e+284], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[N[(B * B + N[(C * C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -1e-3

   1. Initial program 58.7%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 78.1

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

   5. Applied rewrites 78.1%

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

   if -1e-3 < (*.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)))))) < 4.99999999999999968e-50 or 1.00000000000000008e284 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 34.3%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. remove-double-neg N/A

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

      16. sub-neg N/A

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

      17. lower-/.f64 N/A

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

      18. lower--.f64 61.6

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

   7. Applied rewrites 61.6%

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

   if 4.99999999999999968e-50 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 1.00000000000000008e284

   1. Initial program 96.9%

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

   3. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-sqrt.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 87.6

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

   5. Applied rewrites 87.6%

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

Alternative 6: 71.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -0.001:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B \cdot \left(\frac{C - A}{B} + -1\right)\right)\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-50}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\mathsf{fma}\left(A - C, A - C, B \cdot B\right)}}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -0.001)
     (* 180.0 (/ (atan (* (/ 1.0 B) (* B (+ (/ (- C A) B) -1.0)))) PI))
     (if (<= t_0 5e-50)
       (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI))
       (/
        (* 180.0 (atan (/ (- (- C A) (sqrt (fma (- A C) (- A C) (* B B)))) B)))
        PI)))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.001) {
		tmp = 180.0 * (atan(((1.0 / B) * (B * (((C - A) / B) + -1.0)))) / ((double) M_PI));
	} else if (t_0 <= 5e-50) {
		tmp = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((((C - A) - sqrt(fma((A - C), (A - C), (B * B)))) / B))) / ((double) M_PI);
	}
	return tmp;
}

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_0 <= -0.001)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(B * Float64(Float64(Float64(C - A) / B) + -1.0)))) / pi));
	elseif (t_0 <= 5e-50)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - sqrt(fma(Float64(A - C), Float64(A - C), Float64(B * B)))) / B))) / pi);
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.001], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(B * N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e-50], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[(A - C), $MachinePrecision] * N[(A - C), $MachinePrecision] + N[(B * B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -1e-3

   1. Initial program 58.7%

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

   3. Taylor expanded in B around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate--r+ N/A

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

      4. div-sub N/A

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 78.1

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

   5. Applied rewrites 78.1%

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

   if -1e-3 < (*.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)))))) < 4.99999999999999968e-50

   1. Initial program 19.3%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 22.1%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. remove-double-neg N/A

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

      16. sub-neg N/A

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

      17. lower-/.f64 N/A

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

      18. lower--.f64 96.3

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

   7. Applied rewrites 96.3%

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

   if 4.99999999999999968e-50 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 58.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   4. Applied rewrites 58.3%

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

Alternative 7: 71.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -0.001:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B \cdot \left(\frac{C - A}{B} + -1\right)\right)\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-50}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\mathsf{fma}\left(A - C, A - C, B \cdot B\right)}}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -0.001)
     (* 180.0 (/ (atan (* (/ 1.0 B) (* B (+ (/ (- C A) B) -1.0)))) PI))
     (if (<= t_0 5e-50)
       (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI))
       (*
        (atan (/ (- (- C A) (sqrt (fma (- A C) (- A C) (* B B)))) B))
        (/ 180.0 PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.001) {
		tmp = 180.0 * (atan(((1.0 / B) * (B * (((C - A) / B) + -1.0)))) / ((double) M_PI));
	} else if (t_0 <= 5e-50) {
		tmp = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	} else {
		tmp = atan((((C - A) - sqrt(fma((A - C), (A - C), (B * B)))) / B)) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_0 <= -0.001)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(B * Float64(Float64(Float64(C - A) / B) + -1.0)))) / pi));
	elseif (t_0 <= 5e-50)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / Float64(A - C)))) / pi));
	else
		tmp = Float64(atan(Float64(Float64(Float64(C - A) - sqrt(fma(Float64(A - C), Float64(A - C), Float64(B * B)))) / B)) * Float64(180.0 / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.001], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(B * N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e-50], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / N[(A - C), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[(A - C), $MachinePrecision] * N[(A - C), $MachinePrecision] + N[(B * B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -1e-3

   1. Initial program 58.7%

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

   3. Taylor expanded in B around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate--r+ N/A

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

      4. div-sub N/A

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 78.1

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

   5. Applied rewrites 78.1%

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

   if -1e-3 < (*.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)))))) < 4.99999999999999968e-50

   1. Initial program 19.3%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 22.1%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. remove-double-neg N/A

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

      16. sub-neg N/A

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

      17. lower-/.f64 N/A

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

      18. lower--.f64 96.3

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

   7. Applied rewrites 96.3%

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

   if 4.99999999999999968e-50 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 58.3%

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

      1. lift-*.f64 N/A

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

      2. metadata-eval N/A

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

      3. lift-/.f64 N/A

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

      4. times-frac N/A

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

      5. *-commutative N/A

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

      6. times-frac N/A

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

      7. /-rgt-identity N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 58.3

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

   4. Applied rewrites 58.3%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.001:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B \cdot \left(\frac{C - A}{B} + -1\right)\right)\right)}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 5 \cdot 10^{-50}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A - C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\mathsf{fma}\left(A - C, A - C, B \cdot B\right)}}{B}\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -0.07:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{-A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -0.07)
   (* (/ 180.0 PI) (atan (* B (/ 0.5 A))))
   (if (<= A 1.9e-116)
     (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (+ -1.0 (/ (- A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -0.07) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / A)));
	} else if (A <= 1.9e-116) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 + (-A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -0.07) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / A)));
	} else if (A <= 1.9e-116) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 + (-A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -0.07:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / A)))
	elif A <= 1.9e-116:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 + (-A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -0.07)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / A))));
	elseif (A <= 1.9e-116)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(Float64(-A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -0.07)
		tmp = (180.0 / pi) * atan((B * (0.5 / A)));
	elseif (A <= 1.9e-116)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 + (-A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -0.07], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.9e-116], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[((-A) / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -0.070000000000000007

   1. Initial program 22.5%

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

   3. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. distribute-lft-out N/A

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 70.8

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

   5. Applied rewrites 70.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. clear-num N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

   7. Applied rewrites 68.7%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

   9. Applied rewrites 71.1%

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

   10. Taylor expanded in A around -inf

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

       1. associate-*r/ N/A

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

       2. *-commutative N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 71.0

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

   12. Applied rewrites 71.0%

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

   if -0.070000000000000007 < A < 1.9000000000000001e-116

   1. Initial program 58.2%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 56.6

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

   5. Applied rewrites 56.6%

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

   6. Taylor expanded in C around inf

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

   8. Applied rewrites 56.1%

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

   if 1.9000000000000001e-116 < A

   1. Initial program 70.0%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 74.2

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

   5. Applied rewrites 74.2%

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

   6. Taylor expanded in C around 0

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

   8. Applied rewrites 71.8%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -0.07:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{-A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -0.07:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{-A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -0.07)
   (* 180.0 (/ (atan (* B (/ 0.5 A))) PI))
   (if (<= A 1.9e-116)
     (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))
     (* 180.0 (/ (atan (+ -1.0 (/ (- A) B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -0.07) {
		tmp = 180.0 * (atan((B * (0.5 / A))) / ((double) M_PI));
	} else if (A <= 1.9e-116) {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 + (-A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -0.07) {
		tmp = 180.0 * (Math.atan((B * (0.5 / A))) / Math.PI);
	} else if (A <= 1.9e-116) {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 + (-A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -0.07:
		tmp = 180.0 * (math.atan((B * (0.5 / A))) / math.pi)
	elif A <= 1.9e-116:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 + (-A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -0.07)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / A))) / pi));
	elseif (A <= 1.9e-116)
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(Float64(-A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -0.07)
		tmp = 180.0 * (atan((B * (0.5 / A))) / pi);
	elseif (A <= 1.9e-116)
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 + (-A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -0.07], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.9e-116], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[((-A) / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -0.070000000000000007

   1. Initial program 22.5%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 10.9%

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

   6. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 70.7

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

   8. Applied rewrites 70.7%

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

   if -0.070000000000000007 < A < 1.9000000000000001e-116

   1. Initial program 58.2%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 56.6

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

   5. Applied rewrites 56.6%

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

   6. Taylor expanded in C around inf

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

   8. Applied rewrites 56.1%

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

   if 1.9000000000000001e-116 < A

   1. Initial program 70.0%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 74.2

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

   5. Applied rewrites 74.2%

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

   6. Taylor expanded in C around 0

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

   8. Applied rewrites 71.8%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -0.07:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9 \cdot 10^{-116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{-A}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.5e-11)
   (* (/ 180.0 PI) (atan (* B (/ 0.5 A))))
   (* 180.0 (/ (atan (+ (/ (- C A) B) -1.0)) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e-11) {
		tmp = (180.0 / ((double) M_PI)) * atan((B * (0.5 / A)));
	} else {
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e-11) {
		tmp = (180.0 / Math.PI) * Math.atan((B * (0.5 / A)));
	} else {
		tmp = 180.0 * (Math.atan((((C - A) / B) + -1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.5e-11:
		tmp = (180.0 / math.pi) * math.atan((B * (0.5 / A)))
	else:
		tmp = 180.0 * (math.atan((((C - A) / B) + -1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.5e-11)
		tmp = Float64(Float64(180.0 / pi) * atan(Float64(B * Float64(0.5 / A))));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + -1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.5e-11)
		tmp = (180.0 / pi) * atan((B * (0.5 / A)));
	else
		tmp = 180.0 * (atan((((C - A) / B) + -1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.5e-11], N[(N[(180.0 / Pi), $MachinePrecision] * N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -8.50000000000000037e-11

   1. Initial program 23.1%

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

   3. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. distribute-lft-out N/A

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 69.2

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

   5. Applied rewrites 69.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. clear-num N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

   7. Applied rewrites 67.2%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

   9. Applied rewrites 69.5%

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

   10. Taylor expanded in A around -inf

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

       1. associate-*r/ N/A

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

       2. *-commutative N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 69.3

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

   12. Applied rewrites 69.3%

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

   if -8.50000000000000037e-11 < A

   1. Initial program 63.2%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 63.9

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

   5. Applied rewrites 63.9%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(B \cdot \frac{0.5}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -0.07:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -0.07)
   (* 180.0 (/ (atan (* B (/ 0.5 A))) PI))
   (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -0.07) {
		tmp = 180.0 * (atan((B * (0.5 / A))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -0.07) {
		tmp = 180.0 * (Math.atan((B * (0.5 / A))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -0.07:
		tmp = 180.0 * (math.atan((B * (0.5 / A))) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -0.07)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / A))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -0.07)
		tmp = 180.0 * (atan((B * (0.5 / A))) / pi);
	else
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -0.07], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -0.070000000000000007

   1. Initial program 22.5%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 10.9%

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

   6. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 70.7

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

   8. Applied rewrites 70.7%

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

   if -0.070000000000000007 < A

   1. Initial program 62.8%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 63.4

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

   5. Applied rewrites 63.4%

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

   6. Taylor expanded in C around inf

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

   8. Applied rewrites 51.4%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -0.07:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-35}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -7.2e-35)
   (* 180.0 (/ (atan 1.0) PI))
   (* 180.0 (/ (atan (+ -1.0 (/ C B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.2e-35) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-1.0 + (C / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -7.2e-35) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-1.0 + (C / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -7.2e-35:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-1.0 + (C / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -7.2e-35)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(-1.0 + Float64(C / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -7.2e-35)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((-1.0 + (C / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -7.2e-35], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(-1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -7.20000000000000038e-35

   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. Add Preprocessing

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 53.3%

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

   if -7.20000000000000038e-35 < B

   1. Initial program 54.4%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 62.1

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

   5. Applied rewrites 62.1%

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

   6. Taylor expanded in C around inf

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

   8. Applied rewrites 52.4%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -7.2 \cdot 10^{-35}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-1 + \frac{C}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 45.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.15 \cdot 10^{-85}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3 \cdot 10^{-171}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.15e-85)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 3e-171)
     (* 180.0 (/ (atan 0.0) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.15e-85) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 3e-171) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.15e-85) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 3e-171) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.15e-85:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 3e-171:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.15e-85)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 3e-171)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.15e-85)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 3e-171)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.15e-85], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3e-171], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.14999999999999999e-85

   1. Initial program 52.2%

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

   3. Taylor expanded in B around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 50.1%

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

   if -2.14999999999999999e-85 < B < 3e-171

   1. Initial program 57.9%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B}\right)}{\mathsf{PI}\left(\right)} \]

      3. mul0-lft N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B}\right)}{\mathsf{PI}\left(\right)} \]

      4. div0 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \color{blue}{0}\right)}{\mathsf{PI}\left(\right)} \]

      5. metadata-eval 32.1

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

   5. Applied rewrites 32.1%

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

   if 3e-171 < B

   1. Initial program 50.3%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 53.3%

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

Alternative 14: 29.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 3 \cdot 10^{-171}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 3e-171) (* 180.0 (/ (atan 0.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 3e-171) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 3e-171) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 3e-171:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 3e-171)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 3e-171)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 3e-171], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 3e-171

   1. Initial program 55.3%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0} \cdot A}{B}\right)}{\mathsf{PI}\left(\right)} \]

      3. mul0-lft N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \frac{\color{blue}{0}}{B}\right)}{\mathsf{PI}\left(\right)} \]

      4. div0 N/A

         \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \color{blue}{0}\right)}{\mathsf{PI}\left(\right)} \]

      5. metadata-eval 18.8

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

   5. Applied rewrites 18.8%

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

   if 3e-171 < B

   1. Initial program 50.3%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\mathsf{PI}\left(\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 53.3%

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

Alternative 15: 21.1% accurate, 3.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 53.2%

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

3. Taylor expanded in B around inf

   \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{-1}}{\mathsf{PI}\left(\right)} \]
4. Step-by-step derivation

5. Applied rewrites 25.3%

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

Reproduce

herbie shell --seed 2024227 
(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)))