ABCF->ab-angle angle

Percentage Accurate: 53.2% → 81.9%

Time: 12.8s

Alternatives: 16

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: 53.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 1.2e+14)
   (/ (* 180.0 (atan (/ (- (- C A) (hypot (- C A) B)) B))) PI)
   (/ (* 180.0 (atan (/ (* B -0.5) (- C A)))) PI)))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.2e+14) {
		tmp = (180.0 * atan((((C - A) - hypot((C - A), B)) / B))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(((B * -0.5) / (C - A)))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 1.2e+14) {
		tmp = (180.0 * Math.atan((((C - A) - Math.hypot((C - A), B)) / B))) / Math.PI;
	} else {
		tmp = (180.0 * Math.atan(((B * -0.5) / (C - A)))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 1.2e+14:
		tmp = (180.0 * math.atan((((C - A) - math.hypot((C - A), B)) / B))) / math.pi
	else:
		tmp = (180.0 * math.atan(((B * -0.5) / (C - A)))) / math.pi
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 1.2e+14)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(Float64(C - A), B)) / B))) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / Float64(C - A)))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 1.2e+14)
		tmp = (180.0 * atan((((C - A) - hypot((C - A), B)) / B))) / pi;
	else
		tmp = (180.0 * atan(((B * -0.5) / (C - A)))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 1.2e+14], 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], N[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 1.2e14

   1. Initial program 66.0%

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

   4. Applied rewrites 88.5%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-atan.f64 N/A

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

      9. lift-PI.f64 N/A

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

      10. associate-*r/ N/A

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

   6. Applied rewrites 66.0%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lower-hypot.f64 88.5

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

   8. Applied rewrites 88.5%

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

   if 1.2e14 < C

   1. Initial program 20.1%

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

   4. Applied rewrites 47.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-atan.f64 N/A

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

      9. lift-PI.f64 N/A

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

      10. associate-*r/ N/A

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

   6. Applied rewrites 20.1%

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

   7. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 79.9

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

   9. Applied rewrites 79.9%

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

Alternative 2: 79.1% accurate, 0.6× speedup

Math

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   1. Initial program 60.3%

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

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

   5. Applied rewrites 76.6%

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

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

   1. Initial program 27.6%

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

   4. Applied rewrites 27.6%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-atan.f64 N/A

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

      9. lift-PI.f64 N/A

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

      10. associate-*r/ N/A

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

   6. Applied rewrites 27.6%

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

   7. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.4

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

   9. Applied rewrites 99.4%

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

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

   1. Initial program 57.3%

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

   4. Applied rewrites 87.4%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-atan.f64 N/A

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

      9. lift-PI.f64 N/A

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

      10. associate-*r/ N/A

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

   6. Applied rewrites 57.3%

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

   7. Taylor expanded in B around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 77.7

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

   9. Applied rewrites 77.7%

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

4. Final simplification 80.0%

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

Alternative 3: 79.1% accurate, 0.6× speedup

Math

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

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))))))
        (t_1 (/ (- C A) B)))
   (if (<= t_0 -0.5)
     (* 180.0 (/ (atan (+ t_1 -1.0)) PI))
     (if (<= t_0 0.0)
       (/ (* 180.0 (atan (/ (* B -0.5) (- C A)))) PI)
       (/ (* 180.0 (atan (+ t_1 1.0))) 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 t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (atan((t_1 + -1.0)) / ((double) M_PI));
	} else if (t_0 <= 0.0) {
		tmp = (180.0 * atan(((B * -0.5) / (C - A)))) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((t_1 + 1.0))) / ((double) M_PI);
	}
	return tmp;
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   1. Initial program 60.3%

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

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

   5. Applied rewrites 76.6%

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

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

   1. Initial program 27.6%

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

   4. Applied rewrites 27.6%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-atan.f64 N/A

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

      9. lift-PI.f64 N/A

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

      10. associate-*r/ N/A

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

   6. Applied rewrites 27.6%

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

   7. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.4

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

   9. Applied rewrites 99.4%

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

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

   1. Initial program 57.3%

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

   4. Applied rewrites 87.4%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-atan.f64 N/A

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

      9. lift-PI.f64 N/A

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

      10. associate-*r/ N/A

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

   6. Applied rewrites 57.3%

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

   7. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 77.7

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

   9. Applied rewrites 77.7%

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

4. Final simplification 80.0%

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

Alternative 4: 79.1% accurate, 0.6× speedup

Math

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

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))))))
        (t_1 (/ (- C A) B)))
   (if (<= t_0 -0.5)
     (* 180.0 (/ (atan (+ t_1 -1.0)) PI))
     (if (<= t_0 0.0)
       (* 180.0 (/ (atan (* -0.5 (/ B (- C A)))) PI))
       (/ (* 180.0 (atan (+ t_1 1.0))) 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 t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (atan((t_1 + -1.0)) / ((double) M_PI));
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan((-0.5 * (B / (C - A)))) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((t_1 + 1.0))) / ((double) M_PI);
	}
	return tmp;
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   1. Initial program 60.3%

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

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

   5. Applied rewrites 76.6%

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

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

   1. Initial program 27.6%

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

   4. Applied rewrites 27.6%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-atan.f64 N/A

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

      9. lift-PI.f64 N/A

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

      10. associate-*r/ N/A

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

   6. Applied rewrites 27.6%

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

   7. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.4

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

   9. Applied rewrites 99.4%

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

       1. lift-*.f64 N/A

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

       2. lift--.f64 N/A

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

       3. lift-/.f64 N/A

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

       4. lift-atan.f64 N/A

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

       5. lift-PI.f64 N/A

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

       6. associate-/l* N/A

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

       7. *-commutative N/A

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

       8. lower-*.f64 N/A

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

       9. lower-/.f64 99.2

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

       10. lift-/.f64 N/A

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

       11. lift-*.f64 N/A

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

       12. *-commutative N/A

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

       13. associate-/l* N/A

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

       14. lower-*.f64 N/A

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

       15. lower-/.f64 99.2

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

   11. Applied rewrites 99.2%

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

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

   1. Initial program 57.3%

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

   4. Applied rewrites 87.4%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-atan.f64 N/A

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

      9. lift-PI.f64 N/A

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

      10. associate-*r/ N/A

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

   6. Applied rewrites 57.3%

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

   7. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 77.7

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

   9. Applied rewrites 77.7%

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

4. Final simplification 80.0%

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

Alternative 5: 79.1% accurate, 0.6× speedup

Math

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

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))))))
        (t_1 (/ (- C A) B)))
   (if (<= t_0 -0.5)
     (* 180.0 (/ (atan (+ t_1 -1.0)) PI))
     (if (<= t_0 0.0)
       (* 180.0 (/ (atan (* B (/ 0.5 (- A C)))) PI))
       (/ (* 180.0 (atan (+ t_1 1.0))) 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 t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (atan((t_1 + -1.0)) / ((double) M_PI));
	} else if (t_0 <= 0.0) {
		tmp = 180.0 * (atan((B * (0.5 / (A - C)))) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan((t_1 + 1.0))) / ((double) M_PI);
	}
	return tmp;
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   1. Initial program 60.3%

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

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

   5. Applied rewrites 76.6%

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

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

   1. Initial program 27.6%

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

   4. Applied rewrites 27.6%

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

   5. 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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. distribute-lft-in N/A

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

      16. mul-1-neg N/A

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

      17. remove-double-neg N/A

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

      18. lower-/.f64 N/A

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

      19. mul-1-neg N/A

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

      20. unsub-neg N/A

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

      21. lower--.f64 99.2

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

   7. Applied rewrites 99.2%

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

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

   1. Initial program 57.3%

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

   4. Applied rewrites 87.4%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-atan.f64 N/A

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

      9. lift-PI.f64 N/A

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

      10. associate-*r/ N/A

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

   6. Applied rewrites 57.3%

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

   7. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 77.7

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

   9. Applied rewrites 77.7%

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

4. Final simplification 80.0%

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

Alternative 6: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_1 := \frac{C - A}{B}\\ \mathbf{if}\;t\_0 \leq -0.5:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_1 + -1\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{A \cdot 2}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(t\_1 + 1\right)}{\pi}\\ \end{array} \end{array} \]

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))))))
        (t_1 (/ (- C A) B)))
   (if (<= t_0 -0.5)
     (* 180.0 (/ (atan (+ t_1 -1.0)) PI))
     (if (<= t_0 0.0)
       (/ (atan (/ B (* A 2.0))) (* PI 0.005555555555555556))
       (/ (* 180.0 (atan (+ t_1 1.0))) 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 t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (atan((t_1 + -1.0)) / ((double) M_PI));
	} else if (t_0 <= 0.0) {
		tmp = atan((B / (A * 2.0))) / (((double) M_PI) * 0.005555555555555556);
	} else {
		tmp = (180.0 * atan((t_1 + 1.0))) / ((double) M_PI);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (Math.atan((t_1 + -1.0)) / Math.PI);
	} else if (t_0 <= 0.0) {
		tmp = Math.atan((B / (A * 2.0))) / (Math.PI * 0.005555555555555556);
	} else {
		tmp = (180.0 * Math.atan((t_1 + 1.0))) / Math.PI;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	t_1 = (C - A) / B
	tmp = 0
	if t_0 <= -0.5:
		tmp = 180.0 * (math.atan((t_1 + -1.0)) / math.pi)
	elif t_0 <= 0.0:
		tmp = math.atan((B / (A * 2.0))) / (math.pi * 0.005555555555555556)
	else:
		tmp = (180.0 * math.atan((t_1 + 1.0))) / math.pi
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	t_1 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = Float64(180.0 * Float64(atan(Float64(t_1 + -1.0)) / pi));
	elseif (t_0 <= 0.0)
		tmp = Float64(atan(Float64(B / Float64(A * 2.0))) / Float64(pi * 0.005555555555555556));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(t_1 + 1.0))) / pi);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	t_1 = (C - A) / B;
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = 180.0 * (atan((t_1 + -1.0)) / pi);
	elseif (t_0 <= 0.0)
		tmp = atan((B / (A * 2.0))) / (pi * 0.005555555555555556);
	else
		tmp = (180.0 * atan((t_1 + 1.0))) / pi;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], N[(180.0 * N[(N[ArcTan[N[(t$95$1 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[ArcTan[N[(B / N[(A * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(t$95$1 + 1.0), $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)))))) < -0.5

   1. Initial program 60.3%

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

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

   5. Applied rewrites 76.6%

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

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

   1. Initial program 27.6%

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

   3. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 45.6

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

   5. Applied rewrites 45.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-atan.f64 N/A

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

      7. lift-PI.f64 N/A

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

      8. metadata-eval N/A

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

      9. times-frac N/A

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

      10. *-commutative N/A

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

      11. times-frac N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

   7. Applied rewrites 61.3%

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

      1. lift-PI.f64 N/A

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

      2. frac-2neg N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-atan.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-/.f64 N/A

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

      11. clear-num N/A

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

      12. un-div-inv N/A

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

      13. lower-/.f64 N/A

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

   9. Applied rewrites 61.4%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{A \cdot 2}\right)}{\pi \cdot 0.005555555555555556}} \]

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

   1. Initial program 57.3%

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

   4. Applied rewrites 87.4%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-hypot.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-atan.f64 N/A

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

      9. lift-PI.f64 N/A

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

      10. associate-*r/ N/A

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

   6. Applied rewrites 57.3%

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

   7. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 77.7

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

   9. Applied rewrites 77.7%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.5:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{A \cdot 2}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ t_1 := \frac{C - A}{B}\\ \mathbf{if}\;t\_0 \leq -0.5:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_1 + -1\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{A \cdot 2}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(t\_1 + 1\right)}{\pi}\\ \end{array} \end{array} \]

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))))))
        (t_1 (/ (- C A) B)))
   (if (<= t_0 -0.5)
     (* 180.0 (/ (atan (+ t_1 -1.0)) PI))
     (if (<= t_0 0.0)
       (/ (atan (/ B (* A 2.0))) (* PI 0.005555555555555556))
       (* 180.0 (/ (atan (+ t_1 1.0)) 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 t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (atan((t_1 + -1.0)) / ((double) M_PI));
	} else if (t_0 <= 0.0) {
		tmp = atan((B / (A * 2.0))) / (((double) M_PI) * 0.005555555555555556);
	} else {
		tmp = 180.0 * (atan((t_1 + 1.0)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double t_1 = (C - A) / B;
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (Math.atan((t_1 + -1.0)) / Math.PI);
	} else if (t_0 <= 0.0) {
		tmp = Math.atan((B / (A * 2.0))) / (Math.PI * 0.005555555555555556);
	} else {
		tmp = 180.0 * (Math.atan((t_1 + 1.0)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	t_1 = (C - A) / B
	tmp = 0
	if t_0 <= -0.5:
		tmp = 180.0 * (math.atan((t_1 + -1.0)) / math.pi)
	elif t_0 <= 0.0:
		tmp = math.atan((B / (A * 2.0))) / (math.pi * 0.005555555555555556)
	else:
		tmp = 180.0 * (math.atan((t_1 + 1.0)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	t_1 = Float64(Float64(C - A) / B)
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = Float64(180.0 * Float64(atan(Float64(t_1 + -1.0)) / pi));
	elseif (t_0 <= 0.0)
		tmp = Float64(atan(Float64(B / Float64(A * 2.0))) / Float64(pi * 0.005555555555555556));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(t_1 + 1.0)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	t_1 = (C - A) / B;
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = 180.0 * (atan((t_1 + -1.0)) / pi);
	elseif (t_0 <= 0.0)
		tmp = atan((B / (A * 2.0))) / (pi * 0.005555555555555556);
	else
		tmp = 180.0 * (atan((t_1 + 1.0)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], N[(180.0 * N[(N[ArcTan[N[(t$95$1 + -1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[ArcTan[N[(B / N[(A * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(t$95$1 + 1.0), $MachinePrecision]], $MachinePrecision] / 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)))))) < -0.5

   1. Initial program 60.3%

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

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

   5. Applied rewrites 76.6%

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

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

   1. Initial program 27.6%

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

   3. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 45.6

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

   5. Applied rewrites 45.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-atan.f64 N/A

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

      7. lift-PI.f64 N/A

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

      8. metadata-eval N/A

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

      9. times-frac N/A

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

      10. *-commutative N/A

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

      11. times-frac N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

   7. Applied rewrites 61.3%

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

      1. lift-PI.f64 N/A

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

      2. frac-2neg N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-atan.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-/.f64 N/A

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

      11. clear-num N/A

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

      12. un-div-inv N/A

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

      13. lower-/.f64 N/A

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

   9. Applied rewrites 61.4%

      \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{A \cdot 2}\right)}{\pi \cdot 0.005555555555555556}} \]

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

   1. Initial program 57.3%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 77.7

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

   5. Applied rewrites 77.7%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.5:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{A \cdot 2}\right)}{\pi \cdot 0.005555555555555556}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -2.3 \cdot 10^{+31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.36 \cdot 10^{-77}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{C \cdot -2}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -2.3e+31)
   (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
   (if (<= C 1.36e-77)
     (* 180.0 (/ (atan 1.0) PI))
     (/ (atan (/ B (* C -2.0))) (* PI 0.005555555555555556)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.3e+31) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= 1.36e-77) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = atan((B / (C * -2.0))) / (((double) M_PI) * 0.005555555555555556);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.3e+31) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= 1.36e-77) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = Math.atan((B / (C * -2.0))) / (Math.PI * 0.005555555555555556);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -2.3e+31:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= 1.36e-77:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = math.atan((B / (C * -2.0))) / (math.pi * 0.005555555555555556)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -2.3e+31)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= 1.36e-77)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(atan(Float64(B / Float64(C * -2.0))) / Float64(pi * 0.005555555555555556));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -2.3e+31)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= 1.36e-77)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = atan((B / (C * -2.0))) / (pi * 0.005555555555555556);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -2.3e+31], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.36e-77], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(B / N[(C * -2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -2.3e31

   1. Initial program 75.4%

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

   3. Taylor expanded in C around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 68.8

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

   5. Applied rewrites 68.8%

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

   if -2.3e31 < C < 1.36000000000000005e-77

   1. Initial program 60.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 38.6%

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

   if 1.36000000000000005e-77 < C

   1. Initial program 29.2%

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

   3. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-rgt1-in N/A

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

      6. metadata-eval N/A

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

      7. mul0-lft N/A

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

      8. div0 N/A

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(B, \frac{\frac{-1}{2}}{C}, 0\right)\right)}}{\mathsf{PI}\left(\right)} \]

      11. lower-/.f64 62.8

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

   5. Applied rewrites 62.8%

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

   6. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-atan.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-PI.f64 62.9

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

   8. Applied rewrites 62.9%

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

   10. Applied rewrites 63.0%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{C \cdot -2}\right)}{\pi \cdot 0.005555555555555556}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 47.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -2.3 \cdot 10^{+31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.36 \cdot 10^{-77}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C \cdot -2}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -2.3e+31)
   (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
   (if (<= C 1.36e-77)
     (* 180.0 (/ (atan 1.0) PI))
     (* 180.0 (/ (atan (/ B (* C -2.0))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.3e+31) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= 1.36e-77) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((B / (C * -2.0))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.3e+31) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= 1.36e-77) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((B / (C * -2.0))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -2.3e+31:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= 1.36e-77:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((B / (C * -2.0))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -2.3e+31)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= 1.36e-77)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(B / Float64(C * -2.0))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -2.3e+31)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= 1.36e-77)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((B / (C * -2.0))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -2.3e+31], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.36e-77], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(B / N[(C * -2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -2.3e31

   1. Initial program 75.4%

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

   3. Taylor expanded in C around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 68.8

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

   5. Applied rewrites 68.8%

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

   if -2.3e31 < C < 1.36000000000000005e-77

   1. Initial program 60.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 38.6%

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

   if 1.36000000000000005e-77 < C

   1. Initial program 29.2%

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

   3. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-rgt1-in N/A

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

      6. metadata-eval N/A

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

      7. mul0-lft N/A

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

      8. div0 N/A

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(B, \frac{\frac{-1}{2}}{C}, 0\right)\right)}}{\mathsf{PI}\left(\right)} \]

      11. lower-/.f64 62.8

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

   5. Applied rewrites 62.8%

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

   6. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-atan.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-PI.f64 62.9

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

   8. Applied rewrites 62.9%

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

      1. unpow1 N/A

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

      2. metadata-eval N/A

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

      3. pow-prod-up N/A

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

      4. inv-pow N/A

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

      5. lift-/.f64 N/A

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

      6. pow2 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*r/ N/A

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

      11. lift-/.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-atan.f64 N/A

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

      14. lift-PI.f64 N/A

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

      15. associate-*r/ N/A

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

   10. Applied rewrites 62.9%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.3 \cdot 10^{+31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.36 \cdot 10^{-77}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{C \cdot -2}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -2.3 \cdot 10^{+31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.36 \cdot 10^{-77}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -2.3e+31)
   (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
   (if (<= C 1.36e-77)
     (* 180.0 (/ (atan 1.0) PI))
     (* 180.0 (/ (atan (* B (/ -0.5 C))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.3e+31) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= 1.36e-77) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((B * (-0.5 / C))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.3e+31) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= 1.36e-77) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((B * (-0.5 / C))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -2.3e+31:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= 1.36e-77:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((B * (-0.5 / C))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -2.3e+31)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= 1.36e-77)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(-0.5 / C))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -2.3e+31)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= 1.36e-77)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan((B * (-0.5 / C))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -2.3e+31], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.36e-77], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(B * N[(-0.5 / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -2.3e31

   1. Initial program 75.4%

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

   3. Taylor expanded in C around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 68.8

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

   5. Applied rewrites 68.8%

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

   if -2.3e31 < C < 1.36000000000000005e-77

   1. Initial program 60.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 38.6%

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

   if 1.36000000000000005e-77 < C

   1. Initial program 29.2%

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

   3. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-rgt1-in N/A

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

      6. metadata-eval N/A

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

      7. mul0-lft N/A

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

      8. div0 N/A

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(B, \frac{\frac{-1}{2}}{C}, 0\right)\right)}}{\mathsf{PI}\left(\right)} \]

      11. lower-/.f64 62.8

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

   5. Applied rewrites 62.8%

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

      1. lift-/.f64 N/A

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

      2. +-rgt-identity N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 62.8

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

   7. Applied rewrites 62.8%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.3 \cdot 10^{+31}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.36 \cdot 10^{-77}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{-0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3.8 \cdot 10^{-15}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 3.6 \cdot 10^{-96}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3.8e-15)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 3.6e-96)
     (* 180.0 (/ (atan (* B (/ 0.5 A))) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3.8e-15) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 3.6e-96) {
		tmp = 180.0 * (atan((B * (0.5 / A))) / ((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 <= -3.8e-15) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 3.6e-96) {
		tmp = 180.0 * (Math.atan((B * (0.5 / A))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3.8e-15:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 3.6e-96:
		tmp = 180.0 * (math.atan((B * (0.5 / A))) / 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 <= -3.8e-15)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 3.6e-96)
		tmp = Float64(180.0 * Float64(atan(Float64(B * Float64(0.5 / A))) / 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 <= -3.8e-15)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 3.6e-96)
		tmp = 180.0 * (atan((B * (0.5 / A))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3.8e-15], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 3.6e-96], N[(180.0 * N[(N[ArcTan[N[(B * N[(0.5 / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -3.8000000000000002e-15

   1. Initial program 47.8%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 68.8%

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

   if -3.8000000000000002e-15 < B < 3.60000000000000008e-96

   1. Initial program 57.6%

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

   3. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 31.7

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

   5. Applied rewrites 31.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. lift-/.f64 N/A

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

      8. inv-pow N/A

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

      9. lift-*.f64 N/A

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

      10. pow2 N/A

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

      11. pow-prod-up N/A

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

      12. metadata-eval N/A

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

      13. unpow1 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 37.6

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

   7. Applied rewrites 37.6%

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

   if 3.60000000000000008e-96 < B

   1. Initial program 57.0%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 51.0%

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

Alternative 12: 46.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.05 \cdot 10^{-57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 0.58:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.05e-57)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 0.58)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.05e-57) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 0.58) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.05e-57) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 0.58) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.05e-57:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 0.58:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.05e-57)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 0.58)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.05e-57)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 0.58)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.05e-57], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 0.58], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.0500000000000001e-57

   1. Initial program 47.2%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 62.0%

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

   if -2.0500000000000001e-57 < B < 0.57999999999999996

   1. Initial program 63.8%

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

   3. Taylor expanded in C around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 36.8

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

   5. Applied rewrites 36.8%

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

   if 0.57999999999999996 < B

   1. Initial program 49.0%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 58.2%

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

Alternative 13: 61.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq 4.5 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{C \cdot -2}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C 4.5e-17)
   (* 180.0 (/ (atan (+ (/ (- C A) B) 1.0)) PI))
   (/ (atan (/ B (* C -2.0))) (* PI 0.005555555555555556))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= 4.5e-17) {
		tmp = 180.0 * (atan((((C - A) / B) + 1.0)) / ((double) M_PI));
	} else {
		tmp = atan((B / (C * -2.0))) / (((double) M_PI) * 0.005555555555555556);
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= 4.5e-17) {
		tmp = 180.0 * (Math.atan((((C - A) / B) + 1.0)) / Math.PI);
	} else {
		tmp = Math.atan((B / (C * -2.0))) / (Math.PI * 0.005555555555555556);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= 4.5e-17:
		tmp = 180.0 * (math.atan((((C - A) / B) + 1.0)) / math.pi)
	else:
		tmp = math.atan((B / (C * -2.0))) / (math.pi * 0.005555555555555556)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= 4.5e-17)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(C - A) / B) + 1.0)) / pi));
	else
		tmp = Float64(atan(Float64(B / Float64(C * -2.0))) / Float64(pi * 0.005555555555555556));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= 4.5e-17)
		tmp = 180.0 * (atan((((C - A) / B) + 1.0)) / pi);
	else
		tmp = atan((B / (C * -2.0))) / (pi * 0.005555555555555556);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, 4.5e-17], N[(180.0 * N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(B / N[(C * -2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 4.49999999999999978e-17

   1. Initial program 66.7%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 67.4

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

   5. Applied rewrites 67.4%

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

   if 4.49999999999999978e-17 < C

   1. Initial program 23.0%

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

   3. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-rgt1-in N/A

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

      6. metadata-eval N/A

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

      7. mul0-lft N/A

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

      8. div0 N/A

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

          \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(B, \frac{\frac{-1}{2}}{C}, 0\right)\right)}}{\mathsf{PI}\left(\right)} \]

      11. lower-/.f64 69.0

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

   5. Applied rewrites 69.0%

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

   6. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-atan.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-PI.f64 69.1

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

   8. Applied rewrites 69.1%

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

   10. Applied rewrites 69.2%

       \[\leadsto \color{blue}{\frac{\tan^{-1} \left(\frac{B}{C \cdot -2}\right)}{\pi \cdot 0.005555555555555556}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 4.5 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{C \cdot -2}\right)}{\pi \cdot 0.005555555555555556}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.8 \cdot 10^{-165}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.2 \cdot 10^{-187}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.8e-165)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.2e-187)
     (* 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 <= -5.8e-165) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.2e-187) {
		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 <= -5.8e-165) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.2e-187) {
		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 <= -5.8e-165:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.2e-187:
		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 <= -5.8e-165)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.2e-187)
		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 <= -5.8e-165)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.2e-187)
		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, -5.8e-165], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.2e-187], 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 < -5.8e-165

   1. Initial program 51.9%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 55.2%

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

   if -5.8e-165 < B < 1.20000000000000007e-187

   1. Initial program 57.6%

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

   3. Taylor expanded in 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 37.2

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

   5. Applied rewrites 37.2%

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

   if 1.20000000000000007e-187 < B

   1. Initial program 55.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 45.2%

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

Alternative 15: 28.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.2 \cdot 10^{-187}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.2e-187) (* 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 <= 1.2e-187) {
		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 <= 1.2e-187) {
		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 <= 1.2e-187:
		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 <= 1.2e-187)
		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 <= 1.2e-187)
		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, 1.2e-187], 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 < 1.20000000000000007e-187

   1. Initial program 54.0%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 16.2

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

   5. Applied rewrites 16.2%

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

   if 1.20000000000000007e-187 < B

   1. Initial program 55.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 45.2%

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

Alternative 16: 20.8% 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 54.7%

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

3. Taylor expanded in B around inf

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

5. Applied rewrites 19.6%

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

Reproduce

herbie shell --seed 2024214 
(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)))