ABCF->ab-angle angle

Percentage Accurate: 53.7% → 79.2%

Time: 10.6s

Alternatives: 15

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 79.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 61.3%

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

   4. Applied rewrites 61.3%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 75.2

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

   7. Applied rewrites 75.2%

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

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

   1. Initial program 14.2%

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

   4. Applied rewrites 14.2%

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

   5. Taylor expanded in B around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 99.2

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

   7. Applied rewrites 99.2%

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

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

   1. Initial program 58.5%

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

   4. Applied rewrites 58.5%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 79.8

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

   7. Applied rewrites 79.8%

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

4. Final simplification 79.9%

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

Alternative 2: 72.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 61.3%

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

   4. Applied rewrites 61.3%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 75.2

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

   7. Applied rewrites 75.2%

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

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

   1. Initial program 14.2%

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

   3. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 54.7

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

   5. Applied rewrites 54.7%

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

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

   1. Initial program 58.5%

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

   4. Applied rewrites 58.5%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 79.8

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

   7. Applied rewrites 79.8%

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

4. Final simplification 75.0%

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

Alternative 3: 72.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 61.3%

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

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 75.2

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

   5. Applied rewrites 75.2%

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

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

   1. Initial program 14.2%

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

   3. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 54.7

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

   5. Applied rewrites 54.7%

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

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

   1. Initial program 58.5%

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

   4. Applied rewrites 58.5%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 79.8

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

   7. Applied rewrites 79.8%

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

4. Final simplification 75.0%

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

Alternative 4: 72.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 61.3%

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

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 75.2

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

   5. Applied rewrites 75.2%

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

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

   1. Initial program 14.2%

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

   3. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 54.7

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

   5. Applied rewrites 54.7%

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

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

   1. Initial program 58.5%

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

   3. Taylor expanded in B around -inf

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

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 79.8

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

   5. Applied rewrites 79.8%

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

4. Final simplification 75.0%

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

Alternative 5: 67.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 61.3%

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

   4. Applied rewrites 61.3%

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

   5. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-sqrt.f64 N/A

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

      6. +-commutative N/A

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

      7. unpow2 N/A

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

      8. lower-fma.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 55.3

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

   7. Applied rewrites 55.3%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 68.6%

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

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

   1. Initial program 14.2%

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

   3. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 54.7

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

   5. Applied rewrites 54.7%

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

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

   1. Initial program 58.5%

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

   3. Taylor expanded in B around -inf

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

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 79.8

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

   5. Applied rewrites 79.8%

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

4. Final simplification 72.1%

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

Alternative 6: 61.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 61.3%

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

   4. Applied rewrites 61.3%

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

   5. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-sqrt.f64 N/A

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

      6. +-commutative N/A

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

      7. unpow2 N/A

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

      8. lower-fma.f64 N/A

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

      9. unpow2 N/A

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

      10. lower-*.f64 55.3

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

   7. Applied rewrites 55.3%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 68.6%

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

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

   1. Initial program 14.2%

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

   3. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 54.7

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

   5. Applied rewrites 54.7%

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

   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 58.5%

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

   4. Applied rewrites 58.5%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 79.8

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

   7. Applied rewrites 79.8%

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

   8. Taylor expanded in C around 0

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

   10. Applied rewrites 70.4%

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

4. Final simplification 67.9%

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

Alternative 7: 61.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 61.3%

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

   4. Applied rewrites 61.3%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 75.2

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

   7. Applied rewrites 75.2%

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

   8. Taylor expanded in C around inf

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

   10. Applied rewrites 57.8%

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

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

   1. Initial program 14.2%

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

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

      3. distribute-rgt1-in N/A

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

      4. metadata-eval N/A

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

      5. mul0-lft N/A

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

      6. div0 N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 48.7

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

   5. Applied rewrites 48.7%

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

   7. Applied rewrites 48.7%

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

   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 58.5%

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

   4. Applied rewrites 58.5%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 79.8

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

   7. Applied rewrites 79.8%

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

   8. Taylor expanded in C around inf

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

   10. Applied rewrites 63.3%

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

4. Final simplification 59.3%

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

Alternative 8: 57.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.6 \cdot 10^{-216}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi} \cdot 180\\ \mathbf{elif}\;A \leq 9 \cdot 10^{-178}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B} - 1\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{-A}{B} + 1\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.6e-216)
   (* (/ (atan (* 0.5 (/ B A))) PI) 180.0)
   (if (<= A 9e-178)
     (* (atan (- (/ C B) 1.0)) (/ 180.0 PI))
     (* (atan (+ (/ (- A) B) 1.0)) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.6e-216) {
		tmp = (atan((0.5 * (B / A))) / ((double) M_PI)) * 180.0;
	} else if (A <= 9e-178) {
		tmp = atan(((C / B) - 1.0)) * (180.0 / ((double) M_PI));
	} else {
		tmp = atan(((-A / B) + 1.0)) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.6e-216) {
		tmp = (Math.atan((0.5 * (B / A))) / Math.PI) * 180.0;
	} else if (A <= 9e-178) {
		tmp = Math.atan(((C / B) - 1.0)) * (180.0 / Math.PI);
	} else {
		tmp = Math.atan(((-A / B) + 1.0)) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.6e-216:
		tmp = (math.atan((0.5 * (B / A))) / math.pi) * 180.0
	elif A <= 9e-178:
		tmp = math.atan(((C / B) - 1.0)) * (180.0 / math.pi)
	else:
		tmp = math.atan(((-A / B) + 1.0)) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.6e-216)
		tmp = Float64(Float64(atan(Float64(0.5 * Float64(B / A))) / pi) * 180.0);
	elseif (A <= 9e-178)
		tmp = Float64(atan(Float64(Float64(C / B) - 1.0)) * Float64(180.0 / pi));
	else
		tmp = Float64(atan(Float64(Float64(Float64(-A) / B) + 1.0)) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.6e-216)
		tmp = (atan((0.5 * (B / A))) / pi) * 180.0;
	elseif (A <= 9e-178)
		tmp = atan(((C / B) - 1.0)) * (180.0 / pi);
	else
		tmp = atan(((-A / B) + 1.0)) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.6e-216], N[(N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[A, 9e-178], N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[ArcTan[N[(N[((-A) / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.5999999999999999e-216

   1. Initial program 26.5%

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

   3. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 53.5

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

   5. Applied rewrites 53.5%

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

   if -2.5999999999999999e-216 < A < 8.99999999999999957e-178

   1. Initial program 67.9%

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

   4. Applied rewrites 67.9%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 69.5

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

   7. Applied rewrites 69.5%

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

   8. Taylor expanded in C around inf

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

   10. Applied rewrites 69.5%

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

   if 8.99999999999999957e-178 < A

   1. Initial program 74.1%

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

   4. Applied rewrites 74.1%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 77.1

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

   7. Applied rewrites 77.1%

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

   8. Taylor expanded in C around 0

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

   10. Applied rewrites 74.1%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.6 \cdot 10^{-216}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi} \cdot 180\\ \mathbf{elif}\;A \leq 9 \cdot 10^{-178}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B} - 1\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{-A}{B} + 1\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -2.6 \cdot 10^{-216}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi} \cdot 180\\ \mathbf{elif}\;A \leq 3 \cdot 10^{+19}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B} - 1\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -2.6e-216)
   (* (/ (atan (* 0.5 (/ B A))) PI) 180.0)
   (if (<= A 3e+19)
     (* (atan (- (/ C B) 1.0)) (/ 180.0 PI))
     (* (/ (atan (* -2.0 (/ A B))) PI) 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.6e-216) {
		tmp = (atan((0.5 * (B / A))) / ((double) M_PI)) * 180.0;
	} else if (A <= 3e+19) {
		tmp = atan(((C / B) - 1.0)) * (180.0 / ((double) M_PI));
	} else {
		tmp = (atan((-2.0 * (A / B))) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -2.6e-216) {
		tmp = (Math.atan((0.5 * (B / A))) / Math.PI) * 180.0;
	} else if (A <= 3e+19) {
		tmp = Math.atan(((C / B) - 1.0)) * (180.0 / Math.PI);
	} else {
		tmp = (Math.atan((-2.0 * (A / B))) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -2.6e-216:
		tmp = (math.atan((0.5 * (B / A))) / math.pi) * 180.0
	elif A <= 3e+19:
		tmp = math.atan(((C / B) - 1.0)) * (180.0 / math.pi)
	else:
		tmp = (math.atan((-2.0 * (A / B))) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -2.6e-216)
		tmp = Float64(Float64(atan(Float64(0.5 * Float64(B / A))) / pi) * 180.0);
	elseif (A <= 3e+19)
		tmp = Float64(atan(Float64(Float64(C / B) - 1.0)) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(atan(Float64(-2.0 * Float64(A / B))) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -2.6e-216)
		tmp = (atan((0.5 * (B / A))) / pi) * 180.0;
	elseif (A <= 3e+19)
		tmp = atan(((C / B) - 1.0)) * (180.0 / pi);
	else
		tmp = (atan((-2.0 * (A / B))) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -2.6e-216], N[(N[(N[ArcTan[N[(0.5 * N[(B / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[A, 3e+19], N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -2.5999999999999999e-216

   1. Initial program 26.5%

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

   3. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 53.5

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

   5. Applied rewrites 53.5%

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

   if -2.5999999999999999e-216 < A < 3e19

   1. Initial program 65.1%

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

   4. Applied rewrites 65.2%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 60.0

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

   7. Applied rewrites 60.0%

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

   8. Taylor expanded in C around inf

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

   10. Applied rewrites 54.2%

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

   if 3e19 < A

   1. Initial program 80.3%

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

   3. Taylor expanded in A around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 75.3

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

   5. Applied rewrites 75.3%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -2.6 \cdot 10^{-216}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi} \cdot 180\\ \mathbf{elif}\;A \leq 3 \cdot 10^{+19}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B} - 1\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi} \cdot 180\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.35 \cdot 10^{-79}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B} + 1\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-147}:\\ \;\;\;\;\frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B} - 1\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.35e-79)
   (* (atan (+ (/ C B) 1.0)) (/ 180.0 PI))
   (if (<= B 9.2e-147)
     (* (/ (atan (* -2.0 (/ A B))) PI) 180.0)
     (* (atan (- (/ C B) 1.0)) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.35e-79) {
		tmp = atan(((C / B) + 1.0)) * (180.0 / ((double) M_PI));
	} else if (B <= 9.2e-147) {
		tmp = (atan((-2.0 * (A / B))) / ((double) M_PI)) * 180.0;
	} else {
		tmp = atan(((C / B) - 1.0)) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.35e-79) {
		tmp = Math.atan(((C / B) + 1.0)) * (180.0 / Math.PI);
	} else if (B <= 9.2e-147) {
		tmp = (Math.atan((-2.0 * (A / B))) / Math.PI) * 180.0;
	} else {
		tmp = Math.atan(((C / B) - 1.0)) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.35e-79:
		tmp = math.atan(((C / B) + 1.0)) * (180.0 / math.pi)
	elif B <= 9.2e-147:
		tmp = (math.atan((-2.0 * (A / B))) / math.pi) * 180.0
	else:
		tmp = math.atan(((C / B) - 1.0)) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.35e-79)
		tmp = Float64(atan(Float64(Float64(C / B) + 1.0)) * Float64(180.0 / pi));
	elseif (B <= 9.2e-147)
		tmp = Float64(Float64(atan(Float64(-2.0 * Float64(A / B))) / pi) * 180.0);
	else
		tmp = Float64(atan(Float64(Float64(C / B) - 1.0)) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.35e-79)
		tmp = atan(((C / B) + 1.0)) * (180.0 / pi);
	elseif (B <= 9.2e-147)
		tmp = (atan((-2.0 * (A / B))) / pi) * 180.0;
	else
		tmp = atan(((C / B) - 1.0)) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.35e-79], N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 9.2e-147], N[(N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.3500000000000001e-79

   1. Initial program 50.5%

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

   4. Applied rewrites 50.5%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 82.5

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

   7. Applied rewrites 82.5%

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

   8. Taylor expanded in C around inf

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

   10. Applied rewrites 72.6%

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

   if -2.3500000000000001e-79 < B < 9.19999999999999962e-147

   1. Initial program 59.1%

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

   3. Taylor expanded in A around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 50.2

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

   5. Applied rewrites 50.2%

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

   if 9.19999999999999962e-147 < B

   1. Initial program 55.0%

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

   4. Applied rewrites 55.0%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 70.3

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

   7. Applied rewrites 70.3%

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

   8. Taylor expanded in C around inf

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

   10. Applied rewrites 56.5%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.35 \cdot 10^{-79}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B} + 1\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-147}:\\ \;\;\;\;\frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B} - 1\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-284}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B} + 1\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-238}:\\ \;\;\;\;\frac{\tan^{-1} 0}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B} - 1\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.6e-284)
   (* (atan (+ (/ C B) 1.0)) (/ 180.0 PI))
   (if (<= B 4.5e-238)
     (* (/ (atan 0.0) PI) 180.0)
     (* (atan (- (/ C B) 1.0)) (/ 180.0 PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.6e-284) {
		tmp = atan(((C / B) + 1.0)) * (180.0 / ((double) M_PI));
	} else if (B <= 4.5e-238) {
		tmp = (atan(0.0) / ((double) M_PI)) * 180.0;
	} else {
		tmp = atan(((C / B) - 1.0)) * (180.0 / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.6e-284) {
		tmp = Math.atan(((C / B) + 1.0)) * (180.0 / Math.PI);
	} else if (B <= 4.5e-238) {
		tmp = (Math.atan(0.0) / Math.PI) * 180.0;
	} else {
		tmp = Math.atan(((C / B) - 1.0)) * (180.0 / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.6e-284:
		tmp = math.atan(((C / B) + 1.0)) * (180.0 / math.pi)
	elif B <= 4.5e-238:
		tmp = (math.atan(0.0) / math.pi) * 180.0
	else:
		tmp = math.atan(((C / B) - 1.0)) * (180.0 / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.6e-284)
		tmp = Float64(atan(Float64(Float64(C / B) + 1.0)) * Float64(180.0 / pi));
	elseif (B <= 4.5e-238)
		tmp = Float64(Float64(atan(0.0) / pi) * 180.0);
	else
		tmp = Float64(atan(Float64(Float64(C / B) - 1.0)) * Float64(180.0 / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.6e-284)
		tmp = atan(((C / B) + 1.0)) * (180.0 / pi);
	elseif (B <= 4.5e-238)
		tmp = (atan(0.0) / pi) * 180.0;
	else
		tmp = atan(((C / B) - 1.0)) * (180.0 / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.6e-284], N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 4.5e-238], N[(N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.6e-284

   1. Initial program 56.1%

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

   4. Applied rewrites 56.1%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 75.1

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

   7. Applied rewrites 75.1%

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

   8. Taylor expanded in C around inf

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

   10. Applied rewrites 60.4%

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

   if -2.6e-284 < B < 4.49999999999999996e-238

   1. Initial program 36.8%

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

   3. Taylor expanded in C around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(-1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\mathsf{PI}\left(\right)} \]
   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 43.4

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

   5. Applied rewrites 43.4%

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

   if 4.49999999999999996e-238 < B

   1. Initial program 55.9%

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

   4. Applied rewrites 56.0%

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

   5. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 68.5

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

   7. Applied rewrites 68.5%

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

   8. Taylor expanded in C around inf

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

   10. Applied rewrites 53.1%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.6 \cdot 10^{-284}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B} + 1\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-238}:\\ \;\;\;\;\frac{\tan^{-1} 0}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B} - 1\right) \cdot \frac{180}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 9.5 \cdot 10^{-134}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B} + 1\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} -1}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 9.5e-134)
   (* (atan (+ (/ C B) 1.0)) (/ 180.0 PI))
   (* (/ (atan -1.0) PI) 180.0)))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 9.5e-134) {
		tmp = atan(((C / B) + 1.0)) * (180.0 / ((double) M_PI));
	} else {
		tmp = (atan(-1.0) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 9.5e-134) {
		tmp = Math.atan(((C / B) + 1.0)) * (180.0 / Math.PI);
	} else {
		tmp = (Math.atan(-1.0) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 9.5e-134:
		tmp = math.atan(((C / B) + 1.0)) * (180.0 / math.pi)
	else:
		tmp = (math.atan(-1.0) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 9.5e-134)
		tmp = Float64(atan(Float64(Float64(C / B) + 1.0)) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(atan(-1.0) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 9.5e-134)
		tmp = atan(((C / B) + 1.0)) * (180.0 / pi);
	else
		tmp = (atan(-1.0) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 9.5e-134], N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 9.5000000000000008e-134

   1. Initial program 55.1%

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

   4. Applied rewrites 55.1%

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

   5. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 68.6

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

   7. Applied rewrites 68.6%

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

   8. Taylor expanded in C around inf

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

   10. Applied rewrites 53.0%

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

   if 9.5000000000000008e-134 < B

   1. Initial program 54.6%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 50.4%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 9.5 \cdot 10^{-134}:\\ \;\;\;\;\tan^{-1} \left(\frac{C}{B} + 1\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} -1}{\pi} \cdot 180\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.4 \cdot 10^{-103}:\\ \;\;\;\;\frac{\tan^{-1} 1}{\pi} \cdot 180\\ \mathbf{elif}\;B \leq 4.7 \cdot 10^{-141}:\\ \;\;\;\;\frac{\tan^{-1} 0}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} -1}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.4e-103)
   (* (/ (atan 1.0) PI) 180.0)
   (if (<= B 4.7e-141)
     (* (/ (atan 0.0) PI) 180.0)
     (* (/ (atan -1.0) PI) 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.4e-103) {
		tmp = (atan(1.0) / ((double) M_PI)) * 180.0;
	} else if (B <= 4.7e-141) {
		tmp = (atan(0.0) / ((double) M_PI)) * 180.0;
	} else {
		tmp = (atan(-1.0) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.4e-103) {
		tmp = (Math.atan(1.0) / Math.PI) * 180.0;
	} else if (B <= 4.7e-141) {
		tmp = (Math.atan(0.0) / Math.PI) * 180.0;
	} else {
		tmp = (Math.atan(-1.0) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4.4e-103:
		tmp = (math.atan(1.0) / math.pi) * 180.0
	elif B <= 4.7e-141:
		tmp = (math.atan(0.0) / math.pi) * 180.0
	else:
		tmp = (math.atan(-1.0) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -4.4e-103)
		tmp = Float64(Float64(atan(1.0) / pi) * 180.0);
	elseif (B <= 4.7e-141)
		tmp = Float64(Float64(atan(0.0) / pi) * 180.0);
	else
		tmp = Float64(Float64(atan(-1.0) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -4.4e-103)
		tmp = (atan(1.0) / pi) * 180.0;
	elseif (B <= 4.7e-141)
		tmp = (atan(0.0) / pi) * 180.0;
	else
		tmp = (atan(-1.0) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.4e-103], N[(N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[B, 4.7e-141], N[(N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -4.3999999999999999e-103

   1. Initial program 53.6%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 58.5%

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

   if -4.3999999999999999e-103 < B < 4.6999999999999998e-141

   1. Initial program 56.2%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 32.9

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

   5. Applied rewrites 32.9%

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

   if 4.6999999999999998e-141 < B

   1. Initial program 55.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 50.0%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -4.4 \cdot 10^{-103}:\\ \;\;\;\;\frac{\tan^{-1} 1}{\pi} \cdot 180\\ \mathbf{elif}\;B \leq 4.7 \cdot 10^{-141}:\\ \;\;\;\;\frac{\tan^{-1} 0}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} -1}{\pi} \cdot 180\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 28.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 4.7 \cdot 10^{-141}:\\ \;\;\;\;\frac{\tan^{-1} 0}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} -1}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 4.7e-141) (* (/ (atan 0.0) PI) 180.0) (* (/ (atan -1.0) PI) 180.0)))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 4.7e-141) {
		tmp = (atan(0.0) / ((double) M_PI)) * 180.0;
	} else {
		tmp = (atan(-1.0) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 4.7e-141) {
		tmp = (Math.atan(0.0) / Math.PI) * 180.0;
	} else {
		tmp = (Math.atan(-1.0) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 4.7e-141:
		tmp = (math.atan(0.0) / math.pi) * 180.0
	else:
		tmp = (math.atan(-1.0) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 4.7e-141)
		tmp = Float64(Float64(atan(0.0) / pi) * 180.0);
	else
		tmp = Float64(Float64(atan(-1.0) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 4.7e-141)
		tmp = (atan(0.0) / pi) * 180.0;
	else
		tmp = (atan(-1.0) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 4.7e-141], N[(N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 4.6999999999999998e-141

   1. Initial program 54.8%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 18.1

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

   5. Applied rewrites 18.1%

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

   if 4.6999999999999998e-141 < B

   1. Initial program 55.1%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 50.0%

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

4. Final simplification 30.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 4.7 \cdot 10^{-141}:\\ \;\;\;\;\frac{\tan^{-1} 0}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} -1}{\pi} \cdot 180\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 20.2% accurate, 3.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 54.9%

   \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
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 21.8%

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

6. Final simplification 21.8%

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

Reproduce

herbie shell --seed 2024240 
(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)))