ABCF->ab-angle angle

Percentage Accurate: 53.3% → 88.8%

Time: 13.0s

Alternatives: 16

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)\right)\right)}{\pi}\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_1 \leq -0.0002:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (hypot (- C A) B)))) PI)))
        (t_1
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_1 -0.0002)
     t_0
     (if (<= t_1 0.0) (/ (* 180.0 (atan (/ (* B -0.5) (- C A)))) PI) t_0))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((C - A), B)))) / ((double) M_PI));
	double t_1 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_1 <= -0.0002) {
		tmp = t_0;
	} else if (t_1 <= 0.0) {
		tmp = (180.0 * atan(((B * -0.5) / (C - A)))) / ((double) M_PI);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.hypot((C - A), B)))) / Math.PI);
	double t_1 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_1 <= -0.0002) {
		tmp = t_0;
	} else if (t_1 <= 0.0) {
		tmp = (180.0 * Math.atan(((B * -0.5) / (C - A)))) / Math.PI;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.hypot((C - A), B)))) / math.pi)
	t_1 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_1 <= -0.0002:
		tmp = t_0
	elif t_1 <= 0.0:
		tmp = (180.0 * math.atan(((B * -0.5) / (C - A)))) / math.pi
	else:
		tmp = t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - hypot(Float64(C - A), B)))) / pi))
	t_1 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_1 <= -0.0002)
		tmp = t_0;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / Float64(C - A)))) / pi);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - hypot((C - A), B)))) / pi);
	t_1 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_1 <= -0.0002)
		tmp = t_0;
	elseif (t_1 <= 0.0)
		tmp = (180.0 * atan(((B * -0.5) / (C - A)))) / pi;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -0.0002], t$95$0, If[LessEqual[t$95$1, 0.0], N[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -2.0000000000000001e-4 or 0.0 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 61.5%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 88.1%

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

   if -2.0000000000000001e-4 < (*.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 12.2%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 12.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 12.2%

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

   7. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.1

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

   9. Applied rewrites 99.1%

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

Alternative 2: 88.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(C - A, B\right)}{B}\right)}{\pi}\\ t_1 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_1 \leq -0.0002:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot -0.5}{C - A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (/ (* 180.0 (atan (/ (- (- C A) (hypot (- C A) B)) B))) PI))
        (t_1
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_1 -0.0002)
     t_0
     (if (<= t_1 0.0) (/ (* 180.0 (atan (/ (* B -0.5) (- C A)))) PI) t_0))))

C

double code(double A, double B, double C) {
	double t_0 = (180.0 * atan((((C - A) - hypot((C - A), B)) / B))) / ((double) M_PI);
	double t_1 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_1 <= -0.0002) {
		tmp = t_0;
	} else if (t_1 <= 0.0) {
		tmp = (180.0 * atan(((B * -0.5) / (C - A)))) / ((double) M_PI);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (180.0 * Math.atan((((C - A) - Math.hypot((C - A), B)) / B))) / Math.PI;
	double t_1 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_1 <= -0.0002) {
		tmp = t_0;
	} else if (t_1 <= 0.0) {
		tmp = (180.0 * Math.atan(((B * -0.5) / (C - A)))) / Math.PI;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (180.0 * math.atan((((C - A) - math.hypot((C - A), B)) / B))) / math.pi
	t_1 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_1 <= -0.0002:
		tmp = t_0
	elif t_1 <= 0.0:
		tmp = (180.0 * math.atan(((B * -0.5) / (C - A)))) / math.pi
	else:
		tmp = t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(180.0 * atan(Float64(Float64(Float64(C - A) - hypot(Float64(C - A), B)) / B))) / pi)
	t_1 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_1 <= -0.0002)
		tmp = t_0;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * -0.5) / Float64(C - A)))) / pi);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (180.0 * atan((((C - A) - hypot((C - A), B)) / B))) / pi;
	t_1 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_1 <= -0.0002)
		tmp = t_0;
	elseif (t_1 <= 0.0)
		tmp = (180.0 * atan(((B * -0.5) / (C - A)))) / pi;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(180.0 * N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(C - A), $MachinePrecision] ^ 2 + B ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -0.0002], t$95$0, If[LessEqual[t$95$1, 0.0], N[(N[(180.0 * N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / N[(C - A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < -2.0000000000000001e-4 or 0.0 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 61.5%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 88.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 61.4%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lower-hypot.f64 88.1

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

   8. Applied rewrites 88.1%

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

   if -2.0000000000000001e-4 < (*.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 12.2%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 12.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 12.2%

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

   7. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.1

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

   9. Applied rewrites 99.1%

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

Alternative 3: 79.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 59.0%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 87.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 58.9%

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

   7. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 71.7

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

   9. Applied rewrites 71.7%

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

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

   1. Initial program 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. Step-by-step derivation

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 14.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 14.3%

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

   7. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 97.5

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

   9. Applied rewrites 97.5%

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

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

   1. Initial program 63.9%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 1.8%

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

   6. Taylor expanded in B around -inf

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

   8. Applied rewrites 81.0%

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

Alternative 4: 79.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 59.0%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 87.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 58.9%

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

   7. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 71.7

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

   9. Applied rewrites 71.7%

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

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

   1. Initial program 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. Step-by-step derivation

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 14.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 14.3%

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

   7. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 97.5

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

   9. Applied rewrites 97.5%

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

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

   1. Initial program 63.9%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 80.0

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

   5. Applied rewrites 80.0%

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

Alternative 5: 79.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 59.0%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 87.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 58.9%

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

   7. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 71.7

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

   9. Applied rewrites 71.7%

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

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

   1. Initial program 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. Step-by-step derivation

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 14.3%

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

   5. Taylor expanded in B around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. distribute-neg-frac N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. remove-double-neg N/A

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

      16. sub-neg N/A

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

      17. lower-/.f64 N/A

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

      18. lower--.f64 97.4

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

   7. Applied rewrites 97.4%

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

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

   1. Initial program 63.9%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 80.0

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

   5. Applied rewrites 80.0%

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

Alternative 6: 72.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 59.0%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 87.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 58.9%

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

   7. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 71.7

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

   9. Applied rewrites 71.7%

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

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

   1. Initial program 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. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 57.9

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

   5. Applied rewrites 57.9%

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

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

   1. Initial program 63.9%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 80.0

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

   5. Applied rewrites 80.0%

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

Alternative 7: 72.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 59.0%

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

   3. Taylor expanded in B around inf

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 71.7

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

   5. Applied rewrites 71.7%

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

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

   1. Initial program 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. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 57.9

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

   5. Applied rewrites 57.9%

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

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

   1. Initial program 63.9%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 80.0

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

   5. Applied rewrites 80.0%

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

Alternative 8: 42.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -2.65 \cdot 10^{+24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 0.33:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 3.65 \cdot 10^{+120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -2.65e+24)
   (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
   (if (<= C 0.33)
     (* 180.0 (/ (atan 1.0) PI))
     (if (<= C 3.65e+120)
       (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
       (* 180.0 (/ (atan (/ (* B -0.5) C)) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.65e+24) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (C <= 0.33) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (C <= 3.65e+120) {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B * -0.5) / C)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.65e+24) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (C <= 0.33) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (C <= 3.65e+120) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B * -0.5) / C)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if C <= -2.65e+24:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif C <= 0.33:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif C <= 3.65e+120:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B * -0.5) / C)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -2.65e+24)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (C <= 0.33)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (C <= 3.65e+120)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * -0.5) / C)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (C <= -2.65e+24)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (C <= 0.33)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (C <= 3.65e+120)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	else
		tmp = 180.0 * (atan(((B * -0.5) / C)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -2.65e+24], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 0.33], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 3.65e+120], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B * -0.5), $MachinePrecision] / C), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if C < -2.6499999999999999e24

   1. Initial program 81.6%

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

   3. Taylor expanded in C around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 79.7

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

   5. Applied rewrites 79.7%

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

   if -2.6499999999999999e24 < C < 0.330000000000000016

   1. Initial program 58.8%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 33.0%

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

   if 0.330000000000000016 < C < 3.6500000000000002e120

   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 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. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 43.9

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

   5. Applied rewrites 43.9%

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

   if 3.6500000000000002e120 < C

   1. Initial program 8.2%

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

   3. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. distribute-rgt1-in N/A

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

      6. metadata-eval N/A

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

      7. mul0-lft N/A

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

      8. div0 N/A

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 85.6

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

   5. Applied rewrites 85.6%

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

   7. Applied rewrites 85.8%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.65 \cdot 10^{+24}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 0.33:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;C \leq 3.65 \cdot 10^{+120}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot -0.5}{C}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 45.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -9 \cdot 10^{+70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.04 \cdot 10^{-175}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.32 \cdot 10^{+17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -9e+70)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -1.04e-175)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= B 1.32e+17)
       (* 180.0 (/ (atan (/ (* A -2.0) B)) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -9e+70) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -1.04e-175) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (B <= 1.32e+17) {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -9e+70) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -1.04e-175) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (B <= 1.32e+17) {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -9e+70:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -1.04e-175:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif B <= 1.32e+17:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -9e+70)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -1.04e-175)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (B <= 1.32e+17)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -9e+70)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -1.04e-175)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (B <= 1.32e+17)
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -9e+70], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.04e-175], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.32e+17], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -8.9999999999999999e70

   1. Initial program 47.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 72.1%

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

   if -8.9999999999999999e70 < B < -1.03999999999999997e-175

   1. Initial program 69.9%

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

   3. Taylor expanded in C around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 43.4

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

   5. Applied rewrites 43.4%

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

   if -1.03999999999999997e-175 < B < 1.32e17

   1. Initial program 58.4%

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

   3. Taylor expanded in 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. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 40.8

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

   5. Applied rewrites 40.8%

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

   if 1.32e17 < B

   1. Initial program 50.3%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 58.1%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -9 \cdot 10^{+70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.04 \cdot 10^{-175}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.32 \cdot 10^{+17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{-252}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.1e-252)
   (/ (* 180.0 (atan (/ (* B 0.5) A))) PI)
   (if (<= A 1.4e-184)
     (* 180.0 (/ (atan 1.0) PI))
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e-252) {
		tmp = (180.0 * atan(((B * 0.5) / A))) / ((double) M_PI);
	} else if (A <= 1.4e-184) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e-252) {
		tmp = (180.0 * Math.atan(((B * 0.5) / A))) / Math.PI;
	} else if (A <= 1.4e-184) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.1e-252:
		tmp = (180.0 * math.atan(((B * 0.5) / A))) / math.pi
	elif A <= 1.4e-184:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.1e-252)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * 0.5) / A))) / pi);
	elseif (A <= 1.4e-184)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.1e-252)
		tmp = (180.0 * atan(((B * 0.5) / A))) / pi;
	elseif (A <= 1.4e-184)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.1e-252], N[(N[(180.0 * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 1.4e-184], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.0999999999999998e-252

   1. Initial program 40.1%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 70.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 40.1%

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

   7. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 50.8

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

   9. Applied rewrites 50.8%

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

   if -3.0999999999999998e-252 < A < 1.3999999999999999e-184

   1. Initial program 53.8%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 40.5%

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

   if 1.3999999999999999e-184 < A

   1. Initial program 78.5%

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

   3. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 61.3

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

   5. Applied rewrites 61.3%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{-252}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -3.1e-252)
   (* 180.0 (/ (atan (/ (* B 0.5) A)) PI))
   (if (<= A 1.4e-184)
     (* 180.0 (/ (atan 1.0) PI))
     (* 180.0 (/ (atan (/ (* A -2.0) B)) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e-252) {
		tmp = 180.0 * (atan(((B * 0.5) / A)) / ((double) M_PI));
	} else if (A <= 1.4e-184) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((A * -2.0) / B)) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -3.1e-252) {
		tmp = 180.0 * (Math.atan(((B * 0.5) / A)) / Math.PI);
	} else if (A <= 1.4e-184) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((A * -2.0) / B)) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -3.1e-252:
		tmp = 180.0 * (math.atan(((B * 0.5) / A)) / math.pi)
	elif A <= 1.4e-184:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((A * -2.0) / B)) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -3.1e-252)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B * 0.5) / A)) / pi));
	elseif (A <= 1.4e-184)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(A * -2.0) / B)) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -3.1e-252)
		tmp = 180.0 * (atan(((B * 0.5) / A)) / pi);
	elseif (A <= 1.4e-184)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(((A * -2.0) / B)) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -3.1e-252], N[(180.0 * N[(N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 1.4e-184], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(A * -2.0), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -3.0999999999999998e-252

   1. Initial program 40.1%

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

   3. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 50.7

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

   5. Applied rewrites 50.7%

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

   if -3.0999999999999998e-252 < A < 1.3999999999999999e-184

   1. Initial program 53.8%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 40.5%

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

   if 1.3999999999999999e-184 < A

   1. Initial program 78.5%

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

   3. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 61.3

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

   5. Applied rewrites 61.3%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -3.1 \cdot 10^{-252}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.4 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{A \cdot -2}{B}\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -9 \cdot 10^{+70}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-284}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(2 \cdot \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-127}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -9e+70)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -9.5e-284)
     (* 180.0 (/ (atan (* 2.0 (/ C B))) PI))
     (if (<= B 1.1e-127)
       (* 180.0 (/ (atan 0.0) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -9e+70) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -9.5e-284) {
		tmp = 180.0 * (atan((2.0 * (C / B))) / ((double) M_PI));
	} else if (B <= 1.1e-127) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -9e+70) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -9.5e-284) {
		tmp = 180.0 * (Math.atan((2.0 * (C / B))) / Math.PI);
	} else if (B <= 1.1e-127) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -9e+70:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -9.5e-284:
		tmp = 180.0 * (math.atan((2.0 * (C / B))) / math.pi)
	elif B <= 1.1e-127:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -9e+70)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -9.5e-284)
		tmp = Float64(180.0 * Float64(atan(Float64(2.0 * Float64(C / B))) / pi));
	elseif (B <= 1.1e-127)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -9e+70)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -9.5e-284)
		tmp = 180.0 * (atan((2.0 * (C / B))) / pi);
	elseif (B <= 1.1e-127)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -9e+70], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -9.5e-284], N[(180.0 * N[(N[ArcTan[N[(2.0 * N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.1e-127], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -8.9999999999999999e70

   1. Initial program 47.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 72.1%

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

   if -8.9999999999999999e70 < B < -9.5000000000000003e-284

   1. Initial program 70.4%

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

   3. Taylor expanded in C around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 43.4

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

   5. Applied rewrites 43.4%

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

   if -9.5000000000000003e-284 < B < 1.1000000000000001e-127

   1. Initial program 45.7%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   2. 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 38.9

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

   5. Applied rewrites 38.9%

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

   if 1.1000000000000001e-127 < B

   1. Initial program 56.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 44.3%

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

Alternative 13: 59.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -4.2 \cdot 10^{+106}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{B \cdot 0.5}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -4.2e+106)
   (/ (* 180.0 (atan (/ (* B 0.5) A))) PI)
   (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.2e+106) {
		tmp = (180.0 * atan(((B * 0.5) / A))) / ((double) M_PI);
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -4.2e+106) {
		tmp = (180.0 * Math.atan(((B * 0.5) / A))) / Math.PI;
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -4.2e+106:
		tmp = (180.0 * math.atan(((B * 0.5) / A))) / math.pi
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -4.2e+106)
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(B * 0.5) / A))) / pi);
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -4.2e+106)
		tmp = (180.0 * atan(((B * 0.5) / A))) / pi;
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -4.2e+106], N[(N[(180.0 * N[ArcTan[N[(N[(B * 0.5), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -4.2000000000000001e106

   1. Initial program 14.4%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-+.f64 N/A

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

   4. Applied rewrites 58.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 14.5%

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

   7. Taylor expanded in A around -inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 81.5

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

   9. Applied rewrites 81.5%

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

   if -4.2000000000000001e106 < A

   1. Initial program 65.2%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 63.5

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

   5. Applied rewrites 63.5%

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

Alternative 14: 44.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-151}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.1 \cdot 10^{-127}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2e-151)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.1e-127)
     (* 180.0 (/ (atan 0.0) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-151) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.1e-127) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2e-151) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.1e-127) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2e-151:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.1e-127:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2e-151)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.1e-127)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2e-151)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.1e-127)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2e-151], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.1e-127], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.9999999999999999e-151

   1. Initial program 58.0%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 50.8%

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

   if -1.9999999999999999e-151 < B < 1.1000000000000001e-127

   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 33.8

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

   5. Applied rewrites 33.8%

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

   if 1.1000000000000001e-127 < B

   1. Initial program 56.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 44.3%

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

Alternative 15: 29.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.1 \cdot 10^{-127}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.1e-127) (* 180.0 (/ (atan 0.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.1e-127) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.1e-127) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 1.1e-127:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 1.1e-127)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 1.1e-127)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 1.1e-127], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 1.1000000000000001e-127

   1. Initial program 56.7%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 16.8

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

   5. Applied rewrites 16.8%

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

   if 1.1000000000000001e-127 < B

   1. Initial program 56.6%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
   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 44.3%

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

Alternative 16: 21.4% accurate, 3.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.7%

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

3. Taylor expanded in B around inf

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

5. Applied rewrites 18.8%

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

Reproduce

herbie shell --seed 2024237 
(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)))