ABCF->ab-angle angle

Percentage Accurate: 54.1% → 75.4%

Time: 6.8s

Alternatives: 10

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.1% 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: 75.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{+35}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B\_m}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B\_m} - 1\right) \cdot 180}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A -5e+35)
    (* 180.0 (/ (atan (* 0.5 (/ B_m A))) PI))
    (/ (* (atan (- (/ (- C A) B_m) 1.0)) 180.0) PI))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -5e+35) {
		tmp = 180.0 * (atan((0.5 * (B_m / A))) / ((double) M_PI));
	} else {
		tmp = (atan((((C - A) / B_m) - 1.0)) * 180.0) / ((double) M_PI);
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -5e+35) {
		tmp = 180.0 * (Math.atan((0.5 * (B_m / A))) / Math.PI);
	} else {
		tmp = (Math.atan((((C - A) / B_m) - 1.0)) * 180.0) / Math.PI;
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if A <= -5e+35:
		tmp = 180.0 * (math.atan((0.5 * (B_m / A))) / math.pi)
	else:
		tmp = (math.atan((((C - A) / B_m) - 1.0)) * 180.0) / math.pi
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= -5e+35)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B_m / A))) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) / B_m) - 1.0)) * 180.0) / pi);
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (A <= -5e+35)
		tmp = 180.0 * (atan((0.5 * (B_m / A))) / pi);
	else
		tmp = (atan((((C - A) / B_m) - 1.0)) * 180.0) / pi;
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, -5e+35], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B$95$m / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < -5.00000000000000021e35

   1. Initial program 54.1%

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

   2. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 25.6

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

   4. Applied rewrites 25.6%

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

   if -5.00000000000000021e35 < A

   1. Initial program 54.1%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.4

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

   4. Applied rewrites 66.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 67.3%

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

Alternative 2: 75.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{+35}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B\_m}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B\_m} - 1\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A -5e+35)
    (* 180.0 (/ (atan (* 0.5 (/ B_m A))) PI))
    (* (/ (atan (- (/ (- C A) B_m) 1.0)) PI) 180.0))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -5e+35) {
		tmp = 180.0 * (atan((0.5 * (B_m / A))) / ((double) M_PI));
	} else {
		tmp = (atan((((C - A) / B_m) - 1.0)) / ((double) M_PI)) * 180.0;
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -5e+35) {
		tmp = 180.0 * (Math.atan((0.5 * (B_m / A))) / Math.PI);
	} else {
		tmp = (Math.atan((((C - A) / B_m) - 1.0)) / Math.PI) * 180.0;
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if A <= -5e+35:
		tmp = 180.0 * (math.atan((0.5 * (B_m / A))) / math.pi)
	else:
		tmp = (math.atan((((C - A) / B_m) - 1.0)) / math.pi) * 180.0
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= -5e+35)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B_m / A))) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) / B_m) - 1.0)) / pi) * 180.0);
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (A <= -5e+35)
		tmp = 180.0 * (atan((0.5 * (B_m / A))) / pi);
	else
		tmp = (atan((((C - A) / B_m) - 1.0)) / pi) * 180.0;
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, -5e+35], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B$95$m / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < -5.00000000000000021e35

   1. Initial program 54.1%

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

   2. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 25.6

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

   4. Applied rewrites 25.6%

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

   if -5.00000000000000021e35 < A

   1. Initial program 54.1%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.4

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

   4. Applied rewrites 66.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 66.4

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

   6. Applied rewrites 67.3%

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

Alternative 3: 68.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{+35}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B\_m}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.95 \cdot 10^{-30}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B\_m} - 1\right) \cdot 180}{\pi}\\ \mathbf{elif}\;A \leq 4.3 \cdot 10^{-7}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B\_m}{C}\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A}{B\_m} \cdot -2\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A -5e+35)
    (* 180.0 (/ (atan (* 0.5 (/ B_m A))) PI))
    (if (<= A 2.95e-30)
      (/ (* (atan (- (/ C B_m) 1.0)) 180.0) PI)
      (if (<= A 4.3e-7)
        (* (/ (atan (* -0.5 (/ B_m C))) PI) 180.0)
        (* (/ (atan (* (/ A B_m) -2.0)) PI) 180.0))))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -5e+35) {
		tmp = 180.0 * (atan((0.5 * (B_m / A))) / ((double) M_PI));
	} else if (A <= 2.95e-30) {
		tmp = (atan(((C / B_m) - 1.0)) * 180.0) / ((double) M_PI);
	} else if (A <= 4.3e-7) {
		tmp = (atan((-0.5 * (B_m / C))) / ((double) M_PI)) * 180.0;
	} else {
		tmp = (atan(((A / B_m) * -2.0)) / ((double) M_PI)) * 180.0;
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -5e+35) {
		tmp = 180.0 * (Math.atan((0.5 * (B_m / A))) / Math.PI);
	} else if (A <= 2.95e-30) {
		tmp = (Math.atan(((C / B_m) - 1.0)) * 180.0) / Math.PI;
	} else if (A <= 4.3e-7) {
		tmp = (Math.atan((-0.5 * (B_m / C))) / Math.PI) * 180.0;
	} else {
		tmp = (Math.atan(((A / B_m) * -2.0)) / Math.PI) * 180.0;
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if A <= -5e+35:
		tmp = 180.0 * (math.atan((0.5 * (B_m / A))) / math.pi)
	elif A <= 2.95e-30:
		tmp = (math.atan(((C / B_m) - 1.0)) * 180.0) / math.pi
	elif A <= 4.3e-7:
		tmp = (math.atan((-0.5 * (B_m / C))) / math.pi) * 180.0
	else:
		tmp = (math.atan(((A / B_m) * -2.0)) / math.pi) * 180.0
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= -5e+35)
		tmp = Float64(180.0 * Float64(atan(Float64(0.5 * Float64(B_m / A))) / pi));
	elseif (A <= 2.95e-30)
		tmp = Float64(Float64(atan(Float64(Float64(C / B_m) - 1.0)) * 180.0) / pi);
	elseif (A <= 4.3e-7)
		tmp = Float64(Float64(atan(Float64(-0.5 * Float64(B_m / C))) / pi) * 180.0);
	else
		tmp = Float64(Float64(atan(Float64(Float64(A / B_m) * -2.0)) / pi) * 180.0);
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (A <= -5e+35)
		tmp = 180.0 * (atan((0.5 * (B_m / A))) / pi);
	elseif (A <= 2.95e-30)
		tmp = (atan(((C / B_m) - 1.0)) * 180.0) / pi;
	elseif (A <= 4.3e-7)
		tmp = (atan((-0.5 * (B_m / C))) / pi) * 180.0;
	else
		tmp = (atan(((A / B_m) * -2.0)) / pi) * 180.0;
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, -5e+35], N[(180.0 * N[(N[ArcTan[N[(0.5 * N[(B$95$m / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.95e-30], N[(N[(N[ArcTan[N[(N[(C / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 4.3e-7], N[(N[(N[ArcTan[N[(-0.5 * N[(B$95$m / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(A / B$95$m), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if A < -5.00000000000000021e35

   1. Initial program 54.1%

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

   2. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 25.6

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

   4. Applied rewrites 25.6%

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

   if -5.00000000000000021e35 < A < 2.9499999999999999e-30

   1. Initial program 54.1%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.4

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

   4. Applied rewrites 66.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 67.3%

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

   7. Taylor expanded in A around 0

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

   9. Applied rewrites 56.7%

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

   if 2.9499999999999999e-30 < A < 4.3000000000000001e-7

   1. Initial program 54.1%

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

   2. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 25.9

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

   4. Applied rewrites 25.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 25.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

   8. Applied rewrites 25.9%

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

   if 4.3000000000000001e-7 < A

   1. Initial program 54.1%

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

   2. Taylor expanded in A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 23.7

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

   4. Applied rewrites 23.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 23.7

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 23.7

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

   6. Applied rewrites 23.7%

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

Alternative 4: 68.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{+35}:\\ \;\;\;\;\frac{\tan^{-1} \left(0.5 \cdot \frac{B\_m}{A}\right) \cdot 180}{\pi}\\ \mathbf{elif}\;A \leq 2.95 \cdot 10^{-30}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B\_m} - 1\right) \cdot 180}{\pi}\\ \mathbf{elif}\;A \leq 4.3 \cdot 10^{-7}:\\ \;\;\;\;\frac{\tan^{-1} \left(-0.5 \cdot \frac{B\_m}{C}\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{A}{B\_m} \cdot -2\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A -5e+35)
    (/ (* (atan (* 0.5 (/ B_m A))) 180.0) PI)
    (if (<= A 2.95e-30)
      (/ (* (atan (- (/ C B_m) 1.0)) 180.0) PI)
      (if (<= A 4.3e-7)
        (* (/ (atan (* -0.5 (/ B_m C))) PI) 180.0)
        (* (/ (atan (* (/ A B_m) -2.0)) PI) 180.0))))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -5e+35) {
		tmp = (atan((0.5 * (B_m / A))) * 180.0) / ((double) M_PI);
	} else if (A <= 2.95e-30) {
		tmp = (atan(((C / B_m) - 1.0)) * 180.0) / ((double) M_PI);
	} else if (A <= 4.3e-7) {
		tmp = (atan((-0.5 * (B_m / C))) / ((double) M_PI)) * 180.0;
	} else {
		tmp = (atan(((A / B_m) * -2.0)) / ((double) M_PI)) * 180.0;
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= -5e+35) {
		tmp = (Math.atan((0.5 * (B_m / A))) * 180.0) / Math.PI;
	} else if (A <= 2.95e-30) {
		tmp = (Math.atan(((C / B_m) - 1.0)) * 180.0) / Math.PI;
	} else if (A <= 4.3e-7) {
		tmp = (Math.atan((-0.5 * (B_m / C))) / Math.PI) * 180.0;
	} else {
		tmp = (Math.atan(((A / B_m) * -2.0)) / Math.PI) * 180.0;
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if A <= -5e+35:
		tmp = (math.atan((0.5 * (B_m / A))) * 180.0) / math.pi
	elif A <= 2.95e-30:
		tmp = (math.atan(((C / B_m) - 1.0)) * 180.0) / math.pi
	elif A <= 4.3e-7:
		tmp = (math.atan((-0.5 * (B_m / C))) / math.pi) * 180.0
	else:
		tmp = (math.atan(((A / B_m) * -2.0)) / math.pi) * 180.0
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= -5e+35)
		tmp = Float64(Float64(atan(Float64(0.5 * Float64(B_m / A))) * 180.0) / pi);
	elseif (A <= 2.95e-30)
		tmp = Float64(Float64(atan(Float64(Float64(C / B_m) - 1.0)) * 180.0) / pi);
	elseif (A <= 4.3e-7)
		tmp = Float64(Float64(atan(Float64(-0.5 * Float64(B_m / C))) / pi) * 180.0);
	else
		tmp = Float64(Float64(atan(Float64(Float64(A / B_m) * -2.0)) / pi) * 180.0);
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (A <= -5e+35)
		tmp = (atan((0.5 * (B_m / A))) * 180.0) / pi;
	elseif (A <= 2.95e-30)
		tmp = (atan(((C / B_m) - 1.0)) * 180.0) / pi;
	elseif (A <= 4.3e-7)
		tmp = (atan((-0.5 * (B_m / C))) / pi) * 180.0;
	else
		tmp = (atan(((A / B_m) * -2.0)) / pi) * 180.0;
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, -5e+35], N[(N[(N[ArcTan[N[(0.5 * N[(B$95$m / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 2.95e-30], N[(N[(N[ArcTan[N[(N[(C / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], If[LessEqual[A, 4.3e-7], N[(N[(N[ArcTan[N[(-0.5 * N[(B$95$m / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(A / B$95$m), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if A < -5.00000000000000021e35

   1. Initial program 54.1%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.4

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

   4. Applied rewrites 66.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 67.3%

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

   7. Taylor expanded in A around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 25.6

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

   9. Applied rewrites 25.6%

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

   if -5.00000000000000021e35 < A < 2.9499999999999999e-30

   1. Initial program 54.1%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.4

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

   4. Applied rewrites 66.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 67.3%

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

   7. Taylor expanded in A around 0

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

   9. Applied rewrites 56.7%

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

   if 2.9499999999999999e-30 < A < 4.3000000000000001e-7

   1. Initial program 54.1%

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

   2. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 25.9

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

   4. Applied rewrites 25.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 25.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

   8. Applied rewrites 25.9%

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

   if 4.3000000000000001e-7 < A

   1. Initial program 54.1%

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

   2. Taylor expanded in A around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 23.7

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

   4. Applied rewrites 23.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 23.7

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 23.7

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

   6. Applied rewrites 23.7%

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

Alternative 5: 66.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq 2.9 \cdot 10^{+105}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B\_m} - 1\right) \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B\_m}{C}\right) \cdot \frac{180}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= C 2.9e+105)
    (/ (* (atan (- (/ C B_m) 1.0)) 180.0) PI)
    (* (atan (* -0.5 (/ B_m C))) (/ 180.0 PI)))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (C <= 2.9e+105) {
		tmp = (atan(((C / B_m) - 1.0)) * 180.0) / ((double) M_PI);
	} else {
		tmp = atan((-0.5 * (B_m / C))) * (180.0 / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (C <= 2.9e+105) {
		tmp = (Math.atan(((C / B_m) - 1.0)) * 180.0) / Math.PI;
	} else {
		tmp = Math.atan((-0.5 * (B_m / C))) * (180.0 / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if C <= 2.9e+105:
		tmp = (math.atan(((C / B_m) - 1.0)) * 180.0) / math.pi
	else:
		tmp = math.atan((-0.5 * (B_m / C))) * (180.0 / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (C <= 2.9e+105)
		tmp = Float64(Float64(atan(Float64(Float64(C / B_m) - 1.0)) * 180.0) / pi);
	else
		tmp = Float64(atan(Float64(-0.5 * Float64(B_m / C))) * Float64(180.0 / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (C <= 2.9e+105)
		tmp = (atan(((C / B_m) - 1.0)) * 180.0) / pi;
	else
		tmp = atan((-0.5 * (B_m / C))) * (180.0 / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[C, 2.9e+105], N[(N[(N[ArcTan[N[(N[(C / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[ArcTan[N[(-0.5 * N[(B$95$m / C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < 2.9000000000000001e105

   1. Initial program 54.1%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.4

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

   4. Applied rewrites 66.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 67.3%

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

   7. Taylor expanded in A around 0

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

   9. Applied rewrites 56.7%

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

   if 2.9000000000000001e105 < C

   1. Initial program 54.1%

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

   2. Taylor expanded in C around inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 25.9

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

   4. Applied rewrites 25.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

   6. Applied rewrites 25.9%

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

      1. lift-fma.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div0 N/A

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

      4. +-rgt-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 25.9

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

      7. lower-*.f64 N/A

         \[\leadsto \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{B}{C}}\right) \cdot \mathsf{Rewrite=>}\left(lift-*.f64, \left(\frac{1}{\pi} \cdot 180\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{B}{C}}\right) \cdot \left(\mathsf{Rewrite=>}\left(lift-/.f64, \left(\frac{1}{\pi}\right)\right) \cdot 180\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{B}{C}}\right) \cdot \mathsf{Rewrite=>}\left(associate-*l/, \left(\frac{1 \cdot 180}{\pi}\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{B}{C}}\right) \cdot \frac{\mathsf{Rewrite=>}\left(metadata-eval, 180\right)}{\pi} \]

      11. lower-*.f64 N/A

          \[\leadsto \tan^{-1} \left(\frac{-1}{2} \cdot \color{blue}{\frac{B}{C}}\right) \cdot \mathsf{Rewrite=>}\left(lower-/.f64, \left(\frac{180}{\pi}\right)\right) \]

   8. Applied rewrites 25.9%

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

Alternative 6: 61.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq 9.5 \cdot 10^{+192}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B\_m} - 1\right) \cdot 180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B\_m}\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A 9.5e+192)
    (/ (* (atan (- (/ C B_m) 1.0)) 180.0) PI)
    (* (/ (atan (/ (- C A) B_m)) PI) 180.0))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= 9.5e+192) {
		tmp = (atan(((C / B_m) - 1.0)) * 180.0) / ((double) M_PI);
	} else {
		tmp = (atan(((C - A) / B_m)) / ((double) M_PI)) * 180.0;
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= 9.5e+192) {
		tmp = (Math.atan(((C / B_m) - 1.0)) * 180.0) / Math.PI;
	} else {
		tmp = (Math.atan(((C - A) / B_m)) / Math.PI) * 180.0;
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if A <= 9.5e+192:
		tmp = (math.atan(((C / B_m) - 1.0)) * 180.0) / math.pi
	else:
		tmp = (math.atan(((C - A) / B_m)) / math.pi) * 180.0
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= 9.5e+192)
		tmp = Float64(Float64(atan(Float64(Float64(C / B_m) - 1.0)) * 180.0) / pi);
	else
		tmp = Float64(Float64(atan(Float64(Float64(C - A) / B_m)) / pi) * 180.0);
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (A <= 9.5e+192)
		tmp = (atan(((C / B_m) - 1.0)) * 180.0) / pi;
	else
		tmp = (atan(((C - A) / B_m)) / pi) * 180.0;
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, 9.5e+192], N[(N[(N[ArcTan[N[(N[(C / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] * 180.0), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < 9.49999999999999931e192

   1. Initial program 54.1%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.4

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

   4. Applied rewrites 66.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

   6. Applied rewrites 67.3%

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

   7. Taylor expanded in A around 0

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

   9. Applied rewrites 56.7%

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

   if 9.49999999999999931e192 < A

   1. Initial program 54.1%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.4

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

   4. Applied rewrites 66.4%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 35.9

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

   7. Applied rewrites 35.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 35.9

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

   9. Applied rewrites 35.9%

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

Alternative 7: 61.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq 9.5 \cdot 10^{+192}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B\_m} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B\_m}\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= A 9.5e+192)
    (* 180.0 (/ (atan (- (/ C B_m) 1.0)) PI))
    (* (/ (atan (/ (- C A) B_m)) PI) 180.0))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= 9.5e+192) {
		tmp = 180.0 * (atan(((C / B_m) - 1.0)) / ((double) M_PI));
	} else {
		tmp = (atan(((C - A) / B_m)) / ((double) M_PI)) * 180.0;
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (A <= 9.5e+192) {
		tmp = 180.0 * (Math.atan(((C / B_m) - 1.0)) / Math.PI);
	} else {
		tmp = (Math.atan(((C - A) / B_m)) / Math.PI) * 180.0;
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if A <= 9.5e+192:
		tmp = 180.0 * (math.atan(((C / B_m) - 1.0)) / math.pi)
	else:
		tmp = (math.atan(((C - A) / B_m)) / math.pi) * 180.0
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (A <= 9.5e+192)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B_m) - 1.0)) / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(C - A) / B_m)) / pi) * 180.0);
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (A <= 9.5e+192)
		tmp = 180.0 * (atan(((C / B_m) - 1.0)) / pi);
	else
		tmp = (atan(((C - A) / B_m)) / pi) * 180.0;
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[A, 9.5e+192], N[(180.0 * N[(N[ArcTan[N[(N[(C / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < 9.49999999999999931e192

   1. Initial program 54.1%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.4

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

   4. Applied rewrites 66.4%

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

   5. Taylor expanded in A around 0

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

   7. Applied rewrites 56.7%

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

   if 9.49999999999999931e192 < A

   1. Initial program 54.1%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.4

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

   4. Applied rewrites 66.4%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 35.9

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

   7. Applied rewrites 35.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 35.9

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

   9. Applied rewrites 35.9%

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

Alternative 8: 55.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;B\_m \leq 0.00054:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B\_m}\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= B_m 0.00054)
    (* (/ (atan (/ (- C A) B_m)) PI) 180.0)
    (* 180.0 (/ (atan -1.0) PI)))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (B_m <= 0.00054) {
		tmp = (atan(((C - A) / B_m)) / ((double) M_PI)) * 180.0;
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (B_m <= 0.00054) {
		tmp = (Math.atan(((C - A) / B_m)) / Math.PI) * 180.0;
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if B_m <= 0.00054:
		tmp = (math.atan(((C - A) / B_m)) / math.pi) * 180.0
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (B_m <= 0.00054)
		tmp = Float64(Float64(atan(Float64(Float64(C - A) / B_m)) / pi) * 180.0);
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (B_m <= 0.00054)
		tmp = (atan(((C - A) / B_m)) / pi) * 180.0;
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[B$95$m, 0.00054], N[(N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if B < 5.40000000000000007e-4

   1. Initial program 54.1%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.4

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

   4. Applied rewrites 66.4%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 35.9

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

   7. Applied rewrites 35.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 35.9

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

   9. Applied rewrites 35.9%

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

   if 5.40000000000000007e-4 < B

   1. Initial program 54.1%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 40.1%

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

Alternative 9: 48.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;B\_m \leq 8 \cdot 10^{-8}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (*
  B_s
  (if (<= B_m 8e-8)
    (* 180.0 (/ (atan (/ C B_m)) PI))
    (* 180.0 (/ (atan -1.0) PI)))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (B_m <= 8e-8) {
		tmp = 180.0 * (atan((C / B_m)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return B_s * tmp;
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	double tmp;
	if (B_m <= 8e-8) {
		tmp = 180.0 * (Math.atan((C / B_m)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return B_s * tmp;
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	tmp = 0
	if B_m <= 8e-8:
		tmp = 180.0 * (math.atan((C / B_m)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return B_s * tmp

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	tmp = 0.0
	if (B_m <= 8e-8)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return Float64(B_s * tmp)
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp_2 = code(B_s, A, B_m, C)
	tmp = 0.0;
	if (B_m <= 8e-8)
		tmp = 180.0 * (atan((C / B_m)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = B_s * tmp;
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * If[LessEqual[B$95$m, 8e-8], N[(180.0 * N[(N[ArcTan[N[(C / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if B < 8.0000000000000002e-8

   1. Initial program 54.1%

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

   2. Taylor expanded in B around inf

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 66.4

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

   4. Applied rewrites 66.4%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 35.9

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

   7. Applied rewrites 35.9%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 24.2%

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

   if 8.0000000000000002e-8 < B

   1. Initial program 54.1%

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

   2. Taylor expanded in B around inf

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

   4. Applied rewrites 40.1%

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

Alternative 10: 40.1% accurate, 4.1× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \left(180 \cdot \frac{\tan^{-1} -1}{\pi}\right) \end{array} \]

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C) :precision binary64 (* B_s (* 180.0 (/ (atan -1.0) PI))))

C

B\_m = fabs(B);
B\_s = copysign(1.0, B);
double code(double B_s, double A, double B_m, double C) {
	return B_s * (180.0 * (atan(-1.0) / ((double) M_PI)));
}

Java

B\_m = Math.abs(B);
B\_s = Math.copySign(1.0, B);
public static double code(double B_s, double A, double B_m, double C) {
	return B_s * (180.0 * (Math.atan(-1.0) / Math.PI));
}

Python

B\_m = math.fabs(B)
B\_s = math.copysign(1.0, B)
def code(B_s, A, B_m, C):
	return B_s * (180.0 * (math.atan(-1.0) / math.pi))

Julia

B\_m = abs(B)
B\_s = copysign(1.0, B)
function code(B_s, A, B_m, C)
	return Float64(B_s * Float64(180.0 * Float64(atan(-1.0) / pi)))
end

MATLAB

B\_m = abs(B);
B\_s = sign(B) * abs(1.0);
function tmp = code(B_s, A, B_m, C)
	tmp = B_s * (180.0 * (atan(-1.0) / pi));
end

Wolfram

B\_m = N[Abs[B], $MachinePrecision]
B\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[B]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[B$95$s_, A_, B$95$m_, C_] := N[(B$95$s * N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 54.1%

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

2. Taylor expanded in B around inf

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

4. Applied rewrites 40.1%

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

Reproduce

herbie shell --seed 2025157 
(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)))