ABCF->ab-angle angle

Percentage Accurate: 53.8% → 89.0%

Time: 4.7s

Alternatives: 13

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: 53.8% 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: 89.0% accurate, 0.6× speedup

Math

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

FPCore

B\_m = (fabs.f64 B)
B\_s = (copysign.f64 #s(literal 1 binary64) B)
(FPCore (B_s A B_m C)
 :precision binary64
 (let* ((t_0 (+ (- A) C)))
   (*
    B_s
    (if (<=
         (*
          180.0
          (/
           (atan
            (*
             (/ 1.0 B_m)
             (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B_m 2.0))))))
           PI))
         -5.0)
      (* 180.0 (/ (atan (/ (- t_0 (hypot t_0 B_m)) B_m)) PI))
      (* 180.0 (/ (atan (* (/ B_m (- C A)) -0.5)) 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 t_0 = -A + C;
	double tmp;
	if ((180.0 * (atan(((1.0 / B_m) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B_m, 2.0)))))) / ((double) M_PI))) <= -5.0) {
		tmp = 180.0 * (atan(((t_0 - hypot(t_0, B_m)) / B_m)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B_m / (C - A)) * -0.5)) / ((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 t_0 = -A + C;
	double tmp;
	if ((180.0 * (Math.atan(((1.0 / B_m) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B_m, 2.0)))))) / Math.PI)) <= -5.0) {
		tmp = 180.0 * (Math.atan(((t_0 - Math.hypot(t_0, B_m)) / B_m)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B_m / (C - A)) * -0.5)) / 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):
	t_0 = -A + C
	tmp = 0
	if (180.0 * (math.atan(((1.0 / B_m) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B_m, 2.0)))))) / math.pi)) <= -5.0:
		tmp = 180.0 * (math.atan(((t_0 - math.hypot(t_0, B_m)) / B_m)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B_m / (C - A)) * -0.5)) / 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)
	t_0 = Float64(Float64(-A) + C)
	tmp = 0.0
	if (Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B_m) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B_m ^ 2.0)))))) / pi)) <= -5.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(t_0 - hypot(t_0, B_m)) / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B_m / Float64(C - A)) * -0.5)) / 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)
	t_0 = -A + C;
	tmp = 0.0;
	if ((180.0 * (atan(((1.0 / B_m) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B_m ^ 2.0)))))) / pi)) <= -5.0)
		tmp = 180.0 * (atan(((t_0 - hypot(t_0, B_m)) / B_m)) / pi);
	else
		tmp = 180.0 * (atan(((B_m / (C - A)) * -0.5)) / 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_] := Block[{t$95$0 = N[((-A) + C), $MachinePrecision]}, N[(B$95$s * If[LessEqual[N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B$95$m), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B$95$m, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], -5.0], N[(180.0 * N[(N[ArcTan[N[(N[(t$95$0 - N[Sqrt[t$95$0 ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B$95$m / N[(C - A), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64))) < -5

   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. Taylor expanded in A around -inf

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

      1. lower-atan.f64 N/A

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

      2. lower-/.f64 N/A

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

   4. Applied rewrites 78.1%

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

   if -5 < (*.f64 #s(literal 180 binary64) (/.f64 (atan.f64 (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))) (PI.f64)))

   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. Taylor expanded in A around -inf

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

      1. lower-atan.f64 N/A

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

      2. lower-/.f64 N/A

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

   4. Applied rewrites 78.1%

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

   5. Taylor expanded in B around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 36.9

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

   7. Applied rewrites 36.9%

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

Alternative 2: 79.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq -680000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\_m\right)}{B\_m}\right)}{\pi}\\ \mathbf{elif}\;C \leq 1.85 \cdot 10^{+90}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-\left(\mathsf{hypot}\left(B\_m, A\right) + A\right)}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B\_m}{C - A} \cdot -0.5\right)}{\pi}\\ \end{array} \end{array} \]

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 -680000.0)
    (* 180.0 (/ (atan (/ (- C (hypot C B_m)) B_m)) PI))
    (if (<= C 1.85e+90)
      (* 180.0 (/ (atan (/ (- (+ (hypot B_m A) A)) B_m)) PI))
      (* 180.0 (/ (atan (* (/ B_m (- C A)) -0.5)) 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 <= -680000.0) {
		tmp = 180.0 * (atan(((C - hypot(C, B_m)) / B_m)) / ((double) M_PI));
	} else if (C <= 1.85e+90) {
		tmp = 180.0 * (atan((-(hypot(B_m, A) + A) / B_m)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B_m / (C - A)) * -0.5)) / ((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 <= -680000.0) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B_m)) / B_m)) / Math.PI);
	} else if (C <= 1.85e+90) {
		tmp = 180.0 * (Math.atan((-(Math.hypot(B_m, A) + A) / B_m)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B_m / (C - A)) * -0.5)) / 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 <= -680000.0:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B_m)) / B_m)) / math.pi)
	elif C <= 1.85e+90:
		tmp = 180.0 * (math.atan((-(math.hypot(B_m, A) + A) / B_m)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B_m / (C - A)) * -0.5)) / 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 <= -680000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B_m)) / B_m)) / pi));
	elseif (C <= 1.85e+90)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-Float64(hypot(B_m, A) + A)) / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B_m / Float64(C - A)) * -0.5)) / 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 <= -680000.0)
		tmp = 180.0 * (atan(((C - hypot(C, B_m)) / B_m)) / pi);
	elseif (C <= 1.85e+90)
		tmp = 180.0 * (atan((-(hypot(B_m, A) + A) / B_m)) / pi);
	else
		tmp = 180.0 * (atan(((B_m / (C - A)) * -0.5)) / 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, -680000.0], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 1.85e+90], N[(180.0 * N[(N[ArcTan[N[((-N[(N[Sqrt[B$95$m ^ 2 + A ^ 2], $MachinePrecision] + A), $MachinePrecision]) / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B$95$m / N[(C - A), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if C < -6.8e5

   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. Taylor expanded in A around -inf

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

      1. lower-atan.f64 N/A

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

      2. lower-/.f64 N/A

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

   4. Applied rewrites 78.1%

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

   5. Taylor expanded in A around 0

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

   7. Applied rewrites 72.1%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 63.5%

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

   if -6.8e5 < C < 1.85e90

   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. Taylor expanded in C around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-fma.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 44.8

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

   4. Applied rewrites 44.8%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. pow2 N/A

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

      5. pow2 N/A

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

      6. +-commutative N/A

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

      7. pow2 N/A

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

      8. pow2 N/A

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

      9. lower-hypot.f64 63.9

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

   6. Applied rewrites 63.9%

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

   if 1.85e90 < C

   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. Taylor expanded in A around -inf

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

      1. lower-atan.f64 N/A

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

      2. lower-/.f64 N/A

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

   4. Applied rewrites 78.1%

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

   5. Taylor expanded in B around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 36.9

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

   7. Applied rewrites 36.9%

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

Alternative 3: 78.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -4 \cdot 10^{-28}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B\_m}{C - A} \cdot -0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.6 \cdot 10^{-72}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \mathsf{hypot}\left(C, B\_m\right)}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(\left(-B\_m\right) + C\right) - A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

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 -4e-28)
    (* 180.0 (/ (atan (* (/ B_m (- C A)) -0.5)) PI))
    (if (<= A 2.6e-72)
      (* 180.0 (/ (atan (/ (- C (hypot C B_m)) B_m)) PI))
      (* 180.0 (/ (atan (/ (- (+ (- B_m) C) A) B_m)) 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 <= -4e-28) {
		tmp = 180.0 * (atan(((B_m / (C - A)) * -0.5)) / ((double) M_PI));
	} else if (A <= 2.6e-72) {
		tmp = 180.0 * (atan(((C - hypot(C, B_m)) / B_m)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((-B_m + C) - A) / B_m)) / ((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 <= -4e-28) {
		tmp = 180.0 * (Math.atan(((B_m / (C - A)) * -0.5)) / Math.PI);
	} else if (A <= 2.6e-72) {
		tmp = 180.0 * (Math.atan(((C - Math.hypot(C, B_m)) / B_m)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((((-B_m + C) - A) / B_m)) / 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 <= -4e-28:
		tmp = 180.0 * (math.atan(((B_m / (C - A)) * -0.5)) / math.pi)
	elif A <= 2.6e-72:
		tmp = 180.0 * (math.atan(((C - math.hypot(C, B_m)) / B_m)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((((-B_m + C) - A) / B_m)) / 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 <= -4e-28)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B_m / Float64(C - A)) * -0.5)) / pi));
	elseif (A <= 2.6e-72)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - hypot(C, B_m)) / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(Float64(-B_m) + C) - A) / B_m)) / 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 <= -4e-28)
		tmp = 180.0 * (atan(((B_m / (C - A)) * -0.5)) / pi);
	elseif (A <= 2.6e-72)
		tmp = 180.0 * (atan(((C - hypot(C, B_m)) / B_m)) / pi);
	else
		tmp = 180.0 * (atan((((-B_m + C) - A) / B_m)) / 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, -4e-28], N[(180.0 * N[(N[ArcTan[N[(N[(B$95$m / N[(C - A), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.6e-72], N[(180.0 * N[(N[ArcTan[N[(N[(C - N[Sqrt[C ^ 2 + B$95$m ^ 2], $MachinePrecision]), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(N[((-B$95$m) + C), $MachinePrecision] - A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -3.99999999999999988e-28

   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. Taylor expanded in A around -inf

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

      1. lower-atan.f64 N/A

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

      2. lower-/.f64 N/A

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

   4. Applied rewrites 78.1%

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

   5. Taylor expanded in B around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 36.9

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

   7. Applied rewrites 36.9%

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

   if -3.99999999999999988e-28 < A < 2.59999999999999996e-72

   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. Taylor expanded in A around -inf

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

      1. lower-atan.f64 N/A

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

      2. lower-/.f64 N/A

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

   4. Applied rewrites 78.1%

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

   5. Taylor expanded in A around 0

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

   7. Applied rewrites 72.1%

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

   8. Taylor expanded in A around 0

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

   10. Applied rewrites 63.5%

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

   if 2.59999999999999996e-72 < A

   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. 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.4

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

   4. Applied rewrites 65.4%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-neg.f64 66.7

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

   7. Applied rewrites 66.7%

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

Alternative 4: 76.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;C \leq 62000000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(\left(-B\_m\right) + C\right) - A}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B\_m}{C - A} \cdot -0.5\right)}{\pi}\\ \end{array} \end{array} \]

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 62000000.0)
    (* 180.0 (/ (atan (/ (- (+ (- B_m) C) A) B_m)) PI))
    (* 180.0 (/ (atan (* (/ B_m (- C A)) -0.5)) 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 <= 62000000.0) {
		tmp = 180.0 * (atan((((-B_m + C) - A) / B_m)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B_m / (C - A)) * -0.5)) / ((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 <= 62000000.0) {
		tmp = 180.0 * (Math.atan((((-B_m + C) - A) / B_m)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((B_m / (C - A)) * -0.5)) / 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 <= 62000000.0:
		tmp = 180.0 * (math.atan((((-B_m + C) - A) / B_m)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((B_m / (C - A)) * -0.5)) / 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 <= 62000000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(Float64(-B_m) + C) - A) / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B_m / Float64(C - A)) * -0.5)) / 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 <= 62000000.0)
		tmp = 180.0 * (atan((((-B_m + C) - A) / B_m)) / pi);
	else
		tmp = 180.0 * (atan(((B_m / (C - A)) * -0.5)) / 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, 62000000.0], N[(180.0 * N[(N[ArcTan[N[(N[(N[((-B$95$m) + C), $MachinePrecision] - A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B$95$m / N[(C - A), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if C < 6.2e7

   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. 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.4

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

   4. Applied rewrites 65.4%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-neg.f64 66.7

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

   7. Applied rewrites 66.7%

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

   if 6.2e7 < C

   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. Taylor expanded in A around -inf

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

      1. lower-atan.f64 N/A

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

      2. lower-/.f64 N/A

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

   4. Applied rewrites 78.1%

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

   5. Taylor expanded in B around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 36.9

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

   7. Applied rewrites 36.9%

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

Alternative 5: 75.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -3.9 \cdot 10^{-29}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B\_m}{C - A} \cdot -0.5\right)}{\pi}\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B\_m} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - B\_m}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

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 -3.9e-29)
    (* 180.0 (/ (atan (* (/ B_m (- C A)) -0.5)) PI))
    (if (<= A 8.5e-27)
      (* 180.0 (/ (atan (- (/ C B_m) 1.0)) PI))
      (* 180.0 (/ (atan (/ (- (- A) B_m) B_m)) 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 <= -3.9e-29) {
		tmp = 180.0 * (atan(((B_m / (C - A)) * -0.5)) / ((double) M_PI));
	} else if (A <= 8.5e-27) {
		tmp = 180.0 * (atan(((C / B_m) - 1.0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((-A - B_m) / B_m)) / ((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 <= -3.9e-29) {
		tmp = 180.0 * (Math.atan(((B_m / (C - A)) * -0.5)) / Math.PI);
	} else if (A <= 8.5e-27) {
		tmp = 180.0 * (Math.atan(((C / B_m) - 1.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((-A - B_m) / B_m)) / 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 <= -3.9e-29:
		tmp = 180.0 * (math.atan(((B_m / (C - A)) * -0.5)) / math.pi)
	elif A <= 8.5e-27:
		tmp = 180.0 * (math.atan(((C / B_m) - 1.0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((-A - B_m) / B_m)) / 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 <= -3.9e-29)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B_m / Float64(C - A)) * -0.5)) / pi));
	elseif (A <= 8.5e-27)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B_m) - 1.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - B_m) / B_m)) / 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 <= -3.9e-29)
		tmp = 180.0 * (atan(((B_m / (C - A)) * -0.5)) / pi);
	elseif (A <= 8.5e-27)
		tmp = 180.0 * (atan(((C / B_m) - 1.0)) / pi);
	else
		tmp = 180.0 * (atan(((-A - B_m) / B_m)) / 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, -3.9e-29], N[(180.0 * N[(N[ArcTan[N[(N[(B$95$m / N[(C - A), $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 8.5e-27], N[(180.0 * N[(N[ArcTan[N[(N[(C / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - B$95$m), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -3.8999999999999998e-29

   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. Taylor expanded in A around -inf

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

      1. lower-atan.f64 N/A

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

      2. lower-/.f64 N/A

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

   4. Applied rewrites 78.1%

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

   5. Taylor expanded in B around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 36.9

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

   7. Applied rewrites 36.9%

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

   if -3.8999999999999998e-29 < A < 8.50000000000000033e-27

   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. 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.4

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

   4. Applied rewrites 65.4%

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

   5. Taylor expanded in A around 0

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 55.9

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

   7. Applied rewrites 55.9%

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

   if 8.50000000000000033e-27 < A

   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. Taylor expanded in C around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-fma.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 44.8

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

   4. Applied rewrites 44.8%

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

   5. Taylor expanded in A around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 N/A

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

      3. lower--.f64 56.0

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

   7. Applied rewrites 56.0%

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

Alternative 6: 74.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -2.55 \cdot 10^{+75}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B\_m}{A} \cdot 0.5\right)}{\pi} \cdot 180\\ \mathbf{elif}\;A \leq 8.5 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B\_m} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(-A\right) - B\_m}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

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 -2.55e+75)
    (* (/ (atan (* (/ B_m A) 0.5)) PI) 180.0)
    (if (<= A 8.5e-27)
      (* 180.0 (/ (atan (- (/ C B_m) 1.0)) PI))
      (* 180.0 (/ (atan (/ (- (- A) B_m) B_m)) 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 <= -2.55e+75) {
		tmp = (atan(((B_m / A) * 0.5)) / ((double) M_PI)) * 180.0;
	} else if (A <= 8.5e-27) {
		tmp = 180.0 * (atan(((C / B_m) - 1.0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((-A - B_m) / B_m)) / ((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 <= -2.55e+75) {
		tmp = (Math.atan(((B_m / A) * 0.5)) / Math.PI) * 180.0;
	} else if (A <= 8.5e-27) {
		tmp = 180.0 * (Math.atan(((C / B_m) - 1.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((-A - B_m) / B_m)) / 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 <= -2.55e+75:
		tmp = (math.atan(((B_m / A) * 0.5)) / math.pi) * 180.0
	elif A <= 8.5e-27:
		tmp = 180.0 * (math.atan(((C / B_m) - 1.0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((-A - B_m) / B_m)) / 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 <= -2.55e+75)
		tmp = Float64(Float64(atan(Float64(Float64(B_m / A) * 0.5)) / pi) * 180.0);
	elseif (A <= 8.5e-27)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B_m) - 1.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(Float64(-A) - B_m) / B_m)) / 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 <= -2.55e+75)
		tmp = (atan(((B_m / A) * 0.5)) / pi) * 180.0;
	elseif (A <= 8.5e-27)
		tmp = 180.0 * (atan(((C / B_m) - 1.0)) / pi);
	else
		tmp = 180.0 * (atan(((-A - B_m) / B_m)) / 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, -2.55e+75], N[(N[(N[ArcTan[N[(N[(B$95$m / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[A, 8.5e-27], N[(180.0 * N[(N[ArcTan[N[(N[(C / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[((-A) - B$95$m), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -2.55000000000000018e75

   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. 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 26.9

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

   4. Applied rewrites 26.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 26.9

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

   6. Applied rewrites 26.9%

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

   if -2.55000000000000018e75 < A < 8.50000000000000033e-27

   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. 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.4

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

   4. Applied rewrites 65.4%

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

   5. Taylor expanded in A around 0

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 55.9

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

   7. Applied rewrites 55.9%

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

   if 8.50000000000000033e-27 < A

   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. Taylor expanded in C around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-fma.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 44.8

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

   4. Applied rewrites 44.8%

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

   5. Taylor expanded in A around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 N/A

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

      3. lower--.f64 56.0

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

   7. Applied rewrites 56.0%

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

Alternative 7: 70.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -2.55 \cdot 10^{+75}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B\_m}{A} \cdot 0.5\right)}{\pi} \cdot 180\\ \mathbf{elif}\;A \leq 7.8 \cdot 10^{+59}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B\_m}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{-2 \cdot A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

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 -2.55e+75)
    (* (/ (atan (* (/ B_m A) 0.5)) PI) 180.0)
    (if (<= A 7.8e+59)
      (* 180.0 (/ (atan (/ (- C B_m) B_m)) PI))
      (/ (* 180.0 (atan (/ (* -2.0 A) B_m))) 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 <= -2.55e+75) {
		tmp = (atan(((B_m / A) * 0.5)) / ((double) M_PI)) * 180.0;
	} else if (A <= 7.8e+59) {
		tmp = 180.0 * (atan(((C - B_m) / B_m)) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((-2.0 * A) / B_m))) / ((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 <= -2.55e+75) {
		tmp = (Math.atan(((B_m / A) * 0.5)) / Math.PI) * 180.0;
	} else if (A <= 7.8e+59) {
		tmp = 180.0 * (Math.atan(((C - B_m) / B_m)) / Math.PI);
	} else {
		tmp = (180.0 * Math.atan(((-2.0 * A) / B_m))) / 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 <= -2.55e+75:
		tmp = (math.atan(((B_m / A) * 0.5)) / math.pi) * 180.0
	elif A <= 7.8e+59:
		tmp = 180.0 * (math.atan(((C - B_m) / B_m)) / math.pi)
	else:
		tmp = (180.0 * math.atan(((-2.0 * A) / B_m))) / 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 <= -2.55e+75)
		tmp = Float64(Float64(atan(Float64(Float64(B_m / A) * 0.5)) / pi) * 180.0);
	elseif (A <= 7.8e+59)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B_m) / B_m)) / pi));
	else
		tmp = Float64(Float64(180.0 * atan(Float64(Float64(-2.0 * A) / B_m))) / 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 <= -2.55e+75)
		tmp = (atan(((B_m / A) * 0.5)) / pi) * 180.0;
	elseif (A <= 7.8e+59)
		tmp = 180.0 * (atan(((C - B_m) / B_m)) / pi);
	else
		tmp = (180.0 * atan(((-2.0 * A) / B_m))) / 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, -2.55e+75], N[(N[(N[ArcTan[N[(N[(B$95$m / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[A, 7.8e+59], N[(180.0 * N[(N[ArcTan[N[(N[(C - B$95$m), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(N[(-2.0 * A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -2.55000000000000018e75

   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. 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 26.9

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

   4. Applied rewrites 26.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 26.9

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

   6. Applied rewrites 26.9%

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

   if -2.55000000000000018e75 < A < 7.80000000000000043e59

   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. 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.4

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

   4. Applied rewrites 65.4%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-neg.f64 66.7

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

   7. Applied rewrites 66.7%

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

   8. Taylor expanded in A around 0

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

      1. lower--.f64 55.9

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

   10. Applied rewrites 55.9%

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

   if 7.80000000000000043e59 < A

   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. Taylor expanded in C around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-fma.f64 N/A

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

      10. unpow2 N/A

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

      11. lower-*.f64 44.8

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

   4. Applied rewrites 44.8%

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

      1. lift-sqrt.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. pow2 N/A

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

      5. pow2 N/A

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

      6. +-commutative N/A

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

      7. pow2 N/A

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

      8. pow2 N/A

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

      9. lower-hypot.f64 63.9

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

   6. Applied rewrites 63.9%

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

   7. Taylor expanded in A around inf

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

      1. lower-*.f64 23.6

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

   9. Applied rewrites 23.6%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-*r/ N/A

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

       4. lower-/.f64 N/A

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

       5. lower-*.f64 23.6

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

   11. Applied rewrites 23.6%

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

Alternative 8: 70.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq -2.55 \cdot 10^{+75}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B\_m}{A} \cdot 0.5\right)}{\pi} \cdot 180\\ \mathbf{elif}\;A \leq 7.8 \cdot 10^{+59}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B\_m}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

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 -2.55e+75)
    (* (/ (atan (* (/ B_m A) 0.5)) PI) 180.0)
    (if (<= A 7.8e+59)
      (* 180.0 (/ (atan (/ (- C B_m) B_m)) PI))
      (* 180.0 (/ (atan (/ (- C A) B_m)) 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 <= -2.55e+75) {
		tmp = (atan(((B_m / A) * 0.5)) / ((double) M_PI)) * 180.0;
	} else if (A <= 7.8e+59) {
		tmp = 180.0 * (atan(((C - B_m) / B_m)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - A) / B_m)) / ((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 <= -2.55e+75) {
		tmp = (Math.atan(((B_m / A) * 0.5)) / Math.PI) * 180.0;
	} else if (A <= 7.8e+59) {
		tmp = 180.0 * (Math.atan(((C - B_m) / B_m)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - A) / B_m)) / 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 <= -2.55e+75:
		tmp = (math.atan(((B_m / A) * 0.5)) / math.pi) * 180.0
	elif A <= 7.8e+59:
		tmp = 180.0 * (math.atan(((C - B_m) / B_m)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - A) / B_m)) / 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 <= -2.55e+75)
		tmp = Float64(Float64(atan(Float64(Float64(B_m / A) * 0.5)) / pi) * 180.0);
	elseif (A <= 7.8e+59)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B_m) / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / B_m)) / 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 <= -2.55e+75)
		tmp = (atan(((B_m / A) * 0.5)) / pi) * 180.0;
	elseif (A <= 7.8e+59)
		tmp = 180.0 * (atan(((C - B_m) / B_m)) / pi);
	else
		tmp = 180.0 * (atan(((C - A) / B_m)) / 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, -2.55e+75], N[(N[(N[ArcTan[N[(N[(B$95$m / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[A, 7.8e+59], N[(180.0 * N[(N[ArcTan[N[(N[(C - B$95$m), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if A < -2.55000000000000018e75

   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. 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 26.9

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

   4. Applied rewrites 26.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 26.9

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

   6. Applied rewrites 26.9%

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

   if -2.55000000000000018e75 < A < 7.80000000000000043e59

   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. 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.4

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

   4. Applied rewrites 65.4%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-neg.f64 66.7

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

   7. Applied rewrites 66.7%

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

   8. Taylor expanded in A around 0

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

      1. lower--.f64 55.9

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

   10. Applied rewrites 55.9%

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

   if 7.80000000000000043e59 < A

   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. 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.4

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

   4. Applied rewrites 65.4%

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

   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 35.3

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

   7. Applied rewrites 35.3%

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

Alternative 9: 61.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq 7.8 \cdot 10^{+59}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B\_m}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

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 7.8e+59)
    (* 180.0 (/ (atan (/ (- C B_m) B_m)) PI))
    (* 180.0 (/ (atan (/ (- C A) B_m)) 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 <= 7.8e+59) {
		tmp = 180.0 * (atan(((C - B_m) / B_m)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((C - A) / B_m)) / ((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 <= 7.8e+59) {
		tmp = 180.0 * (Math.atan(((C - B_m) / B_m)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(((C - A) / B_m)) / 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 <= 7.8e+59:
		tmp = 180.0 * (math.atan(((C - B_m) / B_m)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(((C - A) / B_m)) / 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 <= 7.8e+59)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B_m) / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - A) / B_m)) / 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 <= 7.8e+59)
		tmp = 180.0 * (atan(((C - B_m) / B_m)) / pi);
	else
		tmp = 180.0 * (atan(((C - A) / B_m)) / 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, 7.8e+59], N[(180.0 * N[(N[ArcTan[N[(N[(C - B$95$m), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(C - A), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < 7.80000000000000043e59

   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. 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.4

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

   4. Applied rewrites 65.4%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-neg.f64 66.7

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

   7. Applied rewrites 66.7%

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

   8. Taylor expanded in A around 0

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

      1. lower--.f64 55.9

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

   10. Applied rewrites 55.9%

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

   if 7.80000000000000043e59 < A

   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. 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.4

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

   4. Applied rewrites 65.4%

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

   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 35.3

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

   7. Applied rewrites 35.3%

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

Alternative 10: 61.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq 1.1 \cdot 10^{+81}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - B\_m}{B\_m}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

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 1.1e+81)
    (* 180.0 (/ (atan (/ (- C B_m) B_m)) PI))
    (* 180.0 (/ (atan (/ (- A) B_m)) 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 <= 1.1e+81) {
		tmp = 180.0 * (atan(((C - B_m) / B_m)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-A / B_m)) / ((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 <= 1.1e+81) {
		tmp = 180.0 * (Math.atan(((C - B_m) / B_m)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-A / B_m)) / 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 <= 1.1e+81:
		tmp = 180.0 * (math.atan(((C - B_m) / B_m)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-A / B_m)) / 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 <= 1.1e+81)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C - B_m) / B_m)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B_m)) / 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 <= 1.1e+81)
		tmp = 180.0 * (atan(((C - B_m) / B_m)) / pi);
	else
		tmp = 180.0 * (atan((-A / B_m)) / 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, 1.1e+81], N[(180.0 * N[(N[ArcTan[N[(N[(C - B$95$m), $MachinePrecision] / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[((-A) / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < 1.09999999999999993e81

   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. 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.4

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

   4. Applied rewrites 65.4%

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

   5. Taylor expanded in B around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-neg.f64 66.7

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

   7. Applied rewrites 66.7%

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

   8. Taylor expanded in A around 0

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

      1. lower--.f64 55.9

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

   10. Applied rewrites 55.9%

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

   if 1.09999999999999993e81 < A

   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. 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.4

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

   4. Applied rewrites 65.4%

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

   5. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lift-neg.f64 N/A

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

      4. lower-/.f64 23.4

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

   7. Applied rewrites 23.4%

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

Alternative 11: 61.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq 1.1 \cdot 10^{+81}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B\_m} - 1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

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 1.1e+81)
    (* 180.0 (/ (atan (- (/ C B_m) 1.0)) PI))
    (* 180.0 (/ (atan (/ (- A) B_m)) 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 <= 1.1e+81) {
		tmp = 180.0 * (atan(((C / B_m) - 1.0)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-A / B_m)) / ((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 <= 1.1e+81) {
		tmp = 180.0 * (Math.atan(((C / B_m) - 1.0)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-A / B_m)) / 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 <= 1.1e+81:
		tmp = 180.0 * (math.atan(((C / B_m) - 1.0)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-A / B_m)) / 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 <= 1.1e+81)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B_m) - 1.0)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B_m)) / 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 <= 1.1e+81)
		tmp = 180.0 * (atan(((C / B_m) - 1.0)) / pi);
	else
		tmp = 180.0 * (atan((-A / B_m)) / 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, 1.1e+81], N[(180.0 * N[(N[ArcTan[N[(N[(C / B$95$m), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[((-A) / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < 1.09999999999999993e81

   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. 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.4

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

   4. Applied rewrites 65.4%

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

   5. Taylor expanded in A around 0

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 55.9

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

   7. Applied rewrites 55.9%

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

   if 1.09999999999999993e81 < A

   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. 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.4

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

   4. Applied rewrites 65.4%

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

   5. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lift-neg.f64 N/A

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

      4. lower-/.f64 23.4

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

   7. Applied rewrites 23.4%

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

Alternative 12: 48.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} B\_m = \left|B\right| \\ B\_s = \mathsf{copysign}\left(1, B\right) \\ B\_s \cdot \begin{array}{l} \mathbf{if}\;A \leq 5.5 \cdot 10^{+57}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B\_m}\right)}{\pi}\\ \end{array} \end{array} \]

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 5.5e+57)
    (* 180.0 (/ (atan -1.0) PI))
    (* 180.0 (/ (atan (/ (- A) B_m)) 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 <= 5.5e+57) {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((-A / B_m)) / ((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 <= 5.5e+57) {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((-A / B_m)) / 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 <= 5.5e+57:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((-A / B_m)) / 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 <= 5.5e+57)
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B_m)) / 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 <= 5.5e+57)
		tmp = 180.0 * (atan(-1.0) / pi);
	else
		tmp = 180.0 * (atan((-A / B_m)) / 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, 5.5e+57], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[((-A) / B$95$m), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if A < 5.5000000000000002e57

   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. 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%

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

   if 5.5000000000000002e57 < A

   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. 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. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 65.4

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

   4. Applied rewrites 65.4%

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

   5. Taylor expanded in A around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lift-neg.f64 N/A

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

      4. lower-/.f64 23.4

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

   7. Applied rewrites 23.4%

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

Alternative 13: 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 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. 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 2025127 
(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)))