ABCF->ab-angle angle

Percentage Accurate: 53.7% → 74.5%

Time: 5.3s

Alternatives: 11

Speedup: 1.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 53.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 74.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;C \leq -2.1 \cdot 10^{+99}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8500000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{hypot}\left(A, B\right) + A}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, \frac{0}{B}\right)\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= C -2.1e+99)
   (* 180.0 (/ (atan (+ 1.0 (/ C B))) PI))
   (if (<= C 8500000.0)
     (* 180.0 (/ (atan (/ (+ (hypot A B) A) (- B))) PI))
     (* 180.0 (/ (atan (fma (/ B C) -0.5 (/ 0.0 B))) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (C <= -2.1e+99) {
		tmp = 180.0 * (atan((1.0 + (C / B))) / ((double) M_PI));
	} else if (C <= 8500000.0) {
		tmp = 180.0 * (atan(((hypot(A, B) + A) / -B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(fma((B / C), -0.5, (0.0 / B))) / ((double) M_PI));
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (C <= -2.1e+99)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(C / B))) / pi));
	elseif (C <= 8500000.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(hypot(A, B) + A) / Float64(-B))) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(fma(Float64(B / C), -0.5, Float64(0.0 / B))) / pi));
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[C, -2.1e+99], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(C / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[C, 8500000.0], N[(180.0 * N[(N[ArcTan[N[(N[(N[Sqrt[A ^ 2 + B ^ 2], $MachinePrecision] + A), $MachinePrecision] / (-B)), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(N[(B / C), $MachinePrecision] * -0.5 + N[(0.0 / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if C < -2.1000000000000001e99

   1. Initial program 85.8%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 91.3

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

   5. Applied rewrites 91.3%

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

   6. Taylor expanded in A around 0

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

   8. Applied rewrites 91.4%

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

   if -2.1000000000000001e99 < C < 8.5e6

   1. Initial program 60.1%

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

   3. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. unpow2 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 76.9

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

   5. Applied rewrites 76.9%

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

   if 8.5e6 < C

   1. Initial program 25.4%

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

   3. Taylor expanded in C around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. unpow2 N/A

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

      7. unpow2 N/A

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

      8. lower-hypot.f64 46.7

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

   5. Applied rewrites 46.7%

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

   6. Taylor expanded in C around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. distribute-rgt1-in N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. mul0-lft N/A

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

      9. metadata-eval N/A

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

      10. mul0-lft N/A

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

      11. lift-/.f64 N/A

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

      12. mul0-lft 67.7

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

   8. Applied rewrites 67.7%

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\mathsf{fma}\left(\frac{B}{C}, -0.5, \frac{0}{B}\right)\right)}}{\pi} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq -2.1 \cdot 10^{+99}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;C \leq 8500000:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\mathsf{hypot}\left(A, B\right) + A}{-B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\mathsf{fma}\left(\frac{B}{C}, -0.5, \frac{0}{B}\right)\right)}{\pi}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ \mathbf{if}\;t\_0 \leq -40:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - B\right)\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (*
          180.0
          (/
           (atan
            (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
           PI))))
   (if (<= t_0 -40.0)
     (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) B))) PI))
     (if (<= t_0 5e-109)
       (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
       (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
	double tmp;
	if (t_0 <= -40.0) {
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / ((double) M_PI));
	} else if (t_0 <= 5e-109) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
	double tmp;
	if (t_0 <= -40.0) {
		tmp = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - B))) / Math.PI);
	} else if (t_0 <= 5e-109) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)
	tmp = 0
	if t_0 <= -40.0:
		tmp = 180.0 * (math.atan(((1.0 / B) * ((C - A) - B))) / math.pi)
	elif t_0 <= 5e-109:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = 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))
	tmp = 0.0
	if (t_0 <= -40.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - B))) / pi));
	elseif (t_0 <= 5e-109)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
	tmp = 0.0;
	if (t_0 <= -40.0)
		tmp = 180.0 * (atan(((1.0 / B) * ((C - A) - B))) / pi);
	elseif (t_0 <= 5e-109)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -40.0], N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e-109], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 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))) < -40

   1. Initial program 59.2%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 75.4%

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

   if -40 < (*.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))) < 5.0000000000000002e-109

   1. Initial program 25.4%

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

   3. Taylor expanded in A around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}}{\pi} \]
   4. 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 52.3

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

   5. Applied rewrites 52.3%

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

   if 5.0000000000000002e-109 < (*.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 61.7%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 80.4

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

   5. Applied rewrites 80.4%

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

Alternative 3: 66.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\\ \mathbf{if}\;t\_0 \leq -40:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-109}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (*
          180.0
          (/
           (atan
            (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
           PI))))
   (if (<= t_0 -40.0)
     (* 180.0 (/ (atan (- (/ C B) 1.0)) PI))
     (if (<= t_0 5e-109)
       (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
       (* 180.0 (/ (atan (+ 1.0 (/ (- C A) B))) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
	double tmp;
	if (t_0 <= -40.0) {
		tmp = 180.0 * (atan(((C / B) - 1.0)) / ((double) M_PI));
	} else if (t_0 <= 5e-109) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = 180.0 * (Math.atan(((1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0)))))) / Math.PI);
	double tmp;
	if (t_0 <= -40.0) {
		tmp = 180.0 * (Math.atan(((C / B) - 1.0)) / Math.PI);
	} else if (t_0 <= 5e-109) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 + ((C - A) / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = 180.0 * (math.atan(((1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0)))))) / math.pi)
	tmp = 0
	if t_0 <= -40.0:
		tmp = 180.0 * (math.atan(((C / B) - 1.0)) / math.pi)
	elif t_0 <= 5e-109:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 + ((C - A) / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = 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))
	tmp = 0.0
	if (t_0 <= -40.0)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) - 1.0)) / pi));
	elseif (t_0 <= 5e-109)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 + Float64(Float64(C - A) / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0)))))) / pi);
	tmp = 0.0;
	if (t_0 <= -40.0)
		tmp = 180.0 * (atan(((C / B) - 1.0)) / pi);
	elseif (t_0 <= 5e-109)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	else
		tmp = 180.0 * (atan((1.0 + ((C - A) / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -40.0], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e-109], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 + N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 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))) < -40

   1. Initial program 59.2%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}}{\pi} \]
   4. 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 73.6

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

   5. Applied rewrites 73.6%

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

   6. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - \color{blue}{1}\right)}{\pi} \]
   7. 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 66.6

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

   8. Applied rewrites 66.6%

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

   if -40 < (*.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))) < 5.0000000000000002e-109

   1. Initial program 25.4%

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

   3. Taylor expanded in A around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}}{\pi} \]
   4. 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 52.3

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

   5. Applied rewrites 52.3%

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

   if 5.0000000000000002e-109 < (*.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 61.7%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 80.4

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

   5. Applied rewrites 80.4%

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

Alternative 4: 61.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -0.5:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-111}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -0.5)
     (* 180.0 (/ (atan (- (/ C B) 1.0)) PI))
     (if (<= t_0 5e-111)
       (* 180.0 (/ (atan (* (/ B A) 0.5)) PI))
       (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (atan(((C / B) - 1.0)) / ((double) M_PI));
	} else if (t_0 <= 5e-111) {
		tmp = 180.0 * (atan(((B / A) * 0.5)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (Math.atan(((C / B) - 1.0)) / Math.PI);
	} else if (t_0 <= 5e-111) {
		tmp = 180.0 * (Math.atan(((B / A) * 0.5)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_0 <= -0.5:
		tmp = 180.0 * (math.atan(((C / B) - 1.0)) / math.pi)
	elif t_0 <= 5e-111:
		tmp = 180.0 * (math.atan(((B / A) * 0.5)) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) - 1.0)) / pi));
	elseif (t_0 <= 5e-111)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(B / A) * 0.5)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = 180.0 * (atan(((C / B) - 1.0)) / pi);
	elseif (t_0 <= 5e-111)
		tmp = 180.0 * (atan(((B / A) * 0.5)) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e-111], N[(180.0 * N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 59.2%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}}{\pi} \]
   4. 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 73.6

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

   5. Applied rewrites 73.6%

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

   6. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - \color{blue}{1}\right)}{\pi} \]
   7. 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 66.6

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

   8. Applied rewrites 66.6%

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

   if -0.5 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 5.0000000000000003e-111

   1. Initial program 25.4%

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

   3. Taylor expanded in A around -inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{1}{2} \cdot \frac{B}{A}\right)}}{\pi} \]
   4. 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 52.3

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

   5. Applied rewrites 52.3%

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

   if 5.0000000000000003e-111 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 61.7%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 80.4

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

   5. Applied rewrites 80.4%

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

   6. Taylor expanded in C around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 68.1

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

   8. Applied rewrites 68.1%

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

Alternative 5: 57.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t\_0 \leq -0.5:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - 1\right)}{\pi}\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-111}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -0.5)
     (* 180.0 (/ (atan (- (/ C B) 1.0)) PI))
     (if (<= t_0 5e-111)
       (* 180.0 (/ (atan 0.0) PI))
       (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))))))

C

double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (atan(((C / B) - 1.0)) / ((double) M_PI));
	} else if (t_0 <= 5e-111) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (1.0 / B) * ((C - A) - Math.sqrt((Math.pow((A - C), 2.0) + Math.pow(B, 2.0))));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = 180.0 * (Math.atan(((C / B) - 1.0)) / Math.PI);
	} else if (t_0 <= 5e-111) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (1.0 / B) * ((C - A) - math.sqrt((math.pow((A - C), 2.0) + math.pow(B, 2.0))))
	tmp = 0
	if t_0 <= -0.5:
		tmp = 180.0 * (math.atan(((C / B) - 1.0)) / math.pi)
	elif t_0 <= 5e-111:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(C / B) - 1.0)) / pi));
	elseif (t_0 <= 5e-111)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (1.0 / B) * ((C - A) - sqrt((((A - C) ^ 2.0) + (B ^ 2.0))));
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = 180.0 * (atan(((C / B) - 1.0)) / pi);
	elseif (t_0 <= 5e-111)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], N[(180.0 * N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] - 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e-111], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 59.2%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}}{\pi} \]
   4. 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 73.6

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

   5. Applied rewrites 73.6%

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

   6. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} - \color{blue}{1}\right)}{\pi} \]
   7. 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 66.6

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

   8. Applied rewrites 66.6%

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

   if -0.5 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 5.0000000000000003e-111

   1. Initial program 25.4%

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

   3. Taylor expanded in C around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-rgt1-in N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 25.0

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

   5. Applied rewrites 25.0%

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

   6. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]
   7. Step-by-step derivation

   8. Applied rewrites 25.0%

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

   if 5.0000000000000003e-111 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 61.7%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 80.4

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

   5. Applied rewrites 80.4%

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

   6. Taylor expanded in C around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 68.1

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

   8. Applied rewrites 68.1%

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

Alternative 6: 46.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -3200:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.9 \cdot 10^{-160}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -3200.0)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B -1.9e-160)
     (* 180.0 (/ (atan (/ (- A) B)) PI))
     (if (<= B 2.6e-116)
       (* 180.0 (/ (atan (/ C B)) PI))
       (* 180.0 (/ (atan -1.0) PI))))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -3200.0) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= -1.9e-160) {
		tmp = 180.0 * (atan((-A / B)) / ((double) M_PI));
	} else if (B <= 2.6e-116) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -3200.0) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= -1.9e-160) {
		tmp = 180.0 * (Math.atan((-A / B)) / Math.PI);
	} else if (B <= 2.6e-116) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -3200.0:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= -1.9e-160:
		tmp = 180.0 * (math.atan((-A / B)) / math.pi)
	elif B <= 2.6e-116:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -3200.0)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= -1.9e-160)
		tmp = Float64(180.0 * Float64(atan(Float64(Float64(-A) / B)) / pi));
	elseif (B <= 2.6e-116)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -3200.0)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= -1.9e-160)
		tmp = 180.0 * (atan((-A / B)) / pi);
	elseif (B <= 2.6e-116)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -3200.0], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, -1.9e-160], N[(180.0 * N[(N[ArcTan[N[((-A) / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.6e-116], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if B < -3200

   1. Initial program 48.5%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 63.9%

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

   if -3200 < B < -1.8999999999999999e-160

   1. Initial program 71.9%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}}{\pi} \]
   4. 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 59.3

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

   5. Applied rewrites 59.3%

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

   6. Taylor expanded in A around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(-1 \cdot \color{blue}{\frac{A}{B}}\right)}{\pi} \]
   7. 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. lower-/.f64 N/A

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

      4. lower-neg.f64 52.1

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

   8. Applied rewrites 52.1%

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

   if -1.8999999999999999e-160 < B < 2.6e-116

   1. Initial program 61.4%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}}{\pi} \]
   4. 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 46.8

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

   5. Applied rewrites 46.8%

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

   6. Taylor expanded in C around inf

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

      1. lift-/.f64 41.0

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

   8. Applied rewrites 41.0%

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

   if 2.6e-116 < B

   1. Initial program 49.9%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 54.3%

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

Alternative 7: 50.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5.5 \cdot 10^{-164}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(1 - \frac{A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5.5e-164)
   (* 180.0 (/ (atan (- 1.0 (/ A B))) PI))
   (if (<= B 2.6e-116)
     (* 180.0 (/ (atan (/ C B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.5e-164) {
		tmp = 180.0 * (atan((1.0 - (A / B))) / ((double) M_PI));
	} else if (B <= 2.6e-116) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5.5e-164) {
		tmp = 180.0 * (Math.atan((1.0 - (A / B))) / Math.PI);
	} else if (B <= 2.6e-116) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5.5e-164:
		tmp = 180.0 * (math.atan((1.0 - (A / B))) / math.pi)
	elif B <= 2.6e-116:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5.5e-164)
		tmp = Float64(180.0 * Float64(atan(Float64(1.0 - Float64(A / B))) / pi));
	elseif (B <= 2.6e-116)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5.5e-164)
		tmp = 180.0 * (atan((1.0 - (A / B))) / pi);
	elseif (B <= 2.6e-116)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5.5e-164], N[(180.0 * N[(N[ArcTan[N[(1.0 - N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.6e-116], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -5.50000000000000027e-164

   1. Initial program 55.2%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 77.5

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

   5. Applied rewrites 77.5%

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

   6. Taylor expanded in C around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 69.6

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

   8. Applied rewrites 69.6%

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

   if -5.50000000000000027e-164 < B < 2.6e-116

   1. Initial program 61.4%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}}{\pi} \]
   4. 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 46.8

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

   5. Applied rewrites 46.8%

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

   6. Taylor expanded in C around inf

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

      1. lift-/.f64 41.0

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

   8. Applied rewrites 41.0%

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

   if 2.6e-116 < B

   1. Initial program 49.9%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 54.3%

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

Alternative 8: 46.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -1.18 \cdot 10^{-55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-116}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -1.18e-55)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 2.6e-116)
     (* 180.0 (/ (atan (/ C B)) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.18e-55) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 2.6e-116) {
		tmp = 180.0 * (atan((C / B)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -1.18e-55) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 2.6e-116) {
		tmp = 180.0 * (Math.atan((C / B)) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -1.18e-55:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 2.6e-116:
		tmp = 180.0 * (math.atan((C / B)) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -1.18e-55)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 2.6e-116)
		tmp = Float64(180.0 * Float64(atan(Float64(C / B)) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -1.18e-55)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 2.6e-116)
		tmp = 180.0 * (atan((C / B)) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -1.18e-55], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 2.6e-116], N[(180.0 * N[(N[ArcTan[N[(C / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -1.18e-55

   1. Initial program 52.4%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 57.3%

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

   if -1.18e-55 < B < 2.6e-116

   1. Initial program 62.9%

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

   3. Taylor expanded in B around inf

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\frac{C}{B} - \left(1 + \frac{A}{B}\right)\right)}}{\pi} \]
   4. 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 49.0

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

   5. Applied rewrites 49.0%

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

   6. Taylor expanded in C around inf

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

      1. lift-/.f64 40.7

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

   8. Applied rewrites 40.7%

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

   if 2.6e-116 < B

   1. Initial program 49.9%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 54.3%

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

Alternative 9: 44.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -4.6 \cdot 10^{-178}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.8 \cdot 10^{-153}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 0}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -4.6e-178)
   (* 180.0 (/ (atan 1.0) PI))
   (if (<= B 1.8e-153)
     (* 180.0 (/ (atan 0.0) PI))
     (* 180.0 (/ (atan -1.0) PI)))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.6e-178) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else if (B <= 1.8e-153) {
		tmp = 180.0 * (atan(0.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -4.6e-178) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else if (B <= 1.8e-153) {
		tmp = 180.0 * (Math.atan(0.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -4.6e-178:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	elif B <= 1.8e-153:
		tmp = 180.0 * (math.atan(0.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -4.6e-178)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	elseif (B <= 1.8e-153)
		tmp = Float64(180.0 * Float64(atan(0.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -4.6e-178)
		tmp = 180.0 * (atan(1.0) / pi);
	elseif (B <= 1.8e-153)
		tmp = 180.0 * (atan(0.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -4.6e-178], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[B, 1.8e-153], N[(180.0 * N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -4.59999999999999989e-178

   1. Initial program 56.1%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 51.0%

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

   if -4.59999999999999989e-178 < B < 1.7999999999999999e-153

   1. Initial program 59.7%

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

   3. Taylor expanded in C around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. distribute-rgt1-in N/A

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

      5. metadata-eval N/A

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

      6. lower-*.f64 33.8

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

   5. Applied rewrites 33.8%

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

   6. Taylor expanded in A around 0

      \[\leadsto 180 \cdot \frac{\tan^{-1} 0}{\pi} \]
   7. Step-by-step derivation

   8. Applied rewrites 33.8%

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

   if 1.7999999999999999e-153 < B

   1. Initial program 51.0%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 52.7%

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

Alternative 10: 39.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -5 \cdot 10^{-310}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -5e-310) (* 180.0 (/ (atan 1.0) PI)) (* 180.0 (/ (atan -1.0) PI))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = 180.0 * (atan(1.0) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(-1.0) / ((double) M_PI));
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -5e-310) {
		tmp = 180.0 * (Math.atan(1.0) / Math.PI);
	} else {
		tmp = 180.0 * (Math.atan(-1.0) / Math.PI);
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -5e-310:
		tmp = 180.0 * (math.atan(1.0) / math.pi)
	else:
		tmp = 180.0 * (math.atan(-1.0) / math.pi)
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -5e-310)
		tmp = Float64(180.0 * Float64(atan(1.0) / pi));
	else
		tmp = Float64(180.0 * Float64(atan(-1.0) / pi));
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -5e-310)
		tmp = 180.0 * (atan(1.0) / pi);
	else
		tmp = 180.0 * (atan(-1.0) / pi);
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -5e-310], N[(180.0 * N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 * N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < -4.999999999999985e-310

   1. Initial program 56.8%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 40.7%

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

   if -4.999999999999985e-310 < B

   1. Initial program 53.8%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 41.0%

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

Alternative 11: 20.8% accurate, 3.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 55.2%

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

3. Taylor expanded in B around inf

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

5. Applied rewrites 22.9%

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

Reproduce

herbie shell --seed 2025082 
(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)))