ABCF->ab-angle angle

Percentage Accurate: 54.0% → 71.1%

Time: 11.4s

Alternatives: 12

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.0% 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: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(C - A\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right) \cdot \frac{1}{B}\\ \mathbf{if}\;t\_0 \leq -0.1:\\ \;\;\;\;\frac{\tan^{-1} t\_0}{\pi} \cdot 180\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (- (- C A) (sqrt (+ (pow B 2.0) (pow (- A C) 2.0)))) (/ 1.0 B))))
   (if (<= t_0 -0.1)
     (* (/ (atan t_0) PI) 180.0)
     (if (<= t_0 0.0)
       (* (atan (* -0.5 (/ B (- C A)))) (/ 180.0 PI))
       (* (/ (atan (+ (/ (- C A) B) 1.0)) PI) 180.0)))))

C

double code(double A, double B, double C) {
	double t_0 = ((C - A) - sqrt((pow(B, 2.0) + pow((A - C), 2.0)))) * (1.0 / B);
	double tmp;
	if (t_0 <= -0.1) {
		tmp = (atan(t_0) / ((double) M_PI)) * 180.0;
	} else if (t_0 <= 0.0) {
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = (atan((((C - A) / B) + 1.0)) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = ((C - A) - Math.sqrt((Math.pow(B, 2.0) + Math.pow((A - C), 2.0)))) * (1.0 / B);
	double tmp;
	if (t_0 <= -0.1) {
		tmp = (Math.atan(t_0) / Math.PI) * 180.0;
	} else if (t_0 <= 0.0) {
		tmp = Math.atan((-0.5 * (B / (C - A)))) * (180.0 / Math.PI);
	} else {
		tmp = (Math.atan((((C - A) / B) + 1.0)) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = ((C - A) - math.sqrt((math.pow(B, 2.0) + math.pow((A - C), 2.0)))) * (1.0 / B)
	tmp = 0
	if t_0 <= -0.1:
		tmp = (math.atan(t_0) / math.pi) * 180.0
	elif t_0 <= 0.0:
		tmp = math.atan((-0.5 * (B / (C - A)))) * (180.0 / math.pi)
	else:
		tmp = (math.atan((((C - A) / B) + 1.0)) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(Float64(C - A) - sqrt(Float64((B ^ 2.0) + (Float64(A - C) ^ 2.0)))) * Float64(1.0 / B))
	tmp = 0.0
	if (t_0 <= -0.1)
		tmp = Float64(Float64(atan(t_0) / pi) * 180.0);
	elseif (t_0 <= 0.0)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) / B) + 1.0)) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = ((C - A) - sqrt(((B ^ 2.0) + ((A - C) ^ 2.0)))) * (1.0 / B);
	tmp = 0.0;
	if (t_0 <= -0.1)
		tmp = (atan(t_0) / pi) * 180.0;
	elseif (t_0 <= 0.0)
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / pi);
	else
		tmp = (atan((((C - A) / B) + 1.0)) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[B, 2.0], $MachinePrecision] + N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 / B), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.1], N[(N[(N[ArcTan[t$95$0], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.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)))))) < -0.10000000000000001

   1. Initial program 63.2%

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

   if -0.10000000000000001 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 0.0

   1. Initial program 14.4%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 14.4

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 14.4

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

   4. Applied rewrites 14.4%

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

   5. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 56.8

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

   7. Applied rewrites 56.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-/.f64 N/A

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

      5. div-inv N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 56.9

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

   9. Applied rewrites 56.9%

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

   10. Taylor expanded in B around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower-/.f64 N/A

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

       4. lower--.f64 99.6

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

   12. Applied rewrites 99.6%

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

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

   1. Initial program 60.6%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 80.3

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

   5. Applied rewrites 80.3%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(C - A\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right) \cdot \frac{1}{B} \leq -0.1:\\ \;\;\;\;\frac{\tan^{-1} \left(\left(\left(C - A\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right) \cdot \frac{1}{B}\right)}{\pi} \cdot 180\\ \mathbf{elif}\;\left(\left(C - A\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right) \cdot \frac{1}{B} \leq 0:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi} \cdot 180\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 68.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi} \cdot 180\\ t_1 := \left(\left(C - A\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right) \cdot \frac{1}{B}\\ \mathbf{if}\;t\_1 \leq -40000000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq -0.5:\\ \;\;\;\;\frac{\tan^{-1} -1}{\pi} \cdot 180\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0 (* (/ (atan (+ (/ (- C A) B) 1.0)) PI) 180.0))
        (t_1
         (* (- (- C A) (sqrt (+ (pow B 2.0) (pow (- A C) 2.0)))) (/ 1.0 B))))
   (if (<= t_1 -40000000000000.0)
     t_0
     (if (<= t_1 -0.5)
       (* (/ (atan -1.0) PI) 180.0)
       (if (<= t_1 0.0) (* (atan (* -0.5 (/ B (- C A)))) (/ 180.0 PI)) t_0)))))

C

double code(double A, double B, double C) {
	double t_0 = (atan((((C - A) / B) + 1.0)) / ((double) M_PI)) * 180.0;
	double t_1 = ((C - A) - sqrt((pow(B, 2.0) + pow((A - C), 2.0)))) * (1.0 / B);
	double tmp;
	if (t_1 <= -40000000000000.0) {
		tmp = t_0;
	} else if (t_1 <= -0.5) {
		tmp = (atan(-1.0) / ((double) M_PI)) * 180.0;
	} else if (t_1 <= 0.0) {
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double t_0 = (Math.atan((((C - A) / B) + 1.0)) / Math.PI) * 180.0;
	double t_1 = ((C - A) - Math.sqrt((Math.pow(B, 2.0) + Math.pow((A - C), 2.0)))) * (1.0 / B);
	double tmp;
	if (t_1 <= -40000000000000.0) {
		tmp = t_0;
	} else if (t_1 <= -0.5) {
		tmp = (Math.atan(-1.0) / Math.PI) * 180.0;
	} else if (t_1 <= 0.0) {
		tmp = Math.atan((-0.5 * (B / (C - A)))) * (180.0 / Math.PI);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(A, B, C):
	t_0 = (math.atan((((C - A) / B) + 1.0)) / math.pi) * 180.0
	t_1 = ((C - A) - math.sqrt((math.pow(B, 2.0) + math.pow((A - C), 2.0)))) * (1.0 / B)
	tmp = 0
	if t_1 <= -40000000000000.0:
		tmp = t_0
	elif t_1 <= -0.5:
		tmp = (math.atan(-1.0) / math.pi) * 180.0
	elif t_1 <= 0.0:
		tmp = math.atan((-0.5 * (B / (C - A)))) * (180.0 / math.pi)
	else:
		tmp = t_0
	return tmp

Julia

function code(A, B, C)
	t_0 = Float64(Float64(atan(Float64(Float64(Float64(C - A) / B) + 1.0)) / pi) * 180.0)
	t_1 = Float64(Float64(Float64(C - A) - sqrt(Float64((B ^ 2.0) + (Float64(A - C) ^ 2.0)))) * Float64(1.0 / B))
	tmp = 0.0
	if (t_1 <= -40000000000000.0)
		tmp = t_0;
	elseif (t_1 <= -0.5)
		tmp = Float64(Float64(atan(-1.0) / pi) * 180.0);
	elseif (t_1 <= 0.0)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) * Float64(180.0 / pi));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	t_0 = (atan((((C - A) / B) + 1.0)) / pi) * 180.0;
	t_1 = ((C - A) - sqrt(((B ^ 2.0) + ((A - C) ^ 2.0)))) * (1.0 / B);
	tmp = 0.0;
	if (t_1 <= -40000000000000.0)
		tmp = t_0;
	elseif (t_1 <= -0.5)
		tmp = (atan(-1.0) / pi) * 180.0;
	elseif (t_1 <= 0.0)
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / pi);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[B, 2.0], $MachinePrecision] + N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 / B), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -40000000000000.0], t$95$0, If[LessEqual[t$95$1, -0.5], N[(N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

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)))))) < -4e13 or 0.0 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64))))))

   1. Initial program 59.1%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 66.4

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

   5. Applied rewrites 66.4%

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

   if -4e13 < (*.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 100.0%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 100.0%

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

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

   1. Initial program 17.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 17.1

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 17.1

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

   4. Applied rewrites 17.1%

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

   5. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 55.0

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

   7. Applied rewrites 55.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-/.f64 N/A

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

      5. div-inv N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 55.0

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

   9. Applied rewrites 55.0%

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

   10. Taylor expanded in B around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower-/.f64 N/A

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

       4. lower--.f64 97.1

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

   12. Applied rewrites 97.1%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(C - A\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right) \cdot \frac{1}{B} \leq -40000000000000:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi} \cdot 180\\ \mathbf{elif}\;\left(\left(C - A\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right) \cdot \frac{1}{B} \leq -0.5:\\ \;\;\;\;\frac{\tan^{-1} -1}{\pi} \cdot 180\\ \mathbf{elif}\;\left(\left(C - A\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right) \cdot \frac{1}{B} \leq 0:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi} \cdot 180\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(C - A\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right) \cdot \frac{1}{B}\\ \mathbf{if}\;t\_0 \leq -0.1:\\ \;\;\;\;\left(\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}}{B}\right) \cdot \frac{1}{\pi}\right) \cdot 180\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (- (- C A) (sqrt (+ (pow B 2.0) (pow (- A C) 2.0)))) (/ 1.0 B))))
   (if (<= t_0 -0.1)
     (*
      (*
       (atan (/ (- (- C A) (sqrt (fma (- C A) (- C A) (* B B)))) B))
       (/ 1.0 PI))
      180.0)
     (if (<= t_0 0.0)
       (* (atan (* -0.5 (/ B (- C A)))) (/ 180.0 PI))
       (* (/ (atan (+ (/ (- C A) B) 1.0)) PI) 180.0)))))

C

double code(double A, double B, double C) {
	double t_0 = ((C - A) - sqrt((pow(B, 2.0) + pow((A - C), 2.0)))) * (1.0 / B);
	double tmp;
	if (t_0 <= -0.1) {
		tmp = (atan((((C - A) - sqrt(fma((C - A), (C - A), (B * B)))) / B)) * (1.0 / ((double) M_PI))) * 180.0;
	} else if (t_0 <= 0.0) {
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / ((double) M_PI));
	} else {
		tmp = (atan((((C - A) / B) + 1.0)) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Julia

function code(A, B, C)
	t_0 = Float64(Float64(Float64(C - A) - sqrt(Float64((B ^ 2.0) + (Float64(A - C) ^ 2.0)))) * Float64(1.0 / B))
	tmp = 0.0
	if (t_0 <= -0.1)
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) - sqrt(fma(Float64(C - A), Float64(C - A), Float64(B * B)))) / B)) * Float64(1.0 / pi)) * 180.0);
	elseif (t_0 <= 0.0)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) / B) + 1.0)) / pi) * 180.0);
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[B, 2.0], $MachinePrecision] + N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 / B), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.1], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[(C - A), $MachinePrecision] * N[(C - A), $MachinePrecision] + N[(B * B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(1.0 / Pi), $MachinePrecision]), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[t$95$0, 0.0], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.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)))))) < -0.10000000000000001

   1. Initial program 63.2%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 63.2

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 63.2

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

   4. Applied rewrites 63.2%

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

   if -0.10000000000000001 < (*.f64 (/.f64 #s(literal 1 binary64) B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) #s(literal 2 binary64)) (pow.f64 B #s(literal 2 binary64)))))) < 0.0

   1. Initial program 14.4%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 14.4

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 14.4

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

   4. Applied rewrites 14.4%

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

   5. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 56.8

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

   7. Applied rewrites 56.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-/.f64 N/A

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

      5. div-inv N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 56.9

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

   9. Applied rewrites 56.9%

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

   10. Taylor expanded in B around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower-/.f64 N/A

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

       4. lower--.f64 99.6

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

   12. Applied rewrites 99.6%

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

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

   1. Initial program 60.6%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 80.3

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

   5. Applied rewrites 80.3%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(C - A\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right) \cdot \frac{1}{B} \leq -0.1:\\ \;\;\;\;\left(\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\mathsf{fma}\left(C - A, C - A, B \cdot B\right)}}{B}\right) \cdot \frac{1}{\pi}\right) \cdot 180\\ \mathbf{elif}\;\left(\left(C - A\right) - \sqrt{{B}^{2} + {\left(A - C\right)}^{2}}\right) \cdot \frac{1}{B} \leq 0:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi} \cdot 180\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.85 \cdot 10^{-7}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 9.6 \cdot 10^{-150}:\\ \;\;\;\;\tan^{-1} \left(\frac{C - \sqrt{\mathsf{fma}\left(B, B, C \cdot C\right)}}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.85e-7)
   (* (atan (* -0.5 (/ B (- C A)))) (/ 180.0 PI))
   (if (<= A 9.6e-150)
     (* (atan (/ (- C (sqrt (fma B B (* C C)))) B)) (/ 180.0 PI))
     (* (/ (atan (+ (/ (- C A) B) 1.0)) PI) 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.85e-7) {
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / ((double) M_PI));
	} else if (A <= 9.6e-150) {
		tmp = atan(((C - sqrt(fma(B, B, (C * C)))) / B)) * (180.0 / ((double) M_PI));
	} else {
		tmp = (atan((((C - A) / B) + 1.0)) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.85e-7)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) * Float64(180.0 / pi));
	elseif (A <= 9.6e-150)
		tmp = Float64(atan(Float64(Float64(C - sqrt(fma(B, B, Float64(C * C)))) / B)) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) / B) + 1.0)) / pi) * 180.0);
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.85e-7], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9.6e-150], N[(N[ArcTan[N[(N[(C - N[Sqrt[N[(B * B + N[(C * C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.85000000000000002e-7

   1. Initial program 22.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 22.8

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 22.8

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

   4. Applied rewrites 22.8%

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

   5. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 68.4

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

   7. Applied rewrites 68.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-/.f64 N/A

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

      5. div-inv N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 68.4

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

   9. Applied rewrites 68.4%

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

   10. Taylor expanded in B around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower-/.f64 N/A

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

       4. lower--.f64 74.7

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

   12. Applied rewrites 74.7%

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

   if -1.85000000000000002e-7 < A < 9.6e-150

   1. Initial program 63.0%

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

   3. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-sqrt.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 61.9

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

   5. Applied rewrites 61.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. div-inv N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

   7. Applied rewrites 61.9%

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

   if 9.6e-150 < A

   1. Initial program 70.2%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 79.1

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

   5. Applied rewrites 79.1%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.85 \cdot 10^{-7}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 9.6 \cdot 10^{-150}:\\ \;\;\;\;\tan^{-1} \left(\frac{C - \sqrt{\mathsf{fma}\left(B, B, C \cdot C\right)}}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi} \cdot 180\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -1.85 \cdot 10^{-7}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 9.6 \cdot 10^{-150}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \sqrt{\mathsf{fma}\left(B, B, C \cdot C\right)}}{B}\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -1.85e-7)
   (* (atan (* -0.5 (/ B (- C A)))) (/ 180.0 PI))
   (if (<= A 9.6e-150)
     (* (/ (atan (/ (- C (sqrt (fma B B (* C C)))) B)) PI) 180.0)
     (* (/ (atan (+ (/ (- C A) B) 1.0)) PI) 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -1.85e-7) {
		tmp = atan((-0.5 * (B / (C - A)))) * (180.0 / ((double) M_PI));
	} else if (A <= 9.6e-150) {
		tmp = (atan(((C - sqrt(fma(B, B, (C * C)))) / B)) / ((double) M_PI)) * 180.0;
	} else {
		tmp = (atan((((C - A) / B) + 1.0)) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -1.85e-7)
		tmp = Float64(atan(Float64(-0.5 * Float64(B / Float64(C - A)))) * Float64(180.0 / pi));
	elseif (A <= 9.6e-150)
		tmp = Float64(Float64(atan(Float64(Float64(C - sqrt(fma(B, B, Float64(C * C)))) / B)) / pi) * 180.0);
	else
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) / B) + 1.0)) / pi) * 180.0);
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -1.85e-7], N[(N[ArcTan[N[(-0.5 * N[(B / N[(C - A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 9.6e-150], N[(N[(N[ArcTan[N[(N[(C - N[Sqrt[N[(B * B + N[(C * C), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -1.85000000000000002e-7

   1. Initial program 22.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 22.8

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 22.8

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

   4. Applied rewrites 22.8%

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

   5. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 68.4

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

   7. Applied rewrites 68.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-/.f64 N/A

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

      5. div-inv N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 68.4

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

   9. Applied rewrites 68.4%

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

   10. Taylor expanded in B around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower-/.f64 N/A

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

       4. lower--.f64 74.7

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

   12. Applied rewrites 74.7%

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

   if -1.85000000000000002e-7 < A < 9.6e-150

   1. Initial program 63.0%

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

   3. Taylor expanded in A around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-sqrt.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-fma.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 61.9

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

   5. Applied rewrites 61.9%

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

   if 9.6e-150 < A

   1. Initial program 70.2%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 79.1

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

   5. Applied rewrites 79.1%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -1.85 \cdot 10^{-7}:\\ \;\;\;\;\tan^{-1} \left(-0.5 \cdot \frac{B}{C - A}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 9.6 \cdot 10^{-150}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \sqrt{\mathsf{fma}\left(B, B, C \cdot C\right)}}{B}\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi} \cdot 180\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{-92}:\\ \;\;\;\;\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{+69}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.5e-92)
   (* (atan (* (/ B A) 0.5)) (/ 180.0 PI))
   (if (<= A 2.1e+69)
     (* (/ (atan (+ (/ C B) 1.0)) PI) 180.0)
     (* (/ (atan (* -2.0 (/ A B))) PI) 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e-92) {
		tmp = atan(((B / A) * 0.5)) * (180.0 / ((double) M_PI));
	} else if (A <= 2.1e+69) {
		tmp = (atan(((C / B) + 1.0)) / ((double) M_PI)) * 180.0;
	} else {
		tmp = (atan((-2.0 * (A / B))) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e-92) {
		tmp = Math.atan(((B / A) * 0.5)) * (180.0 / Math.PI);
	} else if (A <= 2.1e+69) {
		tmp = (Math.atan(((C / B) + 1.0)) / Math.PI) * 180.0;
	} else {
		tmp = (Math.atan((-2.0 * (A / B))) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.5e-92:
		tmp = math.atan(((B / A) * 0.5)) * (180.0 / math.pi)
	elif A <= 2.1e+69:
		tmp = (math.atan(((C / B) + 1.0)) / math.pi) * 180.0
	else:
		tmp = (math.atan((-2.0 * (A / B))) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.5e-92)
		tmp = Float64(atan(Float64(Float64(B / A) * 0.5)) * Float64(180.0 / pi));
	elseif (A <= 2.1e+69)
		tmp = Float64(Float64(atan(Float64(Float64(C / B) + 1.0)) / pi) * 180.0);
	else
		tmp = Float64(Float64(atan(Float64(-2.0 * Float64(A / B))) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.5e-92)
		tmp = atan(((B / A) * 0.5)) * (180.0 / pi);
	elseif (A <= 2.1e+69)
		tmp = (atan(((C / B) + 1.0)) / pi) * 180.0;
	else
		tmp = (atan((-2.0 * (A / B))) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.5e-92], N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], If[LessEqual[A, 2.1e+69], N[(N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.50000000000000067e-92

   1. Initial program 27.5%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 27.5

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 27.5

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

   4. Applied rewrites 27.5%

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

   5. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 60.1

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

   7. Applied rewrites 60.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-/.f64 N/A

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

      5. div-inv N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 60.1

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

   9. Applied rewrites 60.1%

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

   if -8.50000000000000067e-92 < A < 2.10000000000000015e69

   1. Initial program 60.3%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 59.4

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

   5. Applied rewrites 59.4%

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

   6. Taylor expanded in C around inf

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

   8. Applied rewrites 54.1%

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

   if 2.10000000000000015e69 < A

   1. Initial program 86.9%

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

   3. Taylor expanded in A around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 85.1

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

   5. Applied rewrites 85.1%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{-92}:\\ \;\;\;\;\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{+69}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi} \cdot 180\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi} \cdot 180\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{+69}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.5e-92)
   (* (/ (atan (* (/ B A) 0.5)) PI) 180.0)
   (if (<= A 2.1e+69)
     (* (/ (atan (+ (/ C B) 1.0)) PI) 180.0)
     (* (/ (atan (* -2.0 (/ A B))) PI) 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e-92) {
		tmp = (atan(((B / A) * 0.5)) / ((double) M_PI)) * 180.0;
	} else if (A <= 2.1e+69) {
		tmp = (atan(((C / B) + 1.0)) / ((double) M_PI)) * 180.0;
	} else {
		tmp = (atan((-2.0 * (A / B))) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e-92) {
		tmp = (Math.atan(((B / A) * 0.5)) / Math.PI) * 180.0;
	} else if (A <= 2.1e+69) {
		tmp = (Math.atan(((C / B) + 1.0)) / Math.PI) * 180.0;
	} else {
		tmp = (Math.atan((-2.0 * (A / B))) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.5e-92:
		tmp = (math.atan(((B / A) * 0.5)) / math.pi) * 180.0
	elif A <= 2.1e+69:
		tmp = (math.atan(((C / B) + 1.0)) / math.pi) * 180.0
	else:
		tmp = (math.atan((-2.0 * (A / B))) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.5e-92)
		tmp = Float64(Float64(atan(Float64(Float64(B / A) * 0.5)) / pi) * 180.0);
	elseif (A <= 2.1e+69)
		tmp = Float64(Float64(atan(Float64(Float64(C / B) + 1.0)) / pi) * 180.0);
	else
		tmp = Float64(Float64(atan(Float64(-2.0 * Float64(A / B))) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.5e-92)
		tmp = (atan(((B / A) * 0.5)) / pi) * 180.0;
	elseif (A <= 2.1e+69)
		tmp = (atan(((C / B) + 1.0)) / pi) * 180.0;
	else
		tmp = (atan((-2.0 * (A / B))) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.5e-92], N[(N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[A, 2.1e+69], N[(N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[(N[ArcTan[N[(-2.0 * N[(A / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if A < -8.50000000000000067e-92

   1. Initial program 27.5%

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

   3. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 60.0

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

   5. Applied rewrites 60.0%

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

   if -8.50000000000000067e-92 < A < 2.10000000000000015e69

   1. Initial program 60.3%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 59.4

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

   5. Applied rewrites 59.4%

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

   6. Taylor expanded in C around inf

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

   8. Applied rewrites 54.1%

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

   if 2.10000000000000015e69 < A

   1. Initial program 86.9%

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

   3. Taylor expanded in A around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 85.1

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

   5. Applied rewrites 85.1%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right)}{\pi} \cdot 180\\ \mathbf{elif}\;A \leq 2.1 \cdot 10^{+69}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi} \cdot 180\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{-92}:\\ \;\;\;\;\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= A -8.5e-92)
   (* (atan (* (/ B A) 0.5)) (/ 180.0 PI))
   (* (/ (atan (+ (/ (- C A) B) 1.0)) PI) 180.0)))

C

double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e-92) {
		tmp = atan(((B / A) * 0.5)) * (180.0 / ((double) M_PI));
	} else {
		tmp = (atan((((C - A) / B) + 1.0)) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (A <= -8.5e-92) {
		tmp = Math.atan(((B / A) * 0.5)) * (180.0 / Math.PI);
	} else {
		tmp = (Math.atan((((C - A) / B) + 1.0)) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if A <= -8.5e-92:
		tmp = math.atan(((B / A) * 0.5)) * (180.0 / math.pi)
	else:
		tmp = (math.atan((((C - A) / B) + 1.0)) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (A <= -8.5e-92)
		tmp = Float64(atan(Float64(Float64(B / A) * 0.5)) * Float64(180.0 / pi));
	else
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) / B) + 1.0)) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (A <= -8.5e-92)
		tmp = atan(((B / A) * 0.5)) * (180.0 / pi);
	else
		tmp = (atan((((C - A) / B) + 1.0)) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[A, -8.5e-92], N[(N[ArcTan[N[(N[(B / A), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -8.50000000000000067e-92

   1. Initial program 27.5%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 27.5

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-/.f64 N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 27.5

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

   4. Applied rewrites 27.5%

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

   5. Taylor expanded in A around -inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 60.1

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

   7. Applied rewrites 60.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift-/.f64 N/A

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

      5. div-inv N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 60.1

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

   9. Applied rewrites 60.1%

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

   if -8.50000000000000067e-92 < A

   1. Initial program 68.7%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 68.9

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

   5. Applied rewrites 68.9%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -8.5 \cdot 10^{-92}:\\ \;\;\;\;\tan^{-1} \left(\frac{B}{A} \cdot 0.5\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - A}{B} + 1\right)}{\pi} \cdot 180\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 7 \cdot 10^{-9}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} -1}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 7e-9)
   (* (/ (atan (+ (/ C B) 1.0)) PI) 180.0)
   (* (/ (atan -1.0) PI) 180.0)))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 7e-9) {
		tmp = (atan(((C / B) + 1.0)) / ((double) M_PI)) * 180.0;
	} else {
		tmp = (atan(-1.0) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 7e-9) {
		tmp = (Math.atan(((C / B) + 1.0)) / Math.PI) * 180.0;
	} else {
		tmp = (Math.atan(-1.0) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 7e-9:
		tmp = (math.atan(((C / B) + 1.0)) / math.pi) * 180.0
	else:
		tmp = (math.atan(-1.0) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 7e-9)
		tmp = Float64(Float64(atan(Float64(Float64(C / B) + 1.0)) / pi) * 180.0);
	else
		tmp = Float64(Float64(atan(-1.0) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 7e-9)
		tmp = (atan(((C / B) + 1.0)) / pi) * 180.0;
	else
		tmp = (atan(-1.0) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 7e-9], N[(N[(N[ArcTan[N[(N[(C / B), $MachinePrecision] + 1.0), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 6.9999999999999998e-9

   1. Initial program 61.6%

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

   3. Taylor expanded in B around -inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 68.7

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

   5. Applied rewrites 68.7%

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

   6. Taylor expanded in C around inf

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

   8. Applied rewrites 51.9%

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

   if 6.9999999999999998e-9 < B

   1. Initial program 43.6%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 58.8%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 7 \cdot 10^{-9}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C}{B} + 1\right)}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} -1}{\pi} \cdot 180\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq -2.8 \cdot 10^{-70}:\\ \;\;\;\;\frac{\tan^{-1} 1}{\pi} \cdot 180\\ \mathbf{elif}\;B \leq 1.28 \cdot 10^{-146}:\\ \;\;\;\;\frac{\tan^{-1} 0}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} -1}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B -2.8e-70)
   (* (/ (atan 1.0) PI) 180.0)
   (if (<= B 1.28e-146)
     (* (/ (atan 0.0) PI) 180.0)
     (* (/ (atan -1.0) PI) 180.0))))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.8e-70) {
		tmp = (atan(1.0) / ((double) M_PI)) * 180.0;
	} else if (B <= 1.28e-146) {
		tmp = (atan(0.0) / ((double) M_PI)) * 180.0;
	} else {
		tmp = (atan(-1.0) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= -2.8e-70) {
		tmp = (Math.atan(1.0) / Math.PI) * 180.0;
	} else if (B <= 1.28e-146) {
		tmp = (Math.atan(0.0) / Math.PI) * 180.0;
	} else {
		tmp = (Math.atan(-1.0) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= -2.8e-70:
		tmp = (math.atan(1.0) / math.pi) * 180.0
	elif B <= 1.28e-146:
		tmp = (math.atan(0.0) / math.pi) * 180.0
	else:
		tmp = (math.atan(-1.0) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= -2.8e-70)
		tmp = Float64(Float64(atan(1.0) / pi) * 180.0);
	elseif (B <= 1.28e-146)
		tmp = Float64(Float64(atan(0.0) / pi) * 180.0);
	else
		tmp = Float64(Float64(atan(-1.0) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= -2.8e-70)
		tmp = (atan(1.0) / pi) * 180.0;
	elseif (B <= 1.28e-146)
		tmp = (atan(0.0) / pi) * 180.0;
	else
		tmp = (atan(-1.0) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, -2.8e-70], N[(N[(N[ArcTan[1.0], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], If[LessEqual[B, 1.28e-146], N[(N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if B < -2.7999999999999999e-70

   1. Initial program 50.7%

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

   3. Taylor expanded in B around -inf

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

   5. Applied rewrites 56.9%

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

   if -2.7999999999999999e-70 < B < 1.27999999999999992e-146

   1. Initial program 62.7%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 28.6

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

   5. Applied rewrites 28.6%

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

   if 1.27999999999999992e-146 < B

   1. Initial program 55.7%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 50.2%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -2.8 \cdot 10^{-70}:\\ \;\;\;\;\frac{\tan^{-1} 1}{\pi} \cdot 180\\ \mathbf{elif}\;B \leq 1.28 \cdot 10^{-146}:\\ \;\;\;\;\frac{\tan^{-1} 0}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} -1}{\pi} \cdot 180\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 1.28 \cdot 10^{-146}:\\ \;\;\;\;\frac{\tan^{-1} 0}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} -1}{\pi} \cdot 180\\ \end{array} \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (if (<= B 1.28e-146)
   (* (/ (atan 0.0) PI) 180.0)
   (* (/ (atan -1.0) PI) 180.0)))

C

double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.28e-146) {
		tmp = (atan(0.0) / ((double) M_PI)) * 180.0;
	} else {
		tmp = (atan(-1.0) / ((double) M_PI)) * 180.0;
	}
	return tmp;
}

Java

public static double code(double A, double B, double C) {
	double tmp;
	if (B <= 1.28e-146) {
		tmp = (Math.atan(0.0) / Math.PI) * 180.0;
	} else {
		tmp = (Math.atan(-1.0) / Math.PI) * 180.0;
	}
	return tmp;
}

Python

def code(A, B, C):
	tmp = 0
	if B <= 1.28e-146:
		tmp = (math.atan(0.0) / math.pi) * 180.0
	else:
		tmp = (math.atan(-1.0) / math.pi) * 180.0
	return tmp

Julia

function code(A, B, C)
	tmp = 0.0
	if (B <= 1.28e-146)
		tmp = Float64(Float64(atan(0.0) / pi) * 180.0);
	else
		tmp = Float64(Float64(atan(-1.0) / pi) * 180.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(A, B, C)
	tmp = 0.0;
	if (B <= 1.28e-146)
		tmp = (atan(0.0) / pi) * 180.0;
	else
		tmp = (atan(-1.0) / pi) * 180.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[A_, B_, C_] := If[LessEqual[B, 1.28e-146], N[(N[(N[ArcTan[0.0], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision], N[(N[(N[ArcTan[-1.0], $MachinePrecision] / Pi), $MachinePrecision] * 180.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if B < 1.27999999999999992e-146

   1. Initial program 57.2%

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

   3. Taylor expanded in C around inf

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

      1. distribute-rgt1-in N/A

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

      2. metadata-eval N/A

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

      3. mul0-lft N/A

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

      4. div0 N/A

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

      5. metadata-eval 17.1

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

   5. Applied rewrites 17.1%

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

   if 1.27999999999999992e-146 < B

   1. Initial program 55.7%

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

   3. Taylor expanded in B around inf

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

   5. Applied rewrites 50.2%

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

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 1.28 \cdot 10^{-146}:\\ \;\;\;\;\frac{\tan^{-1} 0}{\pi} \cdot 180\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan^{-1} -1}{\pi} \cdot 180\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 21.2% accurate, 3.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.6%

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

3. Taylor expanded in B around inf

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

5. Applied rewrites 22.1%

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

6. Final simplification 22.1%

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

Reproduce

herbie shell --seed 2024235 
(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)))