ABCF->ab-angle angle

Average Error: 29.5 → 12.4

Time: 20.9s

Precision: binary64

Cost: 67465

Math

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

↓

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

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)))

↓

(FPCore (A B C)
 :precision binary64
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (or (<= t_0 -0.5) (not (<= t_0 0.0)))
     (* (atan (/ (- (- C A) (hypot B (- A C))) B)) (/ 180.0 PI))
     (/
      180.0
      (/
       PI
       (atan
        (/
         (fma -0.5 (/ (+ (* B B) (- (* A A) (pow (- A) 2.0))) C) (* A 0.0))
         B)))))))

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));
}

↓

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

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

↓

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

↓

code[A_, B_, C_] := Block[{t$95$0 = N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -0.5], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] * N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision], N[(180.0 / N[(Pi / N[ArcTan[N[(N[(-0.5 * N[(N[(N[(B * B), $MachinePrecision] + N[(N[(A * A), $MachinePrecision] - N[Power[(-A), 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / C), $MachinePrecision] + N[(A * 0.0), $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.5 or -0.0 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 26.0

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

   2. Simplified 8.2

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

      [Start] 26.0	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 26.0	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 26.0	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      *-commutative [=>] 26.0	\[ \color{blue}{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right) \cdot \frac{180}{\pi}} \]
      associate-*l/ [=>] 26.0	\[ \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \cdot \frac{180}{\pi} \]
      *-lft-identity [=>] 26.0	\[ \tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}}}{B}\right) \cdot \frac{180}{\pi} \]
      +-commutative [=>] 26.0	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{{B}^{2} + {\left(A - C\right)}^{2}}}}{B}\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 26.0	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{\color{blue}{B \cdot B} + {\left(A - C\right)}^{2}}}{B}\right) \cdot \frac{180}{\pi} \]
      unpow2 [=>] 26.0	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{B \cdot B + \color{blue}{\left(A - C\right) \cdot \left(A - C\right)}}}{B}\right) \cdot \frac{180}{\pi} \]
      hypot-def [=>] 8.2	\[ \tan^{-1} \left(\frac{\left(C - A\right) - \color{blue}{\mathsf{hypot}\left(B, A - C\right)}}{B}\right) \cdot \frac{180}{\pi} \]

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

   1. Initial program 51.8

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

   2. Simplified 55.1

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

      [Start] 51.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 51.8	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 51.8	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      associate-*l/ [=>] 51.8	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

   3. Applied egg-rr 50.9

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

   4. Taylor expanded in C around inf 42.3

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\color{blue}{-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C} + -1 \cdot \left(A + -1 \cdot A\right)}}{B}\right)}} \]

   5. Simplified 39.2

      \[\leadsto \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\color{blue}{\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{C}, -0 \cdot A\right)}}{B}\right)}} \]
      Proof

      [Start] 42.3	\[ \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C} + -1 \cdot \left(A + -1 \cdot A\right)}{B}\right)}} \]
      fma-def [=>] 42.3	\[ \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\color{blue}{\mathsf{fma}\left(-0.5, \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}}{B}\right)}} \]
      associate--l+ [=>] 39.2	\[ \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{{B}^{2} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}} \]
      unpow2 [=>] 39.2	\[ \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{\color{blue}{B \cdot B} + \left({A}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}} \]
      unpow2 [=>] 39.2	\[ \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(\color{blue}{A \cdot A} - {\left(-1 \cdot A\right)}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}} \]
      mul-1-neg [=>] 39.2	\[ \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\color{blue}{\left(-A\right)}}^{2}\right)}{C}, -1 \cdot \left(A + -1 \cdot A\right)\right)}{B}\right)}} \]
      mul-1-neg [=>] 39.2	\[ \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{C}, \color{blue}{-\left(A + -1 \cdot A\right)}\right)}{B}\right)}} \]
      distribute-rgt1-in [=>] 39.2	\[ \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{C}, -\color{blue}{\left(-1 + 1\right) \cdot A}\right)}{B}\right)}} \]
      metadata-eval [=>] 39.2	\[ \frac{180}{\frac{\pi}{\tan^{-1} \left(\frac{\mathsf{fma}\left(-0.5, \frac{B \cdot B + \left(A \cdot A - {\left(-A\right)}^{2}\right)}{C}, -\color{blue}{0} \cdot A\right)}{B}\right)}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 12.4

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

Alternatives

Alternative 1
Error	15.0
Cost	20429

\[\begin{array}{l} \mathbf{if}\;A \leq -2.6 \cdot 10^{+154}:\\ \;\;\;\;{\left(\frac{\pi}{\frac{\tan^{-1} \left(\frac{\frac{B}{2}}{A}\right)}{0.005555555555555556}}\right)}^{-1}\\ \mathbf{elif}\;A \leq -1.65 \cdot 10^{+89} \lor \neg \left(A \leq -1.05 \cdot 10^{+20}\right):\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - \mathsf{hypot}\left(A - C, B\right)\right) - A}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A}{\frac{C}{A}}}\right)\right)}{\pi}\\ \end{array} \]

Alternative 2
Error	12.2
Cost	20429

\[\begin{array}{l} \mathbf{if}\;A \leq -2.15 \cdot 10^{+154}:\\ \;\;\;\;{\left(\frac{\pi}{\frac{\tan^{-1} \left(\frac{\frac{B}{2}}{A}\right)}{0.005555555555555556}}\right)}^{-1}\\ \mathbf{elif}\;A \leq -1.6 \cdot 10^{+89} \lor \neg \left(A \leq -4.8 \cdot 10^{+21}\right):\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A}{\frac{C}{A}}}\right)\right)}{\pi}\\ \end{array} \]

Alternative 3
Error	12.2
Cost	20428

\[\begin{array}{l} t_0 := \mathsf{hypot}\left(B, A - C\right)\\ \mathbf{if}\;A \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;{\left(\frac{\pi}{\frac{\tan^{-1} \left(\frac{\frac{B}{2}}{A}\right)}{0.005555555555555556}}\right)}^{-1}\\ \mathbf{elif}\;A \leq -2.1 \cdot 10^{+89}:\\ \;\;\;\;\tan^{-1} \left(\frac{\left(C - A\right) - t_0}{B}\right) \cdot \frac{180}{\pi}\\ \mathbf{elif}\;A \leq -1.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A}{\frac{C}{A}}}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + t_0\right)}{B}\right)\\ \end{array} \]

Alternative 4
Error	32.3
Cost	14368

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{if}\;B \leq -5.7 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.36 \cdot 10^{+92}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -7.3 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -7.4 \cdot 10^{-253}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3.1 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 6.3 \cdot 10^{-165}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 1.5 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2 \cdot 10^{-55}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 5
Error	32.3
Cost	14368

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{if}\;B \leq -5.7 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.36 \cdot 10^{+92}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -5.2 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.4 \cdot 10^{-250}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3.5 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2.6 \cdot 10^{-150}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{elif}\;B \leq 9.2 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 2.8 \cdot 10^{-56}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 6
Error	32.3
Cost	14368

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ \mathbf{if}\;B \leq -5.7 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.36 \cdot 10^{+92}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -3.3 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.02 \cdot 10^{-249}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.1 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.7 \cdot 10^{-150}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{elif}\;B \leq 8 \cdot 10^{-64}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{A \cdot -2}{B}\right)\\ \mathbf{elif}\;B \leq 2.4 \cdot 10^{-55}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 7
Error	31.2
Cost	14368

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_1 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;B \leq -5.7 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.36 \cdot 10^{+92}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -15000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.75 \cdot 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -6.1 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -4.8 \cdot 10^{-254}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -4.5 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 1.35 \cdot 10^{-106}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	31.1
Cost	14368

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B - A}{B}\right)\\ t_1 := \frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\frac{\pi}{180}}\\ t_2 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{if}\;B \leq -5.7 \cdot 10^{+116}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.36 \cdot 10^{+92}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;B \leq -420:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.95 \cdot 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;B \leq -3.8 \cdot 10^{-179}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -1.72 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -3.1 \cdot 10^{-273}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 4.5 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	22.4
Cost	14088

\[\begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -4.1 \cdot 10^{-285}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.4 \cdot 10^{-151}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \left(\frac{B}{A} + \frac{B}{\frac{A}{\frac{C}{A}}}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + t_0\right)}{\pi}\\ \end{array} \]

Alternative 10
Error	27.5
Cost	13904

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{if}\;A \leq -1.18 \cdot 10^{+148}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -8.6 \cdot 10^{+89}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.9 \cdot 10^{-74}:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 5.8 \cdot 10^{+37}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)\\ \end{array} \]

Alternative 11
Error	27.6
Cost	13904

\[\begin{array}{l} t_0 := \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{B + C}{B}\right)\\ \mathbf{if}\;A \leq -5.4 \cdot 10^{+150}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq -6.2 \cdot 10^{+90}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;A \leq -1.25 \cdot 10^{-73}:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;A \leq 8 \cdot 10^{+41}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)\\ \end{array} \]

Alternative 12
Error	34.6
Cost	13840

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ t_1 := \frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{if}\;B \leq -2.1 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq -1.18 \cdot 10^{+92}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq -9.5 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;B \leq 8.5 \cdot 10^{-114}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 13
Error	25.5
Cost	13836

\[\begin{array}{l} t_0 := \frac{180 \cdot \tan^{-1} \left(1 + \frac{C - A}{B}\right)}{\pi}\\ \mathbf{if}\;B \leq -1.1 \cdot 10^{-284}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;B \leq 5.9 \cdot 10^{-151}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{elif}\;B \leq 2.25 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\left(-A\right) - B}{B}\right)\\ \end{array} \]

Alternative 14
Error	23.5
Cost	13704

\[\begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -3.1 \cdot 10^{-285}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 5.5 \cdot 10^{-151}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + t_0\right)}{\pi}\\ \end{array} \]

Alternative 15
Error	23.5
Cost	13704

\[\begin{array}{l} t_0 := \frac{C - A}{B}\\ \mathbf{if}\;B \leq -6.3 \cdot 10^{-285}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + t_0\right)}{\pi}\\ \mathbf{elif}\;B \leq 3.5 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{1}{\pi}}{\frac{0.005555555555555556}{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(-1 + t_0\right)}{\pi}\\ \end{array} \]

Alternative 16
Error	29.0
Cost	13576

\[\begin{array}{l} \mathbf{if}\;B \leq -6.5 \cdot 10^{-284}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(1 + \frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{\tan^{-1} \left(B \cdot \frac{0.5}{A}\right)}{\frac{\pi}{180}}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]

Alternative 17
Error	38.3
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-310}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 18
Error	50.4
Cost	13056

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

Reproduce

herbie shell --seed 2023083 
(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)))