Average Error: 28.9 → 16.1
Time: 10.7s
Precision: binary64
\[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.999999968075197:\\ \;\;\;\;\left(180 \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\right) \cdot \frac{1}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 6.889790926715526 \cdot 10^{-76}:\\ \;\;\;\;\frac{1}{\pi} \cdot \left(180 \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\left(A \cdot A + C \cdot C\right) - 2 \cdot \left(C \cdot A\right)}\right)}{B} - 0.5 \cdot \left(B \cdot \sqrt{\frac{1}{\left(A \cdot A + C \cdot C\right) - 2 \cdot \left(C \cdot A\right)}}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B + \left(C - A\right)\right)\right)}{\pi}\\ \end{array}\]
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}
\mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.999999968075197:\\
\;\;\;\;\left(180 \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\right) \cdot \frac{1}{\pi}\\

\mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 6.889790926715526 \cdot 10^{-76}:\\
\;\;\;\;\frac{1}{\pi} \cdot \left(180 \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\left(A \cdot A + C \cdot C\right) - 2 \cdot \left(C \cdot A\right)}\right)}{B} - 0.5 \cdot \left(B \cdot \sqrt{\frac{1}{\left(A \cdot A + C \cdot C\right) - 2 \cdot \left(C \cdot A\right)}}\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B + \left(C - A\right)\right)\right)}{\pi}\\

\end{array}
(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
 (if (<=
      (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))
      -0.999999968075197)
   (* (* 180.0 (atan (/ (- C (+ B A)) B))) (/ 1.0 PI))
   (if (<=
        (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))
        6.889790926715526e-76)
     (*
      (/ 1.0 PI)
      (*
       180.0
       (atan
        (-
         (/ (- C (+ A (sqrt (- (+ (* A A) (* C C)) (* 2.0 (* C A)))))) B)
         (*
          0.5
          (* B (sqrt (/ 1.0 (- (+ (* A A) (* C C)) (* 2.0 (* C A)))))))))))
     (* 180.0 (/ (atan (* (/ 1.0 B) (+ B (- C A)))) PI)))))
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 tmp;
	if (((1.0 / B) * ((C - A) - sqrt(pow((A - C), 2.0) + pow(B, 2.0)))) <= -0.999999968075197) {
		tmp = (180.0 * atan((C - (B + A)) / B)) * (1.0 / ((double) M_PI));
	} else if (((1.0 / B) * ((C - A) - sqrt(pow((A - C), 2.0) + pow(B, 2.0)))) <= 6.889790926715526e-76) {
		tmp = (1.0 / ((double) M_PI)) * (180.0 * atan(((C - (A + sqrt(((A * A) + (C * C)) - (2.0 * (C * A))))) / B) - (0.5 * (B * sqrt(1.0 / (((A * A) + (C * C)) - (2.0 * (C * A))))))));
	} else {
		tmp = 180.0 * (atan((1.0 / B) * (B + (C - A))) / ((double) M_PI));
	}
	return tmp;
}

Error

Bits error versus A

Bits error versus B

Bits error versus C

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.99999996807519698

    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. Using strategy rm

    3. Applied div-inv_binary6426.0

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

    4. Applied associate-*r*_binary6426.0

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

    5. Simplified26.0

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

    6. Taylor expanded around inf 15.1

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

    if -0.99999996807519698 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 6.8897909267155259e-76

    1. Initial program 51.7

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

    3. Applied div-inv_binary6451.7

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

    4. Applied associate-*r*_binary6451.7

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

    5. Simplified51.7

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

    6. Taylor expanded around 0 61.1

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

    7. Simplified26.2

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

    if 6.8897909267155259e-76 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

    1. Initial program 25.0

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

    2. Taylor expanded around -inf 14.1

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

    3. Simplified14.1

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

  4. Final simplification16.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.999999968075197:\\ \;\;\;\;\left(180 \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)\right) \cdot \frac{1}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 6.889790926715526 \cdot 10^{-76}:\\ \;\;\;\;\frac{1}{\pi} \cdot \left(180 \cdot \tan^{-1} \left(\frac{C - \left(A + \sqrt{\left(A \cdot A + C \cdot C\right) - 2 \cdot \left(C \cdot A\right)}\right)}{B} - 0.5 \cdot \left(B \cdot \sqrt{\frac{1}{\left(A \cdot A + C \cdot C\right) - 2 \cdot \left(C \cdot A\right)}}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B + \left(C - A\right)\right)\right)}{\pi}\\ \end{array}\]

Alternatives

Reproduce

herbie shell --seed 2021118 
(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)))