Average Error: 29.6 → 18.1
Time: 9.8s
Precision: binary64
\[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
↓
\[\begin{array}{l} t_0 := \frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\\ \mathbf{if}\;t_0 \leq -0.99999999853945:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;t_0 \leq 3.567253752474156 \cdot 10^{-5}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot \frac{B \cdot B}{A}}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\left(180 \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\right) \cdot \frac{1}{\pi}\\ \end{array} \]
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}
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 -0.99999999853945:\\
\;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\

\mathbf{elif}\;t_0 \leq 3.567253752474156 \cdot 10^{-5}:\\
\;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot \frac{B \cdot B}{A}}{B}\right)}{\pi}\\

\mathbf{else}:\\
\;\;\;\;\left(180 \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\right) \cdot \frac{1}{\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
 (let* ((t_0
         (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))))
   (if (<= t_0 -0.99999999853945)
     (* 180.0 (/ (atan (/ (- C (+ B A)) B)) PI))
     (if (<= t_0 3.567253752474156e-5)
       (* 180.0 (/ (atan (/ (* 0.5 (/ (* B B) A)) B)) PI))
       (* (* 180.0 (atan (/ (- (+ B C) A) B))) (/ 1.0 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 t_0 = (1.0 / B) * ((C - A) - sqrt(pow((A - C), 2.0) + pow(B, 2.0)));
	double tmp;
	if (t_0 <= -0.99999999853945) {
		tmp = 180.0 * (atan((C - (B + A)) / B) / ((double) M_PI));
	} else if (t_0 <= 3.567253752474156e-5) {
		tmp = 180.0 * (atan((0.5 * ((B * B) / A)) / B) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((B + C) - A) / B)) * (1.0 / ((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))))) < -0.999999998539449986

    1. Initial program 26.2

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

    2. Simplified26.2

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

    4. Applied associate--l-_binary6426.2

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

    5. Simplified26.2

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

    7. Applied *-un-lft-identity_binary6426.2

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

    8. Applied *-un-lft-identity_binary6426.2

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

    9. Applied times-frac_binary6426.2

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

    10. Simplified26.2

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

    11. Taylor expanded around inf 14.9

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

    if -0.999999998539449986 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 3.567253752474156e-5

    1. Initial program 50.8

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

    2. Simplified50.8

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

    3. Taylor expanded around -inf 38.5

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

    4. Simplified38.5

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

    if 3.567253752474156e-5 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

    1. Initial program 25.9

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

    2. Simplified25.9

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

    3. Taylor expanded around -inf 14.6

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

    4. Simplified14.6

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

    6. Applied div-inv_binary6414.6

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

    7. Applied associate-*r*_binary6414.6

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

    8. Simplified14.6

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

  4. Final simplification18.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.99999999853945:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 3.567253752474156 \cdot 10^{-5}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0.5 \cdot \frac{B \cdot B}{A}}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\left(180 \cdot \tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)\right) \cdot \frac{1}{\pi}\\ \end{array} \]

Reproduce

herbie shell --seed 2021205 
(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)))