Average Error: 30.3 → 18.7
Time: 13.2s
Precision: binary64
\[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.9999999999938105:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 5.411022703613558 \cdot 10^{-10}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \frac{{B}^{2}}{C}}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \end{array}\]
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 -0.9999999999938105:\\
\;\;\;\;\frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\frac{\pi}{180}}\\

\mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 5.411022703613558 \cdot 10^{-10}:\\
\;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \frac{{B}^{2}}{C}}{B}\right)}{\pi}\\

\mathbf{else}:\\
\;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\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)))))
      -0.9999999999938105)
   (/ (atan (/ (- C (+ B A)) B)) (/ PI 180.0))
   (if (<=
        (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))
        5.411022703613558e-10)
     (* 180.0 (/ (atan (/ (* -0.5 (/ (pow B 2.0) C)) B)) PI))
     (* 180.0 (/ (atan (/ (- (+ B C) A) B)) 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)))) <= -0.9999999999938105) {
		tmp = atan((C - (B + A)) / B) / (((double) M_PI) / 180.0);
	} else if (((1.0 / B) * ((C - A) - sqrt(pow((A - C), 2.0) + pow(B, 2.0)))) <= 5.411022703613558e-10) {
		tmp = 180.0 * (atan((-0.5 * (pow(B, 2.0) / C)) / B) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan(((B + C) - A) / B) / ((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))))) < -0.99999999999381051

    1. Initial program 26.9

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

    2. Simplified26.9

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

    3. Taylor expanded around inf 15.5

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

    5. Applied associate-*r/_binary64_445315.5

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

    6. Simplified15.5

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

    8. Applied associate-/l*_binary64_445615.5

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

    if -0.99999999999381051 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 5.4110227036135582e-10

    1. Initial program 51.1

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

    2. Simplified51.1

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

    3. Taylor expanded around inf 38.8

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

    if 5.4110227036135582e-10 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

    1. Initial program 26.9

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

    2. Simplified26.9

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

    3. Taylor expanded around -inf 15.4

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

  4. Final simplification18.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.9999999999938105:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\frac{\pi}{180}}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 5.411022703613558 \cdot 10^{-10}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-0.5 \cdot \frac{{B}^{2}}{C}}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\pi}\\ \end{array}\]

Reproduce

herbie shell --seed 2021093 
(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)))