Average Error: 29.2 → 24.6
Time: 7.3s
Precision: binary64
\[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\]
↓
\[\begin{array}{l} \mathbf{if}\;B \leq 4.04821618885358 \cdot 10^{+155}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array}\]
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}\;B \leq 4.04821618885358 \cdot 10^{+155}:\\
\;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}}{B}\right)}{\pi}\\

\mathbf{else}:\\
\;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{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 (<= B 4.04821618885358e+155)
   (/
    (* 180.0 (atan (/ (- (- C A) (sqrt (+ (pow (- A C) 2.0) (* B B)))) B)))
    PI)
   (/ (* 180.0 (atan (/ (- C (+ B 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 (B <= 4.04821618885358e+155) {
		tmp = (180.0 * atan(((C - A) - sqrt(pow((A - C), 2.0) + (B * B))) / B)) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan((C - (B + 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 2 regimes

  2. if B < 4.04821618885358008e155

    1. Initial program 26.8

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

    2. Simplified26.8

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

    4. Applied associate-*r/_binary64_172526.8

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

    if 4.04821618885358008e155 < B

    1. Initial program 47.3

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

    2. Simplified47.3

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

    4. Applied associate--l-_binary64_172147.3

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

    6. Applied associate-*r/_binary64_172547.3

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

    7. Taylor expanded around 0 7.8

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

  4. Final simplification24.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq 4.04821618885358 \cdot 10^{+155}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(B + A\right)}{B}\right)}{\pi}\\ \end{array}\]

Reproduce

herbie shell --seed 2020349 
(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)))