Average Error: 29.3 → 22.4
Time: 6.5s
Precision: binary64
\[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\]
↓
\[\begin{array}{l} \mathbf{if}\;C \leq 5.039411572303443 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(\left(\frac{A}{C} + 1\right) \cdot \frac{B}{C}\right) \cdot -0.5\right)}{\pi}\\ \end{array}\]
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}\;C \leq 5.039411572303443 \cdot 10^{-27}:\\
\;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}}{B}\right)}{\pi}\\

\mathbf{else}:\\
\;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(\left(\frac{A}{C} + 1\right) \cdot \frac{B}{C}\right) \cdot -0.5\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 (<= C 5.039411572303443e-27)
   (*
    180.0
    (/ (atan (/ (- (- C A) (sqrt (+ (pow (- A C) 2.0) (* B B)))) B)) PI))
   (* 180.0 (/ (atan (* (* (+ (/ A C) 1.0) (/ B C)) -0.5)) 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 (C <= 5.039411572303443e-27) {
		tmp = 180.0 * (atan(((C - A) - sqrt(pow((A - C), 2.0) + (B * B))) / B) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((((A / C) + 1.0) * (B / C)) * -0.5) / ((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 C < 5.039411572303443e-27

    1. Initial program 22.9

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

    2. Simplified22.9

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

    if 5.039411572303443e-27 < C

    1. Initial program 46.5

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

    2. Simplified46.5

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

    3. Taylor expanded around inf 23.2

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

    4. Simplified21.1

      \[\leadsto 180 \cdot \frac{\tan^{-1} \color{blue}{\left(\left(\left(\frac{A}{C} + 1\right) \cdot \frac{B}{C}\right) \cdot -0.5\right)}}{\pi}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification22.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 5.039411572303443 \cdot 10^{-27}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\left(\left(\frac{A}{C} + 1\right) \cdot \frac{B}{C}\right) \cdot -0.5\right)}{\pi}\\ \end{array}\]

Reproduce

herbie shell --seed 2020358 
(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)))