Average Error: 29.2 → 25.7
Time: 7.6s
Precision: binary64
\[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\]
↓
\[\begin{array}{l} \mathbf{if}\;B \leq -3.032600957837696 \cdot 10^{-278}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}}{B}\right) \cdot 180}{\pi}\\ \mathbf{elif}\;B \leq 1.1652315596202954 \cdot 10^{-273}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - B}{B}\right)}{\pi}\\ \end{array}\]
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 -3.032600957837696 \cdot 10^{-278}:\\
\;\;\;\;\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}}{B}\right) \cdot 180}{\pi}\\

\mathbf{elif}\;B \leq 1.1652315596202954 \cdot 10^{-273}:\\
\;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\

\mathbf{else}:\\
\;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - B}{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 -3.032600957837696e-278)
   (/
    (* (atan (/ (- (- C A) (sqrt (+ (pow (- A C) 2.0) (* B B)))) B)) 180.0)
    PI)
   (if (<= B 1.1652315596202954e-273)
     (* 180.0 (/ (atan (/ 0.0 B)) PI))
     (/ (* 180.0 (atan (/ (- (- C A) B) 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 <= -3.032600957837696e-278) {
		tmp = (atan(((C - A) - sqrt(pow((A - C), 2.0) + (B * B))) / B) * 180.0) / ((double) M_PI);
	} else if (B <= 1.1652315596202954e-273) {
		tmp = 180.0 * (atan(0.0 / B) / ((double) M_PI));
	} else {
		tmp = (180.0 * atan(((C - A) - B) / 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 B < -3.032600957837696e-278

    1. Initial program 29.1

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

    2. Simplified29.1

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

    4. Applied associate-*r/_binary64_206629.1

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

    5. Simplified29.1

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

    if -3.032600957837696e-278 < B < 1.16523155962029538e-273

    1. Initial program 22.2

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

    2. Simplified22.2

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

    3. Taylor expanded around inf 39.9

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{0}}{B}\right)}{\pi}\]

    if 1.16523155962029538e-273 < B

    1. Initial program 30.0

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

    2. Simplified30.0

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

    4. Applied associate-*r/_binary64_206630.0

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

    5. Simplified30.0

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

    6. Taylor expanded around 0 20.4

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

  4. Final simplification25.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;B \leq -3.032600957837696 \cdot 10^{-278}:\\ \;\;\;\;\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}}{B}\right) \cdot 180}{\pi}\\ \mathbf{elif}\;B \leq 1.1652315596202954 \cdot 10^{-273}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{\left(C - A\right) - B}{B}\right)}{\pi}\\ \end{array}\]

Reproduce

herbie shell --seed 2020346 
(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)))