Average Error: 29.3 → 12.2
Time: 7.6s
Precision: binary64
\[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
↓
\[\begin{array}{l} \mathbf{if}\;A \leq -351583884.37308884:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{C}{\frac{A \cdot A}{B}} + \frac{B}{A}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(\mathsf{hypot}\left(B, C - A\right) + \sqrt[3]{A} \cdot \left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right)\right)}{B}\right)}{\pi}\\ \end{array} \]
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}\;A \leq -351583884.37308884:\\
\;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{C}{\frac{A \cdot A}{B}} + \frac{B}{A}\right)\right)}{\pi}\\

\mathbf{else}:\\
\;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(\mathsf{hypot}\left(B, C - A\right) + \sqrt[3]{A} \cdot \left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right)\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 (<= A -351583884.37308884)
   (* 180.0 (/ (atan (* 0.5 (+ (/ C (/ (* A A) B)) (/ B A)))) PI))
   (*
    180.0
    (/
     (atan
      (/ (- C (+ (hypot B (- C A)) (* (cbrt A) (* (cbrt A) (cbrt 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 (A <= -351583884.37308884) {
		tmp = 180.0 * (atan(0.5 * ((C / ((A * A) / B)) + (B / A))) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((C - (hypot(B, (C - A)) + (cbrt(A) * (cbrt(A) * cbrt(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 A < -351583884.3730888

    1. Initial program 48.1

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

    2. Simplified26.1

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

    3. Taylor expanded in A around -inf 22.2

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

    4. Simplified19.9

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

    if -351583884.3730888 < A

    1. Initial program 23.4

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

    2. Simplified9.7

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

    4. Applied add-cube-cbrt_binary649.7

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - \color{blue}{\left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \sqrt[3]{A}}\right) - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi} \]

    5. Applied cancel-sign-sub-inv_binary649.7

      \[\leadsto 180 \cdot \frac{\tan^{-1} \left(\frac{\color{blue}{\left(C + \left(-\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \sqrt[3]{A}\right)} - \mathsf{hypot}\left(B, C - A\right)}{B}\right)}{\pi} \]

    6. Applied associate--l+_binary649.7

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

  4. Final simplification12.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -351583884.37308884:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \left(\frac{C}{\frac{A \cdot A}{B}} + \frac{B}{A}\right)\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C - \left(\mathsf{hypot}\left(B, C - A\right) + \sqrt[3]{A} \cdot \left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right)\right)}{B}\right)}{\pi}\\ \end{array} \]

Reproduce

herbie shell --seed 2021212 
(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)))