Average Error: 29.0 → 16.7
Time: 10.9s
Precision: binary64
\[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.9998668841342558:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(B + A\right)\right)\right)}}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \left(\frac{1}{\sqrt{\pi}} \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\sqrt{\pi}}\right)\\ \end{array}\]
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 -0.9998668841342558:\\
\;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(B + A\right)\right)\right)}}\\

\mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\
\;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\

\mathbf{else}:\\
\;\;\;\;180 \cdot \left(\frac{1}{\sqrt{\pi}} \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\sqrt{\pi}}\right)\\

\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)))))
      -0.9998668841342558)
   (* 180.0 (/ 1.0 (/ PI (atan (* (/ 1.0 B) (- C (+ B A)))))))
   (if (<=
        (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))
        0.0)
     (* 180.0 (/ (atan (* 0.5 (/ B A))) PI))
     (*
      180.0
      (* (/ 1.0 (sqrt PI)) (/ (atan (/ (- (+ B C) A) B)) (sqrt 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)))) <= -0.9998668841342558) {
		tmp = 180.0 * (1.0 / (((double) M_PI) / atan((1.0 / B) * (C - (B + A)))));
	} else if (((1.0 / B) * ((C - A) - sqrt(pow((A - C), 2.0) + pow(B, 2.0)))) <= 0.0) {
		tmp = 180.0 * (atan(0.5 * (B / A)) / ((double) M_PI));
	} else {
		tmp = 180.0 * ((1.0 / sqrt((double) M_PI)) * (atan(((B + C) - A) / B) / sqrt((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))))) < -0.99986688413425584

    1. Initial program 25.9

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

    2. Taylor expanded around inf 14.8

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

    3. Simplified14.8

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

    5. Applied clear-num_binary6414.8

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

    if -0.99986688413425584 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < -0.0

    1. Initial program 51.7

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

    2. Taylor expanded around -inf 31.6

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

    if -0.0 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

    1. Initial program 25.3

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

    3. Applied add-sqr-sqrt_binary6425.9

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

    4. Applied *-un-lft-identity_binary6425.9

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

    5. Applied times-frac_binary6425.3

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

    6. Simplified25.3

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

    7. Taylor expanded around -inf 14.2

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

  4. Final simplification16.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -0.9998668841342558:\\ \;\;\;\;180 \cdot \frac{1}{\frac{\pi}{\tan^{-1} \left(\frac{1}{B} \cdot \left(C - \left(B + A\right)\right)\right)}}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 0:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \left(\frac{1}{\sqrt{\pi}} \cdot \frac{\tan^{-1} \left(\frac{\left(B + C\right) - A}{B}\right)}{\sqrt{\pi}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2021173 
(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)))