ABCF->ab-angle angle

Average Error: 29.9 → 17.2

Time: 15.4s

Precision: binary64

Cost: 48066

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -6.041684305091127 \cdot 10^{-05}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - B\right)\right)}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 7.570244039109216 \cdot 10^{-06}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B + \left(C - A\right)\right)\right)}{\pi}\\ \end{array}\]

FPCore

(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)))))
      -6.041684305091127e-05)
   (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) B))) PI))
   (if (<=
        (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))
        7.570244039109216e-06)
     (* 180.0 (/ (atan (* -0.5 (/ B C))) PI))
     (* 180.0 (/ (atan (* (/ 1.0 B) (+ B (- C A)))) PI)))))

C

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)))) <= -6.041684305091127e-05) {
		tmp = 180.0 * (atan((1.0 / B) * ((C - A) - B)) / ((double) M_PI));
	} else if (((1.0 / B) * ((C - A) - sqrt(pow((A - C), 2.0) + pow(B, 2.0)))) <= 7.570244039109216e-06) {
		tmp = 180.0 * (atan(-0.5 * (B / C)) / ((double) M_PI));
	} else {
		tmp = 180.0 * (atan((1.0 / B) * (B + (C - A))) / ((double) M_PI));
	}
	return tmp;
}

Error

Bits error versus A

Bits error versus B

Bits error versus C

Alternatives

Alternative 1
Error	24.3
Cost	7874

\[\begin{array}{l} \mathbf{if}\;A \leq -2.924442896879295 \cdot 10^{+16}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 2.90550850013554 \cdot 10^{-209}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B + \left(C - A\right)\right)\right)}{\pi}\\ \end{array}\]

Alternative 2
Error	27.5
Cost	8516

\[\begin{array}{l} \mathbf{if}\;A \leq -3.589968849582681 \cdot 10^{+18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.9529422203918626 \cdot 10^{-181}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.50013083195864 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 666343564498.1934:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - A\right)\right)}{\pi}\\ \end{array}\]

Alternative 3
Error	27.8
Cost	8260

\[\begin{array}{l} \mathbf{if}\;A \leq -1.0563671052259552 \cdot 10^{+18}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.5204969349631952 \cdot 10^{-181}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.50013083195864 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 146746525814.26703:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-2 \cdot \frac{A}{B}\right)}{\pi}\\ \end{array}\]

Alternative 4
Error	27.8
Cost	8260

\[\begin{array}{l} \mathbf{if}\;A \leq -1119751190790020.8:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{elif}\;A \leq 1.146505791042985 \cdot 10^{-181}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;A \leq 6.50013083195864 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 599615125497.224:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array}\]

Alternative 5
Error	32.6
Cost	8260

\[\begin{array}{l} \mathbf{if}\;A \leq -3.675120694951763 \cdot 10^{+163}:\\ \;\;\;\;0\\ \mathbf{elif}\;A \leq 1.9529422203918626 \cdot 10^{-181}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{elif}\;A \leq 7.585992475370532 \cdot 10^{-101}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;A \leq 1122888021233.3115:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B} + -1\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{-A}{B}\right)}{\pi}\\ \end{array}\]

Alternative 6
Error	33.4
Cost	8132

\[\begin{array}{l} \mathbf{if}\;B \leq -2.239330435360455 \cdot 10^{-55}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq -1.5375319788050347 \cdot 10^{-267}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 1.0814217060420613 \cdot 10^{-232}:\\ \;\;\;\;0\\ \mathbf{elif}\;B \leq 8.55647483928988 \cdot 10^{-17}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array}\]

Alternative 7
Error	35.2
Cost	7362

\[\begin{array}{l} \mathbf{if}\;B \leq -6.013578425017129 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 1.651668492586382 \cdot 10^{-209}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} -1}{\pi}\\ \end{array}\]

Alternative 8
Error	44.4
Cost	7041

\[\begin{array}{l} \mathbf{if}\;B \leq -6.013578425017129 \cdot 10^{-184}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 2.479290737451585 \cdot 10^{-184}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array}\]

Alternative 9
Error	53.4
Cost	706

\[\begin{array}{l} \mathbf{if}\;B \leq -6.013578425017129 \cdot 10^{-184}:\\ \;\;\;\;1\\ \mathbf{elif}\;B \leq 2.479290737451585 \cdot 10^{-184}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array}\]

Alternative 10
Error	54.6
Cost	385

\[\begin{array}{l} \mathbf{if}\;B \leq -5.27305990700476 \cdot 10^{-185}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Alternative 11
Error	59.8
Cost	64

\[1\]

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))))) < -6.04168430509112727e-5

   1. Initial program 26.4

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

   2. Taylor expanded around inf 14.6

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

   3. Simplified 14.6

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

   if -6.04168430509112727e-5 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))) < 7.57024403910921573e-6

   1. Initial program 53.3

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

   2. Taylor expanded around inf 31.7

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

   3. Simplified 31.7

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

   if 7.57024403910921573e-6 < (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))

   1. Initial program 26.0

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

   2. Taylor expanded around -inf 15.2

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

   3. Simplified 15.2

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

   4. Simplified 15.2

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

4. Final simplification 17.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq -6.041684305091127 \cdot 10^{-05}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - B\right)\right)}{\pi}\\ \mathbf{elif}\;\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right) \leq 7.570244039109216 \cdot 10^{-06}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(-0.5 \cdot \frac{B}{C}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(B + \left(C - A\right)\right)\right)}{\pi}\\ \end{array}\]

Reproduce

herbie shell --seed 2021044 
(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)))