ab-angle->ABCF B

Average Error: 31.3 → 29.3

Time: 2.5min

Precision: binary64

Cost: 72834

Math

\[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -\infty:\\ \;\;\;\;\sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}} \cdot e^{\log \left(\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot -2\right) - 2 \cdot \log \left(\frac{-1}{a}\right)}\\ \mathbf{elif}\;{b}^{2} - {a}^{2} \leq 7.402920023221368 \cdot 10^{+306}:\\ \;\;\;\;\left(\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right)\right) \cdot \sqrt[3]{{\cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}} \cdot e^{\log \left(2 \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right) - 2 \cdot \log \left(\frac{-1}{b}\right)}\\ \end{array}\]

FPCore

(FPCore (a b angle)
 :precision binary64
 (*
  (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* PI (/ angle 180.0))))
  (cos (* PI (/ angle 180.0)))))

↓

(FPCore (a b angle)
 :precision binary64
 (if (<= (- (pow b 2.0) (pow a 2.0)) (- INFINITY))
   (*
    (cbrt (pow (cos (* PI (/ angle 180.0))) 3.0))
    (exp
     (-
      (log (* (sin (* 0.005555555555555556 (* PI angle))) -2.0))
      (* 2.0 (log (/ -1.0 a))))))
   (if (<= (- (pow b 2.0) (pow a 2.0)) 7.402920023221368e+306)
     (*
      (*
       (sin (* 0.005555555555555556 (* PI angle)))
       (* 2.0 (- (pow b 2.0) (pow a 2.0))))
      (cbrt (pow (cos (* 0.005555555555555556 (* PI angle))) 3.0)))
     (*
      (cbrt (pow (cos (* PI (/ angle 180.0))) 3.0))
      (exp
       (-
        (log (* 2.0 (sin (* 0.005555555555555556 (* PI angle)))))
        (* 2.0 (log (/ -1.0 b)))))))))

C

double code(double a, double b, double angle) {
	return ((2.0 * (pow(b, 2.0) - pow(a, 2.0))) * sin(((double) M_PI) * (angle / 180.0))) * cos(((double) M_PI) * (angle / 180.0));
}

↓

double code(double a, double b, double angle) {
	double tmp;
	if ((pow(b, 2.0) - pow(a, 2.0)) <= -((double) INFINITY)) {
		tmp = cbrt(pow(cos(((double) M_PI) * (angle / 180.0)), 3.0)) * exp(log(sin(0.005555555555555556 * (((double) M_PI) * angle)) * -2.0) - (2.0 * log(-1.0 / a)));
	} else if ((pow(b, 2.0) - pow(a, 2.0)) <= 7.402920023221368e+306) {
		tmp = (sin(0.005555555555555556 * (((double) M_PI) * angle)) * (2.0 * (pow(b, 2.0) - pow(a, 2.0)))) * cbrt(pow(cos(0.005555555555555556 * (((double) M_PI) * angle)), 3.0));
	} else {
		tmp = cbrt(pow(cos(((double) M_PI) * (angle / 180.0)), 3.0)) * exp(log(2.0 * sin(0.005555555555555556 * (((double) M_PI) * angle))) - (2.0 * log(-1.0 / b)));
	}
	return tmp;
}

Error

Bits error versus a

Bits error versus b

Bits error versus angle

Alternatives

Alternative 1
Error	30.5
Cost	46401

\[\begin{array}{l} \mathbf{if}\;a \leq -3.2279412078330076 \cdot 10^{+140}:\\ \;\;\;\;\sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}} \cdot e^{\log \left(\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot -2\right) - 2 \cdot \log \left(\frac{-1}{a}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right)\right) \cdot \sqrt[3]{{\cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}^{3}}\\ \end{array}\]

Alternative 2
Error	31.3
Cost	39680

\[\left(\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right)\right) \cdot \sqrt[3]{{\cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}^{3}}\]

Alternative 3
Error	31.3
Cost	39616

\[\left(\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right)\right) \cdot \log \left(e^{\cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}\right)\]

Alternative 4
Error	31.3
Cost	14144

\[\cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\]

Alternative 5
Error	31.3
Cost	14144

\[\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\]

Alternative 6
Error	32.3
Cost	7360

\[\left(2 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\]

Alternative 7
Error	34.2
Cost	832

\[angle \cdot \left(\left(b \cdot b - a \cdot a\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\]

Alternative 8
Error	34.3
Cost	832

\[angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right)\right)\]

Alternative 9
Error	37.9
Cost	1218

\[\begin{array}{l} \mathbf{if}\;b \leq -1.3709945349245143 \cdot 10^{-42}:\\ \;\;\;\;\left(\pi \cdot \left(b \cdot b\right)\right) \cdot \left(angle \cdot 0.011111111111111112\right)\\ \mathbf{elif}\;b \leq 4.581974872422141 \cdot 10^{-78}:\\ \;\;\;\;angle \cdot \left(\left(\pi \cdot \left(a \cdot a\right)\right) \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left(b \cdot b\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \end{array}\]

Alternative 10
Error	37.9
Cost	1218

\[\begin{array}{l} \mathbf{if}\;b \leq -4.5461182162760603 \cdot 10^{-39}:\\ \;\;\;\;\left(\pi \cdot \left(b \cdot b\right)\right) \cdot \left(angle \cdot 0.011111111111111112\right)\\ \mathbf{elif}\;b \leq 1.3157802113335384 \cdot 10^{-73}:\\ \;\;\;\;angle \cdot \left(\left(\pi \cdot \left(a \cdot a\right)\right) \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array}\]

Alternative 11
Error	37.8
Cost	904

\[\begin{array}{l} \mathbf{if}\;b \leq -1.985360085628856 \cdot 10^{-44} \lor \neg \left(b \leq 1.4256809634928402 \cdot 10^{-75}\right):\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left(\pi \cdot \left(a \cdot a\right)\right) \cdot -0.011111111111111112\right)\\ \end{array}\]

Alternative 12
Error	37.9
Cost	904

\[\begin{array}{l} \mathbf{if}\;b \leq -2.0922304355887315 \cdot 10^{-41} \lor \neg \left(b \leq 1.8484039207807332 \cdot 10^{-73}\right):\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left(\pi \cdot \left(a \cdot a\right)\right) \cdot -0.011111111111111112\right)\\ \end{array}\]

Alternative 13
Error	37.9
Cost	904

\[\begin{array}{l} \mathbf{if}\;b \leq -4.3833796797803637 \cdot 10^{-38} \lor \neg \left(b \leq 1.8484039207807332 \cdot 10^{-73}\right):\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left(\left(a \cdot a\right) \cdot -0.011111111111111112\right)\right)\\ \end{array}\]

Alternative 14
Error	43.5
Cost	576

\[angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right)\]

Alternative 15
Error	51.9
Cost	64

\[0\]

Alternative 16
Error	61.8
Cost	64

\[1\]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (pow.f64 b 2) (pow.f64 a 2)) < -inf.0

   1. Initial program 64.0

      \[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\]
   2. Using strategy rm

   3. Applied add-cbrt-cube_binary64_455 64.0

      \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \color{blue}{\sqrt[3]{\left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)}}\]

   4. Simplified 64.0

      \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \sqrt[3]{\color{blue}{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}}\]
   5. Using strategy rm

   6. Applied add-exp-log_binary64_457 64.0

      \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \color{blue}{e^{\log \sin \left(\pi \cdot \frac{angle}{180}\right)}}\right) \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   7. Applied add-exp-log_binary64_457 64.0

      \[\leadsto \left(\left(2 \cdot \color{blue}{e^{\log \left({b}^{2} - {a}^{2}\right)}}\right) \cdot e^{\log \sin \left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   8. Applied add-exp-log_binary64_457 64.0

      \[\leadsto \left(\left(\color{blue}{e^{\log 2}} \cdot e^{\log \left({b}^{2} - {a}^{2}\right)}\right) \cdot e^{\log \sin \left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   9. Applied prod-exp_binary64_468 64.0

      \[\leadsto \left(\color{blue}{e^{\log 2 + \log \left({b}^{2} - {a}^{2}\right)}} \cdot e^{\log \sin \left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   10. Applied prod-exp_binary64_468 64.0

       \[\leadsto \color{blue}{e^{\left(\log 2 + \log \left({b}^{2} - {a}^{2}\right)\right) + \log \sin \left(\pi \cdot \frac{angle}{180}\right)}} \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   11. Simplified 64.0

       \[\leadsto e^{\color{blue}{\log \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}} \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   12. Taylor expanded around -inf 51.4

       \[\leadsto e^{\color{blue}{\log \left(-2 \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) - 2 \cdot \log \left(\frac{-1}{a}\right)}} \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   13. Simplified 51.4

       \[\leadsto e^{\color{blue}{\log \left(\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot -2\right) - 2 \cdot \log \left(\frac{-1}{a}\right)}} \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   14. Simplified 51.4

       \[\leadsto \color{blue}{\sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}} \cdot e^{\log \left(\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot -2\right) - 2 \cdot \log \left(\frac{-1}{a}\right)}}\]

   if -inf.0 < (-.f64 (pow.f64 b 2) (pow.f64 a 2)) < 7.4029200232213676e306

   1. Initial program 25.0

      \[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\]

   2. Taylor expanded around inf 25.1

      \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \color{blue}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\]

   3. Simplified 25.1

      \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \color{blue}{\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\]

   4. Taylor expanded around inf 25.0

      \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right) \cdot \color{blue}{\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\]

   5. Simplified 25.0

      \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right) \cdot \color{blue}{\cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}\]
   6. Using strategy rm

   7. Applied add-cbrt-cube_binary64_455 25.0

      \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right) \cdot \color{blue}{\sqrt[3]{\left(\cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}}\]

   8. Simplified 25.0

      \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right) \cdot \sqrt[3]{\color{blue}{{\cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}^{3}}}\]

   9. Simplified 25.0

      \[\leadsto \color{blue}{\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right) \cdot \sqrt[3]{{\cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}^{3}}}\]

   if 7.4029200232213676e306 < (-.f64 (pow.f64 b 2) (pow.f64 a 2))

   1. Initial program 63.8

      \[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\]
   2. Using strategy rm

   3. Applied add-cbrt-cube_binary64_455 63.8

      \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \color{blue}{\sqrt[3]{\left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)}}\]

   4. Simplified 63.8

      \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \sqrt[3]{\color{blue}{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}}\]
   5. Using strategy rm

   6. Applied add-exp-log_binary64_457 63.8

      \[\leadsto \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \color{blue}{e^{\log \sin \left(\pi \cdot \frac{angle}{180}\right)}}\right) \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   7. Applied add-exp-log_binary64_457 63.8

      \[\leadsto \left(\left(2 \cdot \color{blue}{e^{\log \left({b}^{2} - {a}^{2}\right)}}\right) \cdot e^{\log \sin \left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   8. Applied add-exp-log_binary64_457 63.8

      \[\leadsto \left(\left(\color{blue}{e^{\log 2}} \cdot e^{\log \left({b}^{2} - {a}^{2}\right)}\right) \cdot e^{\log \sin \left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   9. Applied prod-exp_binary64_468 63.8

      \[\leadsto \left(\color{blue}{e^{\log 2 + \log \left({b}^{2} - {a}^{2}\right)}} \cdot e^{\log \sin \left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   10. Applied prod-exp_binary64_468 63.8

       \[\leadsto \color{blue}{e^{\left(\log 2 + \log \left({b}^{2} - {a}^{2}\right)\right) + \log \sin \left(\pi \cdot \frac{angle}{180}\right)}} \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   11. Simplified 63.8

       \[\leadsto e^{\color{blue}{\log \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)}} \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   12. Taylor expanded around -inf 52.2

       \[\leadsto e^{\color{blue}{\log \left(2 \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) - 2 \cdot \log \left(\frac{-1}{b}\right)}} \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   13. Simplified 52.2

       \[\leadsto e^{\color{blue}{\log \left(2 \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right) - 2 \cdot \log \left(\frac{-1}{b}\right)}} \cdot \sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}}\]

   14. Simplified 52.2

       \[\leadsto \color{blue}{\sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}} \cdot e^{\log \left(2 \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right) - 2 \cdot \log \left(\frac{-1}{b}\right)}}\]
3. Recombined 3 regimes into one program.

4. Final simplification 29.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -\infty:\\ \;\;\;\;\sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}} \cdot e^{\log \left(\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot -2\right) - 2 \cdot \log \left(\frac{-1}{a}\right)}\\ \mathbf{elif}\;{b}^{2} - {a}^{2} \leq 7.402920023221368 \cdot 10^{+306}:\\ \;\;\;\;\left(\sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right) \cdot \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right)\right) \cdot \sqrt[3]{{\cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\cos \left(\pi \cdot \frac{angle}{180}\right)}^{3}} \cdot e^{\log \left(2 \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right) - 2 \cdot \log \left(\frac{-1}{b}\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2021040 
(FPCore (a b angle)
  :name "ab-angle->ABCF B"
  :precision binary64
  (* (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* PI (/ angle 180.0)))) (cos (* PI (/ angle 180.0)))))